Broken SU(3) x SU(3) x SU(3) x SU(3) Symmetry
Freund, P. G. O.; Nambu, Y.
1964-10-01
We argue that the "Eight-fold Way" version of the SU(3) symmetry should be extended to a product of up to four separate and badly broken SU(3) groups, including the gamma{sub 5} type SU(3) symmetry. A hierarchy of subgroups (or subalgebras) are considered within this framework, and two candidates are found to be interesting in view of experimental evidence. Main features of the theory are: 1) the baryons belong to a nonet; 2) there is an octet of axial vector gauge mesons in addition to one or two octets of vector mesons; 3) pseudoscalar and scalar mesons exist as "incomplete" multiplets arising from spontaneous breakdown of symmetry.
Configuration-mixed effective SU(3) symmetries
Hess, P O; Hunyadi, M; Kvi, A G; Cseh, J
2002-01-01
The procedure of Jarrio et al. (Nucl. Phys. A 528, 409 (1991)) for the determination of the effective SU(3) symmetry of nuclear states is extended to small deformations and to oblate nuclei. Self-consistency checks are carried out both for light and for heavy nuclei. (orig.)
SU(3) × SU(3) symmetry breaking in a simple model
Wit, Bernard de
1972-01-01
A field-theoretical model, due to Lévy, is studied. It contains a triplet of quarks and a pseudoscalar and a scalar meson nonet. The original SU(3) × SU(3) symmetry is broken by terms linear in the scalar meson fields. A renormalization and regularization procedure is defined in order to remove the
Emergent SU(3) Symmetry in Random Spin-1 Chains.
Quito, V L; Hoyos, José A; Miranda, E
2015-10-16
We show that generic SU(2)-invariant random spin-1 chains have phases with an emergent SU(3) symmetry. We map out the full zero-temperature phase diagram and identify two different phases: (i) a conventional random-singlet phase (RSP) of strongly bound spin pairs [SU(3) "mesons"] and (ii) an unconventional RSP of bound SU(3) "baryons," which are formed, in the great majority, by spin trios located at random positions. The emergent SU(3) symmetry dictates that susceptibilities and correlation functions of both dipolar and quadrupolar spin operators have the same asymptotic behavior. PMID:26550897
Test of SU(3) Symmetry in Hyperon Semileptonic Decays
Pham, T N
2013-01-01
Existing analyzes of baryon semileptonic decays indicate the presence of a small SU(3) symmetry breaking in hyperon semileptonic decays, but to provide evidence for SU(3) symmetry breaking, one would need a relation similar to the Gell-Mann Okubo(GMO) baryon mass formula which is satisfied to a few percents and provides evidence for SU(3) symmetry breaking in the divergence of the vector current matrix element. In this paper, we shall present a similar GMO relation for the hyperon semileptonic decay axial vector form factors. Using these relations and the measured axial vector current to vector current form factor ratios, we show that SU(3) symmetry breaking in hyperon semileptonic decays is of 5-11%.
Test of SU(3) Symmetry in Hyperon Semileptonic Decays
Pham, T N
2014-01-01
Existing analyzes of baryon semileptonic decays indicate the presence of a small SU(3) symmetry breaking in hyperon semileptonic decays, but to provide evidence for SU(3) symmetry breaking, one would need a relation similar to the Gell-Mann--Okubo (GMO) baryon mass formula which is satisfied to a few percents, showing evidence for a small SU(3) symmetry breaking effect in the GMO mass formula. In this talk, I would like to present a similar GMO relation obtained in a recent work for hyperon semileptonic decay axial vector current matrix elements. Using these generalized GMO relations for the measured axial vector current to vector current form factor ratios, it is shown that SU(3) symmetry breaking in hyperon semileptonic decays is of $5-11%$ and confirms the validity of the Cabibbo model for hyperon semi-leptonic decays.
Dibaryonic states and the SU(3) symmetry
The experimental information on dibaryon resonances with and without strangeness is analyzed, with the purpose of finding criteria for their especification as members of SU(3) multiplets formed by six quarks. The identification of a 10 multiplet with J(sup)P =1+ (spin triplet) and a 27 with J(sup)P = 2+ (spin singlet) is suggested. The conventional mass formula is used in this analysis, predicting the masses and decaying properties of several dibaryon states. The possible existence, in the 27, J(sup)P = 2+ representation, of strange states which are stable against strong interactions is discussed, and their experimental search is estimulated. Reactions in which the existence of dibaryon resonances can be detected are discussed, special attention being given to elastic K+d and K-d scattering, for which it is shown that the magnitude of the contributions of dibaryon resonances in intermediate states is of the same order of magnitude as those observed in the differential cross sections. (Author)
Emergent SU(3) symmetry in random spin-1 chains
Quito, Victor; Hoyos, Jose; Miranda, Eduardo
2015-03-01
We propose a system that realizes the idea of an ``emergent symmetry'': its low-temperature behavior has a larger symmetry than the underlying Hamiltonian. This is found in generic SU(2)-invariant random spin-1 chains, whose complete phase diagram we mapped out and characterized both analytically and numerically. The system is shown to have two different low-temperature phases with emergent SU(3) symmetry. In each of them, susceptibilities and correlation functions of both spin and quadrupolar operators are characterized by the same asymptotic exponents, which are dictated by the emergent symmetry group. Both SU(3)-symmetric phases are governed by infinitely disordered ground states. Whereas one of the ground states is formed by random singlets of pairs of spins, the other is less conventional and consists of random-singlet spin trios. This work was supported by FAPESP and CNPq.
BRST symmetries in SU(3) linear sigma model
We study the BRST symmetries in the SU(3) linear sigma model which is constructed through the introduction of a novel matrix for the Goldstone boson fields satisfying geometrical constraints embedded in a SU(2) subgroup. To treat these constraints we exploit the improved Dirac quantization scheme. We also discuss phenomenological aspects in the mean field approach to this model. (orig.)
Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry
Chen, Pochung; Xue, Zhi-Long; McCulloch, I. P.; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S.-K.
2015-04-01
We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU (3 )1 Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.
SU(3) symmetry and scissors mode vibrations in nuclei
Sun Yang; Bhatt, K; Guidry, M
2002-01-01
We show that a nearly perfect SU(3) symmetry emerges from an extended projected shell model. Starting from a deformed potential we construct separate bases for neutron and proton collective rotational states by exact angular momentum projection. These rotational states are then coupled by diagonalizing a residual pairing plus quadrupole interaction. The states obtained exhibit a one-to-one correspondence with an SU(3) spectrum up to high angular momentum and excitation, and their wave functions have a near-maximal overlap with the SU(3) states. They can also be classified as rotational bands built on spin-1 Planck constant phonon excitations, which correspond to a geometrical scissors mode and its generalizations. This work is a direct demonstration that numerical angular momentum projection theory extends the Elliott's original idea to heavy nuclear systems.
The Weak Mixing Angle from an SU(3) Symmetry at a TeV
Dimopoulos, Savas K; Dimopoulos, Savas; Kaplan, David Elazzar
2002-01-01
The measured values of two electroweak gauge couplings appear to obey an approximate 5% SU(3) relation. Unless this is an accident caused by fortuitous Planck-scale physics, it suggests the presence of an SU(3) symmetry near the electroweak scale. We propose this to be a local SU(3) which spontaneously ``mixes'' with SU(2) x U(1) near a TeV. Although all the particles of the standard model are SU(3)-singlets, this symmetry relates the electroweak gauge couplings and can successfully predict the weak mixing angle with a precision of a few percent. Since this mechanism operates at a TeV, it does not require an energy desert and consequently can be embedded in theories of TeV-gravity.
SU(3) Chiral Symmetry in Non-Relativistic Field Theory
Ouellette, S M
2001-01-01
Applications imposing SU(3) chiral symmetry on non-relativistic field theory are considered. The first example is a calculation of the self-energy shifts of the spin-3/2 decuplet baryons in nuclear matter, from the chiral effective Lagrangian coupling octet and decuplet baryon fields. Special attention is paid to the self-energy of the delta baryon near the saturation density of nuclear matter. We find contributions to the mass shifts from contact terms in the effective Lagrangian with coefficients of unknown value. As a second application, we formulate an effecive field theory with manifest SU(2) chiral symmetry for the interactions of K and eta mesons with pions at low energy. SU(3) chiral symmetry is imposed on the effective field theory by a matching calculation onto three-flavor chiral perturbation theory. The effective Lagrangian for the pi-K and pi-eta sectors is worked out to order Q^4; the effective Lagrangian for the K-K sector is worked out to order Q^2 with contact interactions to order Q^4. As an...
SU(3) flavour symmetry breaking and charmed states
By extending the SU(3) flavour symmetry breaking expansion from up, down and strange sea quark masses to partially quenched valence quark masses we propose a method to determine charmed quark hadron masses including possible QCD isospin breaking effects. Initial results for some open charmed pseudoscalar meson states and singly and doubly charmed baryon states are encouraging and demonstrate the potential of the procedure. Essential for the method is the determination of the scale using singlet quantities, and to this end we also give here a preliminary estimation of the recently introduced Wilson flow scales.
SU(3) flavour symmetry breaking and charmed states
Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Najjar, J. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Hyogo (Japan); Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Pleiter, D. [Forschungszentrum Juelich GmbH (Germany). Juelich Supercomputing Centre (JSC); Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Stueben, H. [Hamburg Univ. (Germany). Regionales Rechenzentrum; Zanotti, J.M. [Adelaide Univ. (Australia). CSSM, School of Chemistry and Physics; Collaboration: QCDSF-UKQCD Collaborations
2013-11-15
By extending the SU(3) flavour symmetry breaking expansion from up, down and strange sea quark masses to partially quenched valence quark masses we propose a method to determine charmed quark hadron masses including possible QCD isospin breaking effects. Initial results for some open charmed pseudoscalar meson states and singly and doubly charmed baryon states are encouraging and demonstrate the potential of the procedure. Essential for the method is the determination of the scale using singlet quantities, and to this end we also give here a preliminary estimation of the recently introduced Wilson flow scales.
Rasin, A
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Radiative decays, nonet symmetry, and SU(3) breaking
We reexamine the problem of simultaneously describing in a consistent way all radiative and leptonic decays of light mesons (V→Pγ, P→Vγ, P→γγ, V→e+e-). For this purpose, we rely on the hidden local symmetry model in both its anomalous and non-anomalous sectors. We show that the SU(3) symmetry breaking scheme proposed by Bando, Kugo and Yamawaki, supplemented with nonet symmetry breaking in the pseudoscalar sector, allows one to reach a nice agreement with all data, except for the K*± radiative decay. An extension of this breaking pattern allows one to account for this particular decay mode too. Considered together, the whole set of radiative decays provides a pseudoscalar mixing angle θP≅-11 degree and a value for θV which is ≅3 degree from that of ideal mixing. We also show that it is impossible, in a practical sense, to disentangle the effects of nonet symmetry breaking and those of glue inside the η', using only light meson decays. copyright 1999 The American Physical Society
Charged Fermion Masses and Mixing from a SU(3) Family Symmetry Model
Hernandez-Galeana, Albino
2016-01-01
Within the framework of a Beyond Standard Model (BSM) with a local $SU(3)$ family symmetry, we report an updated fit of parameters which account for the known spectrum of quarks and charged lepton masses and the quark mixing in a $4\\times 4$ non-unitary $V_{CKM}$. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from Dirac See-saw mechanisms implemented by the introduction of a new set of $SU(2)_L$ weak singlet vector-like fermions, $U,D,E,N$, with $N$ a sterile neutrino. The $N_{L,R}$ sterile neutrinos allow the implementation of a $8\\times 8$ general See-saw Majorana neutrino mass matrix with four massless eigenvalues at tree level. Hence, light fermions, including neutrinos, obtain masses from loop radiative corrections mediated by the massive $SU(3)$ gauge bosons. $SU(3)$ family symmetry is broken spontaneously in two stages, whose hierarchy of scales yield an approximate $SU(2)$ global symmetry associated with the $Z_1, Y_1^\\pm$ gauge boson mas...
A model based on gauge symmetry group G = Gsub(Wk) x [SU(3) x SU(3)]sub(c)
The authors formulate a gauge model for basic interactions based on the symmetry group G = Gsub(Wk) x Gsub(c), where Gsub(c) is the chiral symmetry group [SU(3) x SU(3)]sub(c) in colour space. Gsub(Wk) is taken to be the left-right symmetric model SUsub(L)(2) x SUsub(R)(2) x U(1). The chiral colour symmetry is spontaneously broken in such a way that quarks acquire a common mass, an octet of axial gluons become massive but an octet of vector gluons remain massless. In this way quark mass arises from spontaneous colour chiral symmetry breaking. The experimental consequences of the left-right symmetric model are discussed and it is shown that one version of this model gives results similar to the Salam-Weinberg model for the presently available energies. There is also another version, where the results are again similar to the Salam-Weinberg model except that the y dependence for the asymmetry parameter for the deep inelastic scattering of polarized electrons is completely different although its value at y = 0.21 is compatible with experiment. (author)
Account of Nonpolynomial SU(3)-Breaking Effects By Use of Quantum Groups As Flavor Symmetries
Gavrilik, A M
1998-01-01
Using instead of ordinary flavour symmetries SU(n_f) their corresponding quantum (q-deformed) analogs yields new baryon mass sum rules of extreme accuracy. We show, in the 3-flavour case, that such approach accounts for highly nonlinear (nonpolynomial) SU(3)-breaking effects both in the octet and decuplet baryon masses. A version of this approach is considered that involves q-covariant ingredients in the mass operator. The resulting new 'q-deformed' mass relation (q-MR) is simpler than previously derived q-MRs, but requires, for its empirical validity, a fitting to fix the value of the deformation parameter q. Well-known Gell-Mann--Okubo (GMO) octet mass sum rule is found to result not only from usual SU(3), but also from some exotic symmetry corresponding to the q=-1 (i.e., singular) limit of the q-algebra U_q(su_3).
The phenomenological symplectic model with a Davidson potential is used to construct rotational states for a rare-earth nucleus with microscopic wave functions. The energy levels and E2 transitions obtained are in remarkably close agreement (to within a few percent) with those of the rotor model with vibrational shape fluctations that are adiabatically decoupled from the rotational degrees of freedom. An analysis of the states in terms of their SU(3) content shows that SU(3) is a very poor dynamical symmetry but an excellent quasi-dynamical symmetry for the model. It is argued that such quasi-dynamical symmetry can be expected for any Hamiltonian that reproduces the observed low-energy properties of a well-deformed nucleus, whenever the latter are well-described by the nuclear rotor model
$SU(3)_{F}$ Gauge Family Model and New Symmetry Breaking Scale From FCNC Processes
Bao, Shou-Shan; Wu, Yue-Liang
2015-01-01
Based on the $SU(3)_{F}$ gauge family symmetry model which was proposed to explain the observed mass and mixing pattern of neutrinos, we investigate the symmetry breaking, the mixing pattern in quark and lepton sectors, and the contribution of the new gauge bosons to some flavor changing neutral currents (FCNC) processes at low energy. With the current data of the mass differences in the neutral pseudo-scalar $P^{0}-\\bar{P}^{0}$ systems, we find that the $SU(3)_{F}$ symmetry breaking scale can be as low as 300TeV and the mass of the lightest gauge boson be about $100$TeV. Other FCNC processes, such as the lepton flavor number violation process $\\mu^{-}\\rightarrow e^{-}e^{+}e^{-}$ and the semi-leptonic rare decay $K\\rightarrow \\pi \\bar{\
SU(3)c x SU(3)L x U(1)X gauge symmetry from SU(4)PS x SU(4)L+R
Sen, Sutapa; Dixit, Aparna
2004-01-01
We present a 3-3-1 model as a subgroup of SU(4)PS X SU(4)L+R gauge symmetry with symmetry-breaking pattern SU(4)->SU(3) X U(1) for both SU(4) groups. A Pleitez-Frampton type of 3C-3L-1X model is obtained with charged heavy leptons and SU(3)L gauge bosons (B-L= 0) which are not bileptons. The neutral gauge bosons include gamma,Z,Z'and a fourth Z" which decouples from rest but couples to ordinary fermions. The two-body decay rates for Z' are presented along with their mixings and interactions.
Decays of B mesons to two pseudoscalars in broken SU(3) symmetry
The decays of B mesons to two-body hadronic final states are analyzed within the context of broken flavor SU(3) symmetry, extending a previous analysis involving pairs of light pseudoscalars to decays involving one or two charmed quarks in the final state. A systematic program is described for learning information from decay rates regarding (i) SU(3)-violating contributions, (ii) the magnitude of exchange and annihilation diagrams (effects involving the spectator quark), and (iii) strong final-state interactions. The implication of SU(3)-breaking effects for the extraction of weak phases is also examined. The present status of data on these questions is reviewed and suggestions for further experimental study are made
Triplets, Static SU(6), and Spontaneously Broken Chiral SU(3) Symmetry
Nambu, Y.
1966-01-01
I would like to present here my view of the current problems of elementary particle theory. It is largely inspired by the recent successes of SU(3) and SU(6) symmetries, and more or less summarizes what I have been pursuing lately. For the details of individual problems I must refer to the original papers. However, what is emphasized here is not the details, but a coherent overall picture plus some speculations which cannot yet be formulated precisely.
Centre vortices underpin dynamical chiral symmetry breaking in $\\mathrm{SU}(3)$ gauge theory
Trewartha, Daniel; Leinweber, Derek
2015-01-01
The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure $\\mathrm{SU}(3)$ gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smo...
Strange Baryon Electromagnetic Form Factors and SU(3) Flavor Symmetry Breaking
Lin, Huey-Wen; Orginos, Konstantinos
2009-01-01
We study the nucleon, Sigma and cascade octet baryon electromagnetic form factors and the effects of SU(3) flavor symmetry breaking from 2+1-flavor lattice calculations. We find that electric and magnetic radii are similar; the maximum discrepancy is about 10\\%. In the pion-mass region we explore, both the quark-component and full-baryon moments have small SU(3) symmetry breaking. We extrapolate the charge radii and the magnetic moments using three-flavor heavy-baryon chiral perturbation theory (HBXPT). The systematic errors due to chiral and continuum extrapolations remain significant, giving rise to charge radii for $p$ and $\\Sigma^-$ that are 3--4 standard deviations away from the known experimental ones. Within these systematics the predicted $\\Sigma^+$ and $\\Xi^-$ radii are 0.67(5) and 0.306(15)~fm$^2$ respectively. When the next-to-next-to-leading order of HBXPT is included, the extrapolated magnetic moments are less than 3 standard deviations away from PDG values, and the d
General Majorana Neutrino Mass Matrix from a Low Energy SU(3) Family Symmetry with Sterile Neutrinos
Hernandez-Galeana, Albino
2014-01-01
Within the framework of a local SU(3) family symmetry model, we report a general analysis of the mechanism for neutrino mass generation and mixing, including light sterile neutrinos. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from Dirac See-saw mechanisms implemented by the introduction of a new set of $SU(2)_L$ weak singlet vector-like fermions, U,D,E,N, with N a sterile neutrino. Right-handed and the $N_{L,R}$ sterile neutrinos allow the implementation of a 8x8 general Majorana neutrino mass matrix with four or five massless neutrinos at tree level. Hence, light fermions, including light neutrinos get masses from radiative corrections mediated by the massive SU(3) gauge bosons. We report the corresponding Majorana neutrino mass matrix up to one loop. Previous numerical analysis of the free parameters show out solutions for quarks and charged lepton masses within a parameter space region where the vector-like fermion masses $M_U, M_D, M_E$, a...
Relativistic chiral SU(3) symmetry, large Nc sum rules and meson-baryon scattering
The relativistic chiral SU(3) Lagrangian is used to describe kaon-nucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel Bethe-Salpeter equation with the interaction kernel truncated at chiral order Q3 where we include only those terms which are leading in the large Nc limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large Nc baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU(3) symmetry-breaking effects are well controlled by the combined chiral and large Nc expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of plab ≅ 500 MeV. (orig.)
Evidence that centre vortices underpin dynamical chiral symmetry breaking in SU (3) gauge theory
Trewartha, Daniel; Kamleh, Waseem; Leinweber, Derek
2015-07-01
The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure SU (3) gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smoothing the vortex-only gauge fields, we observe dynamical mass generation on the vortex-only backgrounds consistent within errors with the original gauge-field ensemble following the same smoothing. Through visualizations of the instanton-like degrees of freedom in the various gauge-field ensembles, we find evidence of a link between the centre vortex and instanton structure of the vacuum. While vortex removal destabilizes instanton-like objects under O (a4)-improved cooling, vortex-only backgrounds provide gauge-field degrees of freedom sufficient to create instantons upon cooling.
Fouladi, N; Sabri, H
2014-01-01
We consider the possibility of identifying nuclei exhibiting the partial dynamical SU(3) symmetry (SU(3)-PDS) as those having excitation energy ratio R(4/2)>3.00 . For this purpose, the level energy spectra of a set of 51 nuclei in the rare earth and actinide regions which presenting an axially deformed prolate rotational structure were analyzed via nuclear partial dynamical SU(3) symmetry in the framework of interacting boson model, to see if the SU(3)-PDS is broadly applicable, and where, how, and in which nuclei it breaks down. Overall, the PDS works very well, the predictions of such intermediate symmetry structure for energy spectrum were compared with the most recent experimental data and an acceptable degree of agreement is achieved. We conclude that PDS predictions have a more regular behavior in description of axially deformed prolate rotational nuclei than DS, which may lead to accurate predictions of such nuclei, and hence play a significant role in understanding the regular behavior of complex nuc...
LI Jie-Ming; CHEN Qi-Zhou; GUO Shuo-Hong
2001-01-01
The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT). Using this method, wavefunctions are approximated by linear combination of graphs consisting of only one connected Wilson loop. We study the excited state energy and wavefunction in (2 + 1)-D SU(3) LGT up to thc third order. The glueballmass shows a good scaling behavior.``
Polanco-Euán, E N; Sánchez-Colón, G; Bambah, B A
2016-01-01
The SU(3) octet states with baryon number B = 2, hexaquark dibaryons, are considered. Decay coupling constants sum rules for dibaryon octet into two ordinary baryon octets with ?$\\lambda_8$ first order SU(3) symmetry breaking are given. An SU(4) extension of the analysis is commented upon. Possibilities for the experimental observation of multibaryon and anti-multibaryon states are pointed out.
Silva, P J
2016-01-01
The correlations between the modulus of the Polyakov loop, its phase $\\theta$ and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to $\\theta = 0$, $\\pm \\, 2 \\pi /3$. We find that the gluon propagator form factors associated with $\\theta \\approx 0$ differs quantitatively and qualitatively from those associated to $\\theta \\approx \\pm \\, 2 \\pi /3$. This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature $T_c$, the difference between the propagators associated to $\\theta \\approx 0$ and $\\theta \\approx \\pm ...
Hernandez-Galeana, Albino
2013-01-01
We report a global fit of parameters for fermion masses and mixing, including light sterile neutrinos, within a local vector $SU(3)$ family symmetry model. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from {\\bf Dirac See-saw} mechanisms implemented by the introduction of a new set of $SU(2)_L$ weak singlet vector-like fermions, $U,D,E,N$, with $N$ a sterile neutrino. The $N_{L,R}$ sterile neutrinos allow the implementation of a $8\\times 8$ general tree level See-saw Majorana neutrino mass matrix with four massless eigenvalues. Hence, light fermions, including light neutrinos obtain masses from one loop radiative corrections mediated by the massive $SU(3)$ gauge bosons. This BSM model is able to accommodate the known spectrum of quark masses and mixing in a $4\\times 4$ non-unitary $V_{CKM}$ as well as the charged lepton masses. The explored parameter space region provide the vector-like fermion masses: $M_D \\approx 914.365 $GeV, $M_U \\approx 1.5 ...
Galeana, Albino Hernandez
2011-01-01
I report low energy results on the study of fermion masses and mixing for quarks and leptons, including neutrinos within a SU(3) flavor symmetry model, where ordinary heavy fermions, top and bottom quarks and tau lepton become massive at tree level from {\\bf Dirac See-saw} mechanisms implemented by the introduction a new set of $SU(2)_L$ weak singlet vector-like fermions $U,D,E,N$, with $N$ a sterile neutrino. Light fermions obtain masses from one loop radiative corrections mediated by the massive SU(3) gauge bosons. Recent results shows the existence of a low energy space parameter where this model is able to accommodate the known spectrum of quark masses and mixing in a $4\\times 4$ non-unitary $V_{CKM}$ as well as the charged lepton masses. Motivated by the recent LSND and MiniBooNe short-baseline neutrino oscillation experiments we fit for the 3+1 scenario the neutrino squared mass differences $m_2^2 - m_1^2\\approx 7.6\\times 10^{-5}\\;\\text{eV}^2$, $m_3^2 - m_2^2\\approx 2.43\\times 10^{-3} \\text{eV}^2$ and $...
Silva, P. J.; Oliveira, O.
2016-06-01
The correlations between the modulus of the Polyakov loop, its phase θ , and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to θ =0 , ±2 π /3 . We find that the gluon propagator form factors associated with θ ≈0 differ quantitatively and qualitatively from those associated to θ ≈±2 π /3 . This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature Tc, the difference between the propagators associated to θ ≈0 and θ ≈±2 π /3 allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.
Bazzocchi, F; Picariello, M; Torrente-Lujan, E
2008-01-01
We present a common explanation of the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF). Our starting point is a SU(3)xU(1) flavor symmetry and a SO(10) GUT, a basic ingredient of our theory which plays a major role is that two different breaking pattern of the flavor symmetry are at work. On one side, the dynamical breaking of SU(3)xU(1) flavor symmetry into U(2)xZ_3 explains why one family is much heavier than the others. On the other side, an explicit symmetry breaking of SU(3) into a discrete flavor symmetry leads to the observed tribimaximal mixing for the leptons. We write an explicit model where this discrete symmetry group is A4. Naturalness of the charged fermion mass hierarchy appears as a consequence of the continuous SU(3) flavor symmetry. Moreover, the same discrete A4-GUT invariant operators are the root of the large lepton mixing, small Cabibbo angle, and neutrino masses.
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil)
2007-01-01
The coupling constants $g_L$ and $g_X$ of some versions of the $SU(3)_L\\otimes U(1)_X$ extension of the standard model are related through to relationship $g^2_X/g^2_L= \\sin^2\\theta_W/(1 - 4\\sin^2\\theta_W)$. This fact suggest that the $SU(3)_L\\otimes U(1)_X$ gauge symmetry in this class of models can be broken dynamically to the standard model at TeV scale without requiring the introduction of fundamental scalars. This possibility was investigated by Das and Jain who considered only the first...
Approximate Noether gauge symmetries of the Bardeen model
Camci, U. [Akdeniz University, Department of Physics, Faculty of Science, Antalya (Turkey)
2014-12-01
We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis of the spacetime of the Bardeen model up to third-order approximate Noether gauge symmetries is presented. (orig.)
An SO(10) model with SU(3) x SU(2)L x SU(2)R x U(1)B-L x D intermediate symmetry
We construct a SO(10) model with intermediate symmetry SU(3) x SU(2)L x SU(2)R x U(1)B-L x D and baryon and lepton number conserved between the two highest scales. The experimental values of sin2 θw and αs are consistent with the lower bound on τP → e++π0 and with a mass value for ντ around 1 eV. (orig.)
We utilize Foldy's canonical representation (m,5/2) + -m,5/2) involving degrees of freedom pertaining to a spin of 5/2 units and make a unitary transformation to the current picture thereby deriving an expressing for the total angular momentum consisting of a together conserved orbital plus an intrinsic spin -1/2 part and yet another separately conserved SU(3)-unitary spin part. We demonstrate this explicity by algebraically deducing the Cartan-Weyl basis for The newly emerging invariance algebra whose eight generators are expressed in terms of three fundamental matrices representing spin-5/2 and proving that this basis excitingly coincides with that of the SU(3) algebra. The derivation of SU(6) in automatically achieved in our theory as a materials consequence Of the SU(3)-symmetry already derived and an SU(2)-spin symmetry guaranteed by the commentativity of Foldys mean sprin operators that find their find their natural places in the unitary-spin parts of the expressions for the Poincare generators, with the Dirac-type hamiltonian acting as the time-transtation generator. As a prelude aderivation of SU(2) is, initially presented working with Foldy's canomical representation (m,3/2) + (-m,3/2). In the process of deriving SU(2), an invariance under the discrete symmetrIc group S3 is also simultaneously datained. (author)
Gauge bosons and fermions in SU(3)C x SU(4)L x U(1)X model with SU(2)H xU(1)AH symmetry
Sen, Sutapa
2009-01-01
We present a phenomenological study of neutral gauge bosons and fermions in an extended Standard model with SU(3)C x SU(4)L x U(1)X gauge symmetry.The model includes gauge bosons and fermions without exotic charges and is distinguished by the symmetry-breaking patern SU(4)L->SU(2)L x SU(2)H x U(1)AH. This introduces an extended electroweak symmetry group SU(2)L x SU(2)H at low energies.We recover the fermion spectra of an anomaly-free three-family 3-4-1 modelwithout exotic chargesfor U(1)X charge X = T3R+(B-L)/2.The interaction of physical neutral gauge bosons Zprime,Z double prime and exotic fermions are presented along with their masses and mixing angle.The electroweak constraints from oblique corections on the model are also calculated.
We construct an SU(3)LxU(1)N gauge model based on an S2L permutation symmetry for left-handed μ and τ families, which provides the almost maximal atmospheric neutrino mixing and the large solar neutrino mixing of the large mixing angle type. Neutrinos acquire one-loop radiative masses induced by the radiative mechanism of the Zee type as well as tree level masses induced by the type II seesaw mechanism utilizing interactions of lepton triplets with an SU(3)-sextet scalar. The atmospheric neutrino mixing controlled by the tree-level and radiative masses turns out to be almost maximal owing to the presence of S2L supplemented by a Z4 discrete symmetry. These symmetries ensure the near equality between the νe-νμ and νe-ντ radiative masses dominated by contributions from heavy leptons contained in the third members of lepton triplets, whose Yukawa interactions conserve S2L even after the spontaneous breaking. The solar neutrino mixing controlled by radiative masses, including a νμ-ντ mass, which are taken to be of similar order, turns out to be described by large solar neutrino mixing angles
SO(10) model with SU(3) x SU(2)/sub L/ x SU(2)/sub R/ x U(1)/sub B-L/ x D intermediate symmetry
Buccella, F.; Rosa, L.
1987-10-01
We construct a SO(10) model with intermediate symmetry SU(3) x SU(2)/sub L/ x SU(2)/sub R/ x U(1)/sub B-L/ x D and baryon and lepton number conserved between the two highest scales. The experimental values of sin/sup 2/ theta/sub w/ and ..cap alpha../sub s/ are consistent with the lower bound on tau/sub P/ -> e/sup +/+..pi../sup 0/ and with a mass value for ..nu../sub tau/ around 1 eV.
An SO(10) model with SU(3)⊗ SU(2) L ⊗ SU(2) R ⊗ U(1) B-L ⊗ D intermediate symmetry
Buccella, F.; Rosa, L.
1987-09-01
We construct a SO(10) model with intermediate symmetry 10052_2005_Article_BF01573937_TeX2GIFE1.gif SU(3) ⊗ SU(2)_L ⊗ SU(2)_R ⊗ U(1)_{B - L} ⊗ D and baryon and lepton number conserved between the two highest scales. The experimental values of sin2θ w and α s are consistent with the lower bound on τ p→ e ++π0 and with a mass value for v τ around 1 eV.
Energy of Bardeen Model Using Approximate Symmetry Method
Sharif, M.; Waheed, Saira
2010-01-01
In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to evaluate the third-order approximate symmetries of the orbital and geodesic equations. It is shown that energy must be re-scaled by some factor in the third-order approximation. We discuss the insights of this re-scaling factor.
Complete sets of low-lying 1/2- and 3/2- levels in 185W and 187W have been obtained using measurements of primary γ-rays following average resonance neutron capture at mean incident neutron energies of 2 and 24 keV. The results are discussed in terms of both the Nilsson model and the SU(3) boson-fermion symmetry scheme appropriate to this region. The data highlights the advantages and deficiencies of both frameworks, and shows that neither is able to describe the complete spectrum of low-lying low-spin energy levels. The two approaches are outlined and compared and the role of the missing degrees of freedom in each is discussed. (orig.)
Boika, T; Polyakov, M V
2014-01-01
We study the implications of the flavour SU(3) symmetry for various interpretations of the neutron anomaly in the $\\gamma N\\to\\eta N$ cross section. We show that the explanation of the neutron anomaly due to interference of known N(1535) and N(1650) resonances implies that N(1650) resonance should have a huge coupling to $\\phi$-meson -- at least 5 times larger than the corresponding $\\rho^0$ coupling. In terms of quark degrees of freedom this means that the well-known N(1650) resonance must be a "cryptoexotic pentaquark"-- its wave function should contain predominantly an $s\\bar s$ component. It turns out that the "conventional" interpretation of the neutron anomaly by the interference of known resonances metamorphoses into unconventional physics picture of N(1650).
The su(3) mean field approximation describes collective nuclear rotation in a density matrix formalism. The densities ρ=q-i l/2 are 3x3 Hermitian matrices in the su(3) dual space, where q is the expectation of the quadrupole moment and l is the expectation of the angular momentum. The mean field approximation restricts these densities to a level surface of the su(3) Casimirs. Each level surface is a coadjoint orbit of the canonical transformation group SU(3). For each density ρ, the su(3) mean field Hamiltonian h[ρ] is an element of the su(3) Lie algebra. A model su(3) energy functional and the symplectic structure on the coadjoint orbit determine uniquely the su(3) mean field Hamiltonian. The densities in time-dependent su(3) mean field theory obey the dynamical equation i ρ radical = [h[ρ],ρ] on a coadjoint orbit. The cranked mean field Hamiltonian is hΩ=h+iΩ, where Ω is the angular velocity of the rotating principal axis frame. A rotating equilibrium density ρ-tilde in the body-fixed frame is a self-consistent solution to the equation [hΩ[ρ-tilde],ρ-tilde]=0. (author)
Quark Yukawa pattern from spontaneous breaking of flavour $SU(3)^3$
Nardi, Enrico
2015-01-01
A $SU(3)_Q \\times SU(3)_u \\times SU(3)_d$ invariant scalar potential breaking spontaneously the quark flavour symmetry can explain the standard model flavour puzzle. The approximate alignment in flavour space of the vacuum expectation values of the up and down `Yukawa fields' results as a dynamical effect. The observed quark mixing angles, the weak CP violating phase, and hierarchical quark masses can be all reproduced at the cost of introducing additional (auxiliary) scalar multiplets, but without the need of introducing hierarchical parameters.
Hsu, Jong-Ping
2013-01-01
Gravitational field is the manifestation of space-time translational ($T_4$) gauge symmetry, which enables gravitational interaction to be unified with the strong and the electroweak interactions. Such a total-unified model is based on a generalized Yang-Mills framework in flat space-time. Following the idea of Glashow-Salam-Ward-Weinberg, we gauge the groups $T_4 \\times (SU_3)_{color} \\times SU_2 \\times U_1\\times U_{1b}$ on equal-footing, so that we have the total-unified gauge covariant derivative ${\\bf \\d}_{\\mu} = \\p_{\\mu} - ig\\phi_{\\mu}^{\
ZHANG Shun-Li; QU Chang-Zheng
2006-01-01
@@ The concept of approximate generalized conditional symmetry (AGCS) as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cer tain types of AGCSs is derived.
Re-Scaling of Energy in the Stringy Charged Black Hole Solutions using Approximate Symmetries
Sharif, M.; Waheed, Saira
2010-01-01
This paper is devoted to study the energy problem in general relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged black hole solutions. It is concluded that energy must be re-scaled by some factor in the second-order approximation.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
We consider symmetry properties of differential equations in non-relativistic quantum mechanics and classical mechanics. Special emphasis is given to periodically driven systems. For a model system connections between symmetries of corresponding classical and quantal systems are established. The fundamental difference between variational symmetries and symmetries of the Euler-Lagrange-equations is discussed for the special case of classical mechanics. For nonintegrable systems with quasiregular regions in phase space we introduce the notion of approximate symmetry. As an example, we demonstrate the accuracy of such symmetry properties in certain domains of phase space for a periodically driven anharmonic oscillator. (orig.)
Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter
In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained
Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter
Mahdavi, Abolhassan, E-mail: ad.mahdavi@kiau.ac.ir [Karaj Branch Islamic University, Department of Mathematics (Iran, Islamic Republic of); Nadjafikhah, Mehdi, E-mail: mnadjafikhah@iust.ac.ir [Iran University of Science and Technology, School of Mathematics (Iran, Islamic Republic of); Toomanian, Megerdich, E-mail: megerdich.toomanian@kiau.ac.ir [Karaj Branch Islamic University, Department of Mathematics (Iran, Islamic Republic of)
2015-12-15
In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained.
Kaon-Baryon Couplings and the Goldberger-Treiman Relation in SU(3) x SU(3)
Nasrallah, N F
2007-01-01
The coupling constants G_(K N Lambda) and G_(K N Sigma) are obtained from the Goldberger-Treiman relation in the strange channel with chiral symmetry breaking taken into account. The results, G_(K N Lambda)=-12.3+-1.2 and G_(K N Sigma)=5.5+-.5 come close to the SU(3) values.
无
2009-01-01
An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders,educing the related homotopy series solutions.Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation.Higher order similarity solutions can be obtained by solving linear variable coefficients ordinary differential equations.The auxiliary parameter has an effect on the convergence of homotopy series solutions.Series solutions and similarity reduction equations from the approximate symmetry method can be retrieved from the approximate homotopy symmetry method.
Approximate restoration of translational and rotational symmetries within the Lipkin method
Gao, Y; Toivanen, P
2015-01-01
Background: Nuclear self-consistent mean-field approaches are rooted in the density functional theory and, through the spontaneous symmetry breaking mechanism, allow for including important correlations, while keeping the simplicity of the approach. Because real ground states should have all symmetries of the nuclear Hamiltonian, these methods require subsequent symmetry restoration. Purpose: We implement and study Lipkin method of approximate variation after projection applied to the restoration of the translational or rotational symmetries. Methods: We use Lipkin operators up to quadratic terms in momenta or angular momenta with self-consistently determined values of the Peierls-Yoccoz translational masses or moments of inertia, respectively. Calculations based on Skyrme energy-density functional are performed for heavy, deformed, and paired nuclei. Results: In deformed nuclei, the Peierls-Yoccoz translational masses along three different principal-axes directions of the intrinsic system can be different, w...
The group SU(3) is parameterized in terms of generalized open-quotes Euler anglesclose quotes. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made
Properties of non-BPS SU(3) monopoles
This paper is concerned with magnetic monopole solutions of SU(3) Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The different SU(2) embeddings, which correspond to the fundamental monopoles, as well the embedding along composite root are studied. The interaction of two different fundamental monopoles is considered. Dissolution of a single fundamental non-BPS SU(3) monopole in the limit of the minimal symmetry breaking is analyzed. (author)
SU(3) flux tube gluon condensate
Dzhunushaliev, Vladimir
2010-01-01
The distribution of a gluon condensate in a flux tube is calculated. The result is that the chromoelectric fields are confined with a surrounding coset chromomagnetic field. Such picture presents the concrete realization of dual QCD model in a scalar model of the flux tube. In the scalar model the SU(3) gauge fields are separated on two parts: (1) is the $SU(2) \\subset SU(3)$ subgroup, (2) is the coset $SU(3) / SU(2)$. The SU(2) degrees of freedom are almost classical and the coset degrees of freedom are quantum ones. A nonperturbative approach for the quantization of the coset degrees of freedom is applied. In this approach 2-point Green's function is a bilinear combination of scalar fields and 4-point Green's function is the product of 2-points Green's functions. The gluon condensate is an effective Lagrangian describing the SU(2) gauge field with broken gauge symmetry and coupling with the scalar field. Corresponding field equations give us the flux tube.
Approximate symmetries in atomic nuclei from a large-scale shell-model perspective
In this paper, we review recent developments that aim to achieve further understanding of the structure of atomic nuclei, by capitalizing on exact symmetries as well as approximate symmetries found to dominate low-lying nuclear states. The findings confirm the essential role played by the Sp(3, ℝ) symplectic symmetry to inform the interaction and the relevant model spaces in nuclear modeling. The significance of the Sp(3, ℝ) symmetry for a description of a quantum system of strongly interacting particles naturally emerges from the physical relevance of its generators, which directly relate to particle momentum and position coordinates, and represent important observables, such as, the many-particle kinetic energy, the monopole operator, the quadrupole moment and the angular momentum. We show that it is imperative that shell-model spaces be expanded well beyond the current limits to accommodate particle excitations that appear critical to enhanced collectivity in heavier systems and to highly-deformed spatial structures, exemplified by the second 0+ state in 12C (the challenging Hoyle state) and 8Be. While such states are presently inaccessible by large-scale no-core shell models, symmetry-based considerations are found to be essential. (author)
Alkhalifah, Tariq Ali
2012-04-30
Traveltime information is crucial for parameter estimation, especially if the medium is described by a set of anisotropy parameters. We can efficiently estimate these parameters if we are able to relate them analytically to traveltimes, which is generally hard to do in inhomogeneous media. I develop traveltime approximations for transversely isotropic media with a horizontal symmetry axis (HTI) as simplified and even linear functions of the anisotropy parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to the anellipticity parameter, η and the azimuth of the symmetry axis (typically associated with the fracture direction) from a generally inhomogeneous, elliptically anisotropic background medium. Such a perturbation is convenient since the elliptically anisotropic information might be obtained from well velocities in HTI media. Thus, we scan for only η and the symmetry-axis azimuth. The resulting approximations can provide a reasonably accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations. They also help extend the inhomogenous background isotropic or elliptically anisotropic models to an HTI one with a smoothly variable η and symmetry-axis azimuth. © 2012 European Association of Geoscientists & Engineers.
CP violation and flavor SU(3) breaking in D-meson decays
We carry out a systematic flavor SU(3) analysis of D-meson decays including the leading order symmetry breaking effects. We find that SU(3) breaking can easily account for the recent LHCb measurement of the difference in CP asymmetries in the decays of D0 into K+K- and π+π- mesons, once an enhancement mechanism, similar to the Δ=1/2 rule in neutral kaon decays is assumed. As a byproduct of the analysis, one can make predictions regarding the individual asymmetries in K+K-, π+π-, as well as the D0→π0π0 decay channels. Moreover, we find that the asymmetry in the decay D+→π+π0 vanishes in the leading approximation.
Exact and approximate symmetries for light propagation equations with higher order nonlinearity
Garcia, Martin E; Tatarinova, Larisa L
2010-01-01
For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit analytical expression for the self-focusing position, where the intensity tends to infinity, is found. Based on an approximated Lie symmetry group, solutions to the eikonal equations with arbitrary nonlinear refractive index are constructed. Comparison between exact and approximate solutions is presented. Approximate solutions to the nonlinear Schrodinger equation in (1+2) dimensions with arbitrary refractive index and initial intensity distribution are obtained. A particular case of refractive index consisting of Kerr refraction and multiphoton ionization is considered. It is demonstrated that the beam collapse can take place not only at the beam axis but also in an off-axis ring region around it. An analytical condition distinguishing these two cases is obtained and expli...
Color-charge separation in trapped SU(3) fermionic atoms
Cold fermionic atoms with three different hyperfine states with SU(3) symmetry confined in one-dimensional optical lattices show color-charge separation, generalizing the conventional spin-charge separation for interacting SU(2) fermions in one dimension. Through time-dependent density-matrix renormalization-group simulations, we explore the features of this phenomenon for a generalized SU(3) Hubbard Hamiltonian. In our numerical simulations of finite-size systems, we observe different velocities of the charge and color degrees of freedom when a Gaussian wave packet or a charge (color) density response to a local perturbation is evolved. The differences between attractive and repulsive interactions are explored and we note that neither a small anisotropy of the interaction, breaking the SU(3) symmetry, nor the filling impedes the basic observation of these effects.
Spontaneous Breaking of $SU3_{f}$ Down to Isospin
Törnqvist, N A
1996-01-01
The mechanism where flavor symmetry of the standard model is broken spontaneously within the strong interactions of QCD is generalized for models involving nonets of pseudoscalar and vector mesons. After the breaking of chiral symmetry by the vacuum, creating singlets and degenerate octets of massive vector mesons and near massless pseudoscalars, also the SU3f symmetric spectrum is shown to be unstable with respect to s quark loops, and broken into a stable isospin symmetric mass spectrum close to the physical one.
New fixed point action for SU(3) lattice gauge theory
Blatter, Marc; Niedermayer, Ferenc
1996-01-01
We present a new fixed point action for SU(3) lattice gauge theory, which has --- compared to earlier published fixed point actions --- shorter interaction range and smaller violations of rotational symmetry in the static $q\\bar{q}$-potential even at shortest distances.
New fixed point action for SU(3) lattice gauge theory
We present a new fixed point action for SU(3) lattice gauge theory, which has - compared to earlier published fixed point actions - shorter interaction range and smaller violations of rotational symmetry in the static qq potential even at shortest distances. (orig.)
M Hamzavi; S M Ikhdair
2014-07-01
The Hellmann potential is simply a superposition of an attractive Coulomb potential $−a/r$ plus a Yukawa potential e${}^{−δr} /r$. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.
Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein's field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to test particles. There have been various proposals to define the energy content, but they have not met with great success. Here we propose a definition using 'slightly broken' Noether symmetries. We check whether this definition is physically acceptable. The procedure adopted is to appeal to 'approximate symmetries' as defined in Lie analysis and use them in the limit of the exact symmetry holding. A problem is noted with the use of the proposal for plane-fronted gravitational waves. To attain a better understanding of the implications of this proposal we also use an artificially constructed time-varying nonvacuum metric and evaluate its Weyl and stress-energy tensors so as to obtain the gravitational and matter components separately and compare them with the energy content obtained by our proposal. The procedure is also used for cylindrical gravitational wave solutions. The usefulness of the definition is demonstrated by the fact that it leads to a result on whether gravitational waves suffer self-damping.
New origin for approximate symmetries from distant breaking in extra dimensions
The recently proposed theories with TeV-scale quantum gravity do not have the usual ultraviolet desert between approximately 103-1019 GeV where effective field theory ideas apply. Consequently, the success of the desert in explaining approximate symmetries is lost, and theories of flavor, neutrino masses, proton longevity or supersymmetry breaking, lose their usual habitat. In this paper we show that these ideas can find a new home in an infrared desert: the large space in the extra dimensions. The main idea is that symmetries are primordially exact on our brane, but are broken at O(1) on distant branes. This breaking is communicated to us in a distance-suppressed way by bulk messengers. We illustrate these ideas in a number of settings: (1) We construct theories for the fermion mass hierarchy which avoid problems with large flavor-changing neutral currents. (2) We re-iterate that proton stability can arise if baryon number is gauged in the bulk. (3) We study limits on light gauge fields and scalars in the bulk coming from rare decays, astrophysics and cosmology. (4) We remark that the same ideas can be used to explain small neutrino masses, as well as hierarchical supersymmetry breaking. (5) We construct a theory with bulk technicolor, avoiding the difficulties with extended technicolor. There are also a number of interesting experimental signals of these ideas: (1) Attractive or repulsive, isotope dependent sub-millimeter forces approximately 106 times gravitational strength, from the exchange of light bulk particles. (2) Novel Higgs decays to light generation fermions plus bulk scalars. (3) Collider production of bulk vector and scalar fields, leading to γ or jet+ missing energy signals as in the case of bulk graviton production, with comparable or larger rates
Symmetry-broken local-density approximation for one-dimensional systems
Rogers, Fergus J M; Loos, Pierre-François
2016-01-01
Within density-functional theory, the local-density approximation (LDA) correlation functional is typically built by fitting the difference between the near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG), together with analytic perturbative results from the high- and low-density regimes. Near-exact energies are obtained by performing accurate diffusion Monte Carlo calculations, while HF energies are usually assumed to be the Fermi fluid HF energy. However, it has been known since the seminal work of Overhauser that one can obtain lower, symmetry-broken (SB) HF energies at any density. Here, we have computed the SBHF energies of the one-dimensional UEG and constructed a SB version of the LDA (SBLDA) from the results. We compare the performance of the LDA and SBLDA functionals when applied to one-dimensional systems, including atoms and molecules. Generalization to higher dimensions is also discussed.
SU(3)direct-product U(1) model for electroweak interactions
We consider a gauge model based on a SU(3)direct-product U(1) symmetry in which the lepton number is violated explicitly by charged scalar and gauge bosons, including a vector field with double electric charge
SU(3)-Flavor Anatomy of Non-Leptonic Charm Decays
Hiller, Gudrun; Schacht, Stefan
2012-01-01
We perform a comprehensive SU(3)-flavor analysis of charmed mesons decaying to two pseudoscalar SU(3)-octet mesons. Taking into account SU(3)-breaking effects induced by the splitting of the quark masses, m_s != m_{u,d}, we find that existing data can be described by SU(3)-breaking of the order 30%. The requisite penguin enhancement to accomodate all data on CP violation tends to be even larger than the one extracted from Delta a_{CP}^{dir}(K^+K^-,pi^+pi^-) alone, strengthening explanations beyond the standard model. Despite the large number of matrix elements, correlations between CP asymmetries allow potentially to differentiate between different scenarios for the underlying dynamics, as well as between the standard model and various extensions characterized by SU(3) symmetry and its subgroups. We investigate how improved measurements of the direct CP asymmetries in singly-Cabibbo-suppressed decays can further substantiate the interpretation of the data. We show that particularly informative are the asymmet...
Higgs Phenomenology in the Minimal $SU(3)_L\\times U(1)_X$ Model
Okada, Hiroshi; Okada, Nobuchika; Orikasa, Yuta; Yagyu, Kei
2016-01-01
We investigate the phenomenology of a model based on the $SU(3)_c\\times SU(3)_L\\times U(1)_X$ gauge theory, the so-called 331 model. In particular, we focus on the Higgs sector of the model which is composed of three $SU(3)_L$ triplet Higgs fields, and this corresponds to the minimal form to realize phenomenologically acceptable scenario. After the spontaneous symmetry breaking $SU(3)_L\\times U(1)_X\\to SU(2)_L\\times U(1)_Y$, our Higgs sector effectively becomes that with two $SU(2)_L$ doublet...
Jia, L Y
2016-01-01
The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work we show that this symmetry is preserved in the subspace truncated at a certain generalized seniority, and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, we study the particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and others.
Masmoudi, Nabil
2014-01-01
We present an approximate, but efficient and sufficiently accurate P-wave ray tracing and dynamic ray tracing procedure for 3D inhomogeneous, weakly orthorhombic media with varying orientation of symmetry planes. In contrast to commonly used approaches, the orthorhombic symmetry is preserved at any point of the model. The model is described by six weak-anisotropy parameters and three Euler angles, which may vary arbitrarily, but smoothly, throughout the model. We use the procedure for the calculation of rays and corresponding two-point traveltimes in a VSP experiment in a part of the BP benchmark model generalized to orthorhombic symmetry.
Inertial parameters in the interacting boson fermion approximation
The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors)
Symmetry-broken local-density approximation for one-dimensional systems
Rogers, Fergus J. M.; Ball, Caleb J.; Loos, Pierre-François
2016-06-01
Within density-functional theory, the local-density approximation (LDA) correlation functional is typically built by fitting the difference between the near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG), together with analytic perturbative results from the high- and low-density regimes. Near-exact energies are obtained by performing accurate diffusion Monte Carlo calculations, while HF energies are usually assumed to be the Fermi fluid HF energy. However, it has been known since the seminal work of A. W. Overhauser [Phys. Rev. Lett. 3, 414 (1959), 10.1103/PhysRevLett.3.414; Phys. Rev. 128, 1437 (1962), 10.1103/PhysRev.128.1437] that one can obtain lower, symmetry-broken (SB) HF energies at any density. Here, we have computed the SBHF energies of the one-dimensional UEG and constructed a SB version of the LDA (SBLDA) from the results. We compare the performance of the LDA and SBLDA functionals when applied to one-dimensional systems, including atoms and molecules. Generalization to higher dimensions is also discussed.
Leptonic SU(3), grand unification, and higher-dimensionality gravidynamics
Baaklini, N.S. (International Centre for Theoretical Physics, Trieste (Italy) Dahr el Chir Science Centre, Dhour el Choueir (Lebanon))
1990-06-01
Two considerations pertaining to the electroweak symmetry of leptons, and to higher-dimensionality gravidynamic spacetime-internal unification, lead us to suggest the gauging of SU(15), for each generation of leptons and quarks. On one hand, the electroweak leptonic sector is governed by SU(3), while the quark sector is standard. On the other hand, the Lorentz symmetry of Weyl fermions is generalized to spin-containing SU(2{ital n},C). Sketching the basic elements of the corresponding higher-dimensionality gravidynamics, we point out an associated quark-lepton unification scheme which does not require {ital V}+{ital A} generations.
Denominator function for canonical SU(3) tensor operators
The definition of a canonical unit SU(3) tensor operator is given in terms of its characteristic null space as determined by group-theoretic properties of the intertwining number. This definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique (up to +- phases) construction of all SU(3) WCG coefficients (Wigner--Clebsch--Gordan). Using this construction, an explicit SU(3)-invariant denominator function characterizing completely the canonically defined WCG coefficients is obtained. It is shown that this denominator function (squared) is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials. These polynomials, denoted G/sup t//sub q/, are defined over three (shift) parameters and three barycentric coordinates. The properties of these polynomials (hence, of the corresponding invariant denominator function) are developed in detail: These include a derivation of their degree, symmetries, and zeros. The symmetries are those induced on the shift parameters and barycentric coordinates by the transformations of a 3 x 3 array under row interchange, column interchange, and transposition (the group of 72 operations leaving a 3 x 3 determinant invariant). Remarkably, the zeros of the general G/sup t//sub q/ polynomial are in position and multiplicity exactly those of the SU(3) weight space associated with irreducible representation [q-1,t-1,0]. The results obtained are an essential step in the derivation of a fully explicit and comprehensible algebraic expression for all SU(3) WCG coefficients
This collection of specially written essays and articles celebrates the sixtieth birthday of Professor Yuval Ne'eman. Professor Ne'eman has been active at the forefront of many areas of modern physics; from SU(3) to Gravity. This book pays tribute to him by reporting and reflecting on the recent developments in these areas. The 36 contributions, all by internationally known and distinguished scientists are grouped under five main headings. The first, on Groups and Gauges has 5 articles, all of which are indexed separately. The second, on Particles has 11 articles, 10 indexed separately. The third, on Science Policy contains 5 articles, 1 indexed separately. The fourth on Astronomy and Astrophysics has 5 articles, 4 indexed separately. The final section on Gravity and Supergravity has 10 articles, all indexed separately. The resulting book will be of interest to researchers in cosmology and astrophysics, particle theory and relativity, and anyone who wishes to keep up to date with the interrelations between these subject areas. (UK)
Sameer M. Ikhdair; Sever, Ramazan
2009-01-01
We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of the two Dirac particles are obtained, in closed form, by means of the Nikiforov-Uvarov method which is based on solving the second-order linear differential equation by re...
Applications of flavor symmetry to the phenomenology of elementary particles
Some applications of flavor symmetry are examined. Approximate flavor symmetries and their consequences in the MSSM (Minimal Supersymmetric Standard Model) are considered, and found to give natural values for the possible B- and L-violating couplings that are empirically acceptable, except for the case of proton decay. The coupling constants of SU(3) are calculated and used to parameterize the decays of the D mesons in broken flavor SU(3). The resulting couplings are used to estimate the long-distance contributions to D-meson mixing
Coupled SU(3)-structures and Supersymmetry
Anna Fino; Alberto Raffero
2015-01-01
We review coupled ${\\rm SU}(3)$-structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behaviour of flows of ${\\rm SU}(3)$-structures with respect to the coupled condition.
A class of optimal tests for symmetry based on local Edgeworth approximations
Cassart, Delphine; Paindaveine, Davy; 10.3150/10-BEJ298
2011-01-01
The objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding symmetry into adequate families of asymmetric (local) alternatives. We construct such families by considering non-Gaussian generalizations of classical first-order Edgeworth expansions indexed by a measure of skewness such that (i) location, scale and skewness play well-separated roles (diagonality of the corresponding information matrices) and (ii) the classical tests based on the Pearson--Fisher coefficient of skewness are optimal in the vicinity of Gaussian densities.
SU(3)-flavons in pati-salam-GUTs
Pati-Salam GUTs are a first step in the direction of a complete fermion unification. As left-right-symmetric extensions of the SM they contain a right-handed neutrino. In addition the symmetry leads to a correlation between leptons and quarks. Thus they provide a framework to study mechanisms generating flavour structures simultaneously in quark and lepton sector. We study a SU(3) flavour symmetry and show how the spontaneous breaking of this symmetry by flavons may generate tribimaximal mixing for the leptons as well as nearly diagonal mixing in the quarks. Within this framework we present a supersymmetric model containing flavoured Higgs fields which may lead to a matter-Higgs-unification. We investigate which flavon representations are useful in constructing models leading to the desired CKM- and PMNS-mechanisms. Furthermore we discuss the problems of this approach and present possible solutions.
Breban, Romulus
2015-01-01
In previous work we discussed the problem of how a 4D observer perceives a 5D space-time and postulated that 4D perception is greatly facilitated if the 5D space-time is symmetric. In particular, if the 5D geometry is independent of the fifth coordinate then the 5D physics can be interpreted as 4D quantum mechanics. In this work we address the case where symmetry is approximate, focusing on the case where the 5D geometry depends weakly on the fifth coordinate. We show that concepts developed for the case of exact symmetry approximatively hold when other concepts such as decaying quantum states, resonant quantum scattering and friction are adopted as well. We briefly comment on the optical model and Millikan's experiment.
String completion of an SU(3)c ⊗ SU(3)L ⊗ U(1)X electroweak model
Addazi, Andrea; Valle, J. W. F.; Vaquera-Araujo, C. A.
2016-08-01
The extended electroweak SU(3)c ⊗ SU(3)L ⊗ U(1)X symmetry framework "explaining" the number of fermion families is revisited. While 331-based schemes can not easily be unified within the conventional field theory sense, we show how to do it within an approach based on D-branes and (un)oriented open strings, on Calabi-Yau singularities. We show how the theory can be UV-completed in a quiver setup, free of gauge and string anomalies. Lepton and baryon numbers are perturbatively conserved, so neutrinos are Dirac-type, and their lightness results from a novel TeV scale seesaw mechanism. Dynamical violation of baryon number by exotic instantons could induce neutron-antineutron oscillations, with proton decay and other dangerous R-parity violating processes strictly forbidden.
String completion of an SU(3c⊗SU(3L⊗U(1X electroweak model
Andrea Addazi
2016-08-01
Full Text Available The extended electroweak SU(3c⊗SU(3L⊗U(1X symmetry framework “explaining” the number of fermion families is revisited. While 331-based schemes can not easily be unified within the conventional field theory sense, we show how to do it within an approach based on D-branes and (unoriented open strings, on Calabi–Yau singularities. We show how the theory can be UV-completed in a quiver setup, free of gauge and string anomalies. Lepton and baryon numbers are perturbatively conserved, so neutrinos are Dirac-type, and their lightness results from a novel TeV scale seesaw mechanism. Dynamical violation of baryon number by exotic instantons could induce neutron–antineutron oscillations, with proton decay and other dangerous R-parity violating processes strictly forbidden.
String completion of an $\\mathrm{SU(3)_c \\otimes SU(3)_L \\otimes U(1)_X}$ electroweak model
Addazi, Andrea; Vaquera-Araujo, C A
2016-01-01
The extended electroweak $\\mathrm{SU(3)_c \\otimes SU(3)_L \\otimes U(1)_X}$ symmetry framework "explaining" the number of fermion families is revisited. While $331$-based schemes can not easily be unified within the conventional field theory sense, we show how to do it within an approach based on D-branes and (un)oriented open strings, on Calabi-Yau singularities. We show how the theory can be UV-completed in a quiver setup, free of gauge and string anomalies. Lepton and baryon numbers are perturbatively conserved, so neutrinos are Dirac-type, and their lightness results from a novel TeV scale seesaw mechanism. Dynamical violation of baryon number by exotic instantons could induce neutron-antineutron oscillations, with proton decay and R-parity violation strictly forbidden.
The space expansion of magnetic field with median plane symmetry in Taylor series is derived in cylindrical coordinate system. The expansion is expressed with the field distribution in the median plane, which may be an analytic expression or the field values at the discrete nodes. The discrete values are fitted with bicubic spline functions and the corresponding computer program is also given
Random matrix theory and acoustic resonances in plates with an approximate symmetry
Andersen, Anders Peter; Ellegaard, C.; Jackson, A.D.;
2001-01-01
the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes...
Sameer M. Ikhdair
2011-01-01
By using an improved approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation for the generalized Morse potential with arbitrary spin-orbit quantum number {\\kappa}. In the presence of spin and pseudospin symmetry, the analytic bound state energy eigenvalues and the associated upper- and lower-spinor components of two Dirac particles are found by using the basic concepts of the Nikiforov-Uvarov method. We study the special cases when {\\kappa}=\\pm...
Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry
Sameer M. Ikhdair
2012-01-01
Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the ...
Fixed point actions in SU(3) gauge theory: surface tension and topology
Farchioni, F.; Papa, A.
1997-01-01
This work is organized in two independent parts. In the first part are presented some results concerning the surface tension in SU(3) obtained with a parametrized fixed point action. In the second part, a new, approximately scale-invariant, parametrized fixed point action is proposed which is suitable to study the topology in SU(3).
Fixed point actions in SU(3) gauge theory: surface tension and topology
This work is organized in two independent parts. In the first part are presented some results concerning the surface tension in SU(3) obtained with a parametrized fixed point action. In the second part, a new, approximately scale-invariant, parametrized fixed point action is proposed which is suitable to study the topology in SU(3). (orig.)
A novel improved action for SU(3) lattice gauge theory
Langfeld, Kurt
2004-01-01
SU(3) lattice gauge theory is studied by means of an improved action where a $2 \\times 2$ Wilson loop is supplemented to the standard plaquette term. By contrast to earlier studies using a tree level improvement, the prefactor of the $2 \\times 2$ Wilson term is determined by minimizing the breaking of rotational symmetry detected from the static quark-antiquark potential. On coarse lattices, the novel action is superior to the Iwasaki action and comparable with DBW2 action. The scaling behavi...
Minimally allowed beta beata 0_nu rates from approximate flavor symmetries
Jenkins, James [Los Alamos National Laboratory
2008-01-01
Neutrinoless double beta decay ({beta}{beta}0{nu}) is the only realistic probe of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to m{sub ee} , the e - e element of the Majorana mass matrix. This is expected to hold true for small {beta}{beta}{nu} rates ({Gamma}{sub {beta}{beta}0{nu}}), even in the presence of new physics. Naively, current data allows for vanishing m{sub ee} , but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. Hence, Majorana neutrinos imply nonzero {Gamma}{sub {beta}{beta}0{nu}}. I perform a spurion analysis to break all possible abelian symmetries that guarantee {Gamma}{sub {beta}{beta}0{nu}} = 0 and search for minimally allowed m{sub ee} values. Specifically, I survey 259 broken structures to yield m{sub ee} values and current phenomenological constraints under a variety of scenarios. This analysis also extracts predictions for both neutrino oscillation parameters and kinematic quantities. Assuming reasonable tuning levels, I find that m{sub ee} > 4 x 10{sup -6} eV at 99% confidence. Bounds below this value would indicate the Dirac neutrino nature or the existence of new light (eV-MeV scale) degrees of freedom that can potentially be probed elsewhere. This limit can be raised by improvements in neutrino parameter measurements, particularly of the reactor mixing angle, depending on the best fit parameter values. Such improvements will also significantly constrain the available model space and aid in future constructions.
Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry
Ikhdair, Sameer M
2012-01-01
Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C_{s} from the valence energy spectrum of particle and also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter {\\alpha}. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) s...
Hernández, A. E. Cárcamo; Mart'\\inez, R.; Ochoa, F.
2013-01-01
We take up again the study of the mass spectrum of the quark sector in a model with gauge symmetry $SU(3)_{c}\\otimes SU(3)_{L}\\otimes U(1)_{X}$ (331). In a special type II-like 331 model, we obtain specific zero-texture mass matrices for the quarks which predict four massless quarks ($u,c,d,s$) and two massive quarks ($b,t$) at the electroweak scale ($\\sim $ GeV). By considering the mixing between the SM quarks and new exotic quarks at large scales predicted by the model, we find that a third...
Nucleon instability in a supersymmetric SU(3)c x SU(3)L x U(1) model
We construct the supersymmetric version of a model based on the gauge group SU(3)c x SU(3)L x U(1). We discuss the mechanism of baryon number violation which induces nucleon decay, and derive bounds on the relevant couplings. (author)
This work uses FORM software aspects for obtaining a series of formal results in the non-Abelian gauge theory, with SU(3) group. The work also studies field transformation, Lagrangian density invariance, field equations, energy distribution and the theory reparametrization in terms of fields associated to particles which are possible to be detected in accelerators
Flux tubes in the SU(3) vacuum
Cardaci, Mario S.; Cea, Paolo; Cosmai, Leonardo; Falcone, Rossella; Papa, Alessandro
2011-01-01
We analyze the distribution of the chromoelectric field generated by a static quark-antiquark pair in the SU(3) vacuum. We find that the transverse profile of the flux tube resembles the dual version of the Abrikosov vortex field distribution and give an estimate of the London penetration length in the confined vacuum.
A Nearly Quaternionic Structure on SU(3)
Macia, Oscar
2009-01-01
It is shown that the compact Lie group SU(3) admits an Sp(2)Sp(1)-structure whose distinguished 2-forms $\\omega_1,\\omega_2,\\omega_3$ span a differential ideal. This is achieved by first reducing the structure further to a subgroup isomorphic to SO(3).
Axially symmetric SU(3) gravitating skyrmions
Ioannidou, Theodora [Maths Division, School of Technology, Aristotle University of Thessaloniki, Thessaloniki 54124 (Greece)]. E-mail: ti3@auth.gr; Kleihaus, Burkhard [Institut fuer Physik, Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)]. E-mail: kleihaus@theorie.physik.uni-oldenburg.de; Zakrzewski, Wojtek [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)]. E-mail: w.j.zakrzewski@durham.ac.uk
2004-10-21
Axially symmetric gravitating multi-skyrmion configurations are obtained using the harmonic map ansatz introduced in [J. Math. Phys. 40 (1999) 6353]. In particular, the effect of gravity on the energy and baryon densities of the SU(3) non-gravitating multi-skyrmion configurations is studied in detail.
Axially symmetric SU(3) Gravitating Skyrmions
Ioannidou, T A; Zakrzewski, W J; Ioannidou, Theodora; Kleihaus, Burkhard; Zakrzewski, Wojtek
2004-01-01
Axially symmetric gravitating multi-skyrmion configurations are obtained using the harmonic map ansatz introduced in [1]. In particular, the effect of gravity on the energy and baryon densities of the SU(3) non-gravitating multi-skyrmion configurations is studied in detail.
Axially symmetric SU(3) gravitating skyrmions
Axially symmetric gravitating multi-skyrmion configurations are obtained using the harmonic map ansatz introduced in [J. Math. Phys. 40 (1999) 6353]. In particular, the effect of gravity on the energy and baryon densities of the SU(3) non-gravitating multi-skyrmion configurations is studied in detail
Flux tubes in the SU(3) vacuum
Cardaci, M. S.; Cea, P.; Cosmai, L.; Falcone, R.; Papa, A.
We analyze the distribution of the chromoelectric field generated by a static quark-antiquark pair in the SU(3) vacuum. We find that the transverse profile of the flux tube resembles the dual version of the Abrikosov vortex field distribution and give an estimate of the London penetration length in the confined vacuum.
The strong CP problem and nucleon stability in the [SU(3)]3 trinification model
We argue the Peccei-Quinn mechanism in the [SU(3)]3 trinification model. It turns out that the introduction of the Peccei-Quinn symmetry by allowing a third Higgs 27-plet leads to baryon-number conservation. Related discussions are included also. (orig.)
The energy content of the Lee-Kim-Myung slowly-rotating black hole (Lee et al., Eur. Phys. J. C 70, 361 (2010)), in the Horava-Lifshitz (HL) theory of gravity is investigated by using approximate Lie symmetry methods for differential equations. The energy of this slowly-rotating black hole in the HL gravity is found to be is rescaled by a r-dependent factor. From the rescaling of energy, the rotation is observed to be added to the mass of the black hole, and this effect decreases with increasing coordinate r. This expression of energy rescaling reduces to the Schwarzschild mass for the limits in which the Lee-Kim-Myung slowly rotating black hole solution in the HL gravity reduces to the Schwarzschild solution in general relativity.
Quasi-SU(3) truncation scheme for even-even sd-shell nuclei
Vargas, C E; Draayer, J P
2000-01-01
The Quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even-even and odd-even nuclei. It manifests itself through a dominance of single-particle and quadrupole-quadrupole terms in the Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In a recent work was shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible represntations (irreps) of SU(3) are needed to describe the Yrast band, the leading S = 0 irrep augmented with the leading S = 1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a "realistic but schematic" Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of 20-Ne, 22-Ne, 24-Mg and 28-Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well ...
Vortices and the SU(3) string tension
Kovács, T. G.; Tomboulis, E. T.
1998-01-01
We present simulation results comparing the SU(3) heavy quark potential extracted from the full Wilson loop expectation to that extracted from the expectation of the Wilson loop fluctuation solely by elements of Z(3). The two potentials are found to coincide. This agreement is stable under multiple smoothings of the configurations which remove short distance fluctuations, and thus reflects long-distance physics. It strongly indicates that the asymptotic string tension arises from thick center...
Tables of SU(3) isoscalar factors
The Clebsch-Gordan coefficients of SU(3) are useful in calculations involving baryons and mesons, as well as in calculations involving arbitrary numbers of quarks. For the latter case, one needs the coupling constants between states of nonintegral hypercharges. The existing published tables are insufficient for many such applications, and therefore we have compiled this collection. This report supplies the isoscalar factors required to reconstruct the Clebsch-Gordan coefficients for a large set of products of representations
In this paper we will study triangles in SU(3). The orbit space of congruence classes of triangles in SU(3) has dimension 8. Each corner is made up of a pair of tangent vectors (X,Y), and we consider the 8 functions trX2, i trX3, trY2, i trY3, trXY, i trY2Y, i trXY2, trX2Y2 which are invariant under the full isometry group of SU(3). We show that these 8 corner invariants determine the isometry class of the triangle. We give relations (laws of trigonometry) between the invariants at the different corners, enabling us to determine the invariants at the remaining corners, including the values of the remaining side and angles, if we know one set of corner invariants. The invariants that only depend on one tangent vector we will call side invariants, while those that depend on two tangent vectors will be called angular invariants. For each triangle we then have 6 side invariants and 12 angular invariants. Hence we need 18 - 8 = 10 laws of trigonometry. The basic tool for deriving these laws is a formula expressing tr(exp X exp Y) in terms of the corner invariants
Phenomenology of the SU(3)_C \\otimes SU(2)_L \\otimes SU(3)_R \\otimes U(1)_X gauge model
Dong, P V; Loi, D V; Nhuan, N T; Ngan, N T K
2016-01-01
We study the left-right asymmetric model based on SU(3)_C\\otimes SU(2)_L \\otimes SU(3)_R\\otimes U(1)_X gauge group, which improves the theoretical and phenomenological aspects of the known left-right symmetric model. This new gauge symmetry yields that the fermion generation number is three, and the tree-level flavor-changing neutral currents arise in both gauge and scalar sectors. Also, it can provide the observed neutrino masses as well as dark matter automatically. Further, we investigate the mass spectrum of the gauge and scalar fields. All the gauge interactions of the fermions and scalars are derived. We examine the tree-level contributions of the new neutral vector, Z'_R, and new neutral scalar, H_2, to flavor-violating neutral meson mixings, say K-\\bar{K}, B_d-\\bar{B}_d, and B_s-\\bar{B}_s, which strongly constrain the new physics scale as well as the elements of the right-handed quark mixing matrices. The bounds for the new physics scale are in agreement with those coming from the \\rho-parameter as we...
Chiral-symmetry restoration in baryon-rich environments
Chiral symmetry restoration in an environment rich in baryons is studied by computer simulation methods in SU(2) and SU(3) gauge theories in the quenched approximation. The basic theory of symmetry restoration as a function of chemical potential is illustrated and the implementation of the ideas on a lattice is made explicit. A simple mean field model is presented to guide one's expectations. The second order conjugate-gradient iterative method and the pseudo-fermion Monte Carlo procedure are convergent methods of calculating the fermion propagator in an environment rich in baryons. Computer simulations of SU(3) gauge theory show an abrupt chiral symmetry restoring transition and the critical chemical potential and induced baryon density are estimated crudely. A smoother transition is observed for the color group SU(2)
Particle-hole excitations in the interacting boson model; 4, the U(5)-SU(3) coupling
De Coster, C; Heyde, Kris L G; Jolie, J; Lehmann, H; Wood, J L
1999-01-01
In the extended interacting boson model (EIBM) both particle- and hole-like bosons are incorporated to encompass multi-particle-multi-hole excitations at and near to closed shells.We apply the group theoretical concepts of the EIBM to the particular case of two coexisting systems in the same nucleus exhibiting a U(5) (for the regular configurations) and an SU(3) symmetry (for the intruder configurations).Besides the description of ``global'' symmetry aspects in terms of I-spin , also the very specific local mixing effects characteristic for the U(5)-SU(3) symmetry coupling are studied.The model is applied to the Po isotopes and a comparison with a morerealistic calculation is made.
Two Dimensional Hamiltonian with Generalized Shape Invariance Symmetry
Panahi-Talemi, H.; Jafarizadeh, M. A.
2002-01-01
The two dimensional Hamiltonian with generalized shape invariance symmetry over $S^2$, has been obtained via Fourier transformation over the three coordinates of the $SU(3)$ Casimir operator defined on $SU(3)/SU(2)$ symmetric space. It is shown that the generalized shape invariance is equivalent to $SU(3)$ symmetry and that there is one to one correspondence between the representations of the generalized shape invariance and $SU(3)$ Verma modules. Also the two dimensional Hamiltonian in $\\mat...
Reducing democratic type II supergravity on SU(3) x SU(3) structures
Cassani, Davide
2008-01-01
Type II supergravity on backgrounds admitting SU(3) x SU(3) structure and general fluxes is considered. Using the generalized geometry formalism, we study dimensional reductions leading to N=2 gauged supergravity in four dimensions, possibly with tensor multiplets. In particular, a geometric formula for the full N=2 scalar potential is given. Then we implement a truncation ansatz, and derive the complete N=2 bosonic action. While the NSNS contribution is obtained via a direct dimensional reduction, the contribution of the RR sector is computed starting from the democratic formulation and demanding consistency with the reduced equations of motion.
Higgs Phenomenology in the Minimal $SU(3)_L\\times U(1)_X$ Model
Okada, Hiroshi; Orikasa, Yuta; Yagyu, Kei
2016-01-01
We investigate the phenomenology of a model based on the $SU(3)_c\\times SU(3)_L\\times U(1)_X$ gauge theory, the so-called 331 model. In particular, we focus on the Higgs sector of the model which is composed of three $SU(3)_L$ triplet Higgs fields, and this corresponds to the minimal form to realize phenomenologically acceptable scenario. After the spontaneous symmetry breaking $SU(3)_L\\times U(1)_X\\to SU(2)_L\\times U(1)_Y$, our Higgs sector effectively becomes that with two $SU(2)_L$ doublet scalar fields, in which the first and the second generation quarks couple to the different Higgs doublet from that couples to the third generation quarks. This structure causes the flavour changing neutral current mediated by Higgs bosons at the tree level. By taking an alignment limit of the mass matrix for the CP-even Higgs bosons, which is naturally realized in the case with the breaking scale of $SU(3)_L\\times U(1)_X$ to be much larger than that of $SU(2)_L\\times U(1)_Y$, we can avoid current constraints from flavour...
More flavor SU(3) tests for new physics in CP violating B decays
The recent LHCb measurements of the Bs→K−π+ and Bs→K+K− rates and CP asymmetries are in agreement with U-spin expectations from Bd→K+π− and Bd→π+π− results. We derive the complete set of isospin, U-spin, and SU(3) relations among the CP asymmetries in two-body charmless B→PP and B→PV decays, some of which are novel. To go beyond the unbroken SU(3) limit, we present relations which are properly defined and normalized to allow incorporation of SU(3) breaking in the simplest manner. We show that there are no CP relations beyond first order in SU(3) and isospin breaking. We also consider the corresponding relations for charm decays. Comparing parametrizations of the leading order sum rules with data can shed light on the applicability and limitations of both the flavor symmetry and factorization-based descriptions of SU(3) breaking. Two factorization relations can already be tested, and we show they agree with current data
Hernández, A E Cárcamo; Ochoa, F
2013-01-01
We take up again the study of the mass spectrum of the quark sector in a model with gauge symmetry $SU(3)_{c}\\otimes SU(3)_{L}\\otimes U(1)_{X}$ (331). In a special type II-like 331 model, we obtain specific zero-texture mass matrices for the quarks which predict four massless quarks ($u,c,d,s$) and two massive quarks ($b,t$) at the electroweak scale ($\\sim $ GeV). By considering the mixing between the SM quarks and new exotic quarks at large scales predicted by the model, we find that a third quark (associated to the charm quark) acquires a mass. The remaining light quarks ($u,d,s$) get small masses ($\\sim$ MeV) via radiative corrections.
Exceptional Lie algebras, SU(3) and Jordan pairs: part 2. Zorn-type representations
A representation of the exceptional Lie algebras reflecting a simple unifying view, based on realizations in terms of Zorn-type matrices, is presented. The role of the underlying Jordan pair and Jordan algebra content is crucial in the development of the structure. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. The applications in physics are outlined. (paper)
Dark Matter from a Classically Scale-Invariant $SU(3)_X$
Karam, Alexandros; Tamvakis, Kyriakos
2016-01-01
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra $SU(3)_X$ gauge factor gets completely broken by the vevs of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic $Z_2\\times Z_2'$ discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability ...
SU(3)-flavour breaking in octet baryon masses and axial couplings
Carrillo-Serrano, Manuel E.; Cloët, Ian C.; Thomas, Anthony W.(CSSM and ARC Centre of Excellence for Particle Physics at the Tera-scale, School of Chemistry and Physics, University of Adelaide, Adelaide, SA 5005, Australia 1 1 http://www.physics.adelaide.edu.au/cssm .)
2014-01-01
The lightest baryon octet is studied within a covariant and confining Nambu--Jona-Lasinio model. By solving the relativistic Faddeev equations including scalar and axialvector diquarks, we determine the masses and axial charges for \\Delta S = 0 transitions. For the latter the degree of violation of SU(3) symmetry arising because of the strange spectator quark(s) is found to be up to 10%.
Two and three dimensional Hamiltonians with generalized and ordinary shape invariance symmetry
Two and three dimensional Hamiltonians with generalized and ordinary shape invariance symmetry have been obtained by Fourier transforming over some coordinates of the SU(3) Casimir operator defined on SU(3)/SU(2) symmetric space. It is shown that the generalized shape invariance of the two dimensional Hamiltonian is equivalent to SU(3) symmetry while in the three dimensional one, the ordinary shape invariance is equivalent to contracted SU(3) and there is one to one correspondence between the representations of the generalized shape invariance symmetry of the two (three) dimensional Hamiltonian and SU(3) [contracted SU(3)] Verma bases
New phases of SU(3) and SU(4) at finite temperature
The addition of an adjoint Polyakov loop term to the action of a pure gauge theory at finite temperature leads to new phases of SU(N) gauge theories. For SU(3), a new phase is found which breaks Z(3) symmetry in a novel way; for SU(4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2), representing a partially-confined phase in which quarks are confined, but diquarks are not. The overall phase structure and thermodynamics is consistent with a theoretical model of the effective potential for the Polyakov loop based on perturbation theory
Symmetry breaking patterns of the 3-3-1 model at finite temperature
Borges, J Sá
2016-01-01
We consider the minimal version of an extension of the standard electroweak model based on the $SU(3)_c \\times SU(3)_L \\times U(1)_X$ gauge symmetry (the 3-3-1 model). We analyze the most general potential constructed from three scalars in the triplet representation of $SU(3)_L$, whose neutral components develop nonzero vacuum expectation values, giving mass for all the model massive particles. {}For a convenient choice of parameters, we obtain the particle spectrum for the two symmetry breaking scales: one where the $SU(3)_L \\times U(1)_X$ group is broken down to $SU(2)_L\\times U(1)_Y$ and a lower scale similar to the standard model one. Within the approximations used, we show that the model encodes two first-order phase transitions, respecting the pattern of symmetry restoration. The last transition, corresponding to the standard electroweak one, is found to be very weak first-order, most likely turning second-order or a crossover in practice. We determine the respective critical temperatures for symmetry r...
Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators
Pushpa,; Li, Tianjun; Negi, O P S
2012-01-01
An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are suitably handled with quaternions and octonions in order to obtain their generators, commutation rules and symmetry properties. Accordingly, Casimir operators for SU(2)and SU(3) flavor symmetries are also constructed for the proper testing of these symmetries in terms of quaternions and octonions.
We generalize the finite-range momentum- and density-dependent Seyler-Blanchard nucleon-nucleon effective interaction to the case of interaction between two baryons. This effective interaction is then used to describe dense hadronic matter relevant to neutron stars in the non-relativistic Thomas-Fermi approach. We investigate the behaviour of nuclear symmetry energy in dense nuclear and hyperon matter relevant to neutron stars. It is found that the nuclear symmetry energy always increases with density in hyperon matter unlike the situation in nuclear matter. This rising characteristic of the symmetry energy in the presence of hyperons may have significant implications on the mass-radius relationship and the cooling properties of neutron stars. We have also noted that with the appearance of hyperons, the equation of state calculated in this model remains causal at high density. (author)
Mean field analysis of SU(3) lattice Yang-Mills theory at finite temperature
The phase diagram of the SU(3) four-dimensional space-time lattice Yang-Mills field theory at finite temperature is analysed by the extended mean-field technique. With this technique, finite temperature effects are present already at the saddle point approximation. A reasonable quantitative agreement with Monte Carlo numerical simulations is obtained. (author)
Phenomenological aspects of a left-right model based on SU(3)
Doas, Alex G.; Nishi, Celso C. [Universidade Federal do ABC (UFABC), SP (Brazil)
2011-07-01
Full text: Motivated by the problem of explaining the observed maximal parity violation in the electroweak interactions, we develop a model based on the SU(3){sub L} x SU(3){sub R} x U(1){sub X} gauge symmetry, where anomalies cancellation restricts the number of families is restricted to be a multiple of three. Left-right symmetry is fully realized in the model and the standard model arises in the low energy limit. The fermionic representation content has, besides standard model fields, nine additional neutrinos which could be linked with problems like neutrino oscillation, warm dark matter and baryogenesis; six new quarks which could show up at the TeV; and also new gauge bosons whose production and associated effects observed in colliders shall indicate the parity restoration. Our focus will be mainly on the spontaneous symmetry breakdown patterns leading to a compatible scenario for particle interactions with the well tested standard model. In order to break the symmetries we take into account a set of scalar fields representation content composed by: two sextets and two bi-triplets. These fields are sufficient to implement a successful mass generation mechanisms, furnishing also a consistent mixing among the fermions. We discuss the main phenomenological issues of the model. (author)
Form factors in SU(3)-invariant integrable models
Belliard, S; Ragoucy, E; Slavnov, N A
2013-01-01
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.
On some properties of SU(3) Fusion Coefficients
Coquereaux, Robert
2016-01-01
Three aspects of the SU(3) fusion coefficients are revisited: the generating polynomials of fusion coefficients are written explicitly; some curious identities generalizing the classical Freudenthal-de Vries formula are derived; and the properties of the fusion coefficients under conjugation of one of the factors, previously analysed in the classical case, are extended to the affine algebra of su(3) at finite level.
The Gauge Bosons Masses in a SU(2)_TC x SU(3)_L x U(1)_X Extension of the Standard Model
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil)
2010-01-01
The gauge symmetry breaking in 3-3-1 models can be implemented dynamically because at the scale of a few TeVs the U(1)_X coupling constant becomes strong. The exotic quark T introduced in the model will form a condensate breaking SU(3)_L x U(1)_X to electroweak symmetry. In this work we explore the full realization of the dynamical symmetry breaking of an 3-3-1 model to U(1)_{em} considering a model based on SU(2)_TC x SU(3)_L x U(1)_X. We compute the mass generated for the charged and neutra...
Confining properties of the classical SU(3) Yang - Mills theory
Dzhunushaliev, V D
1996-01-01
The spherically and cylindrically symmetric solutions of the $SU(3)$ Yang - Mills theory are obtained. The corresponding gauge potential has the confining properties. It is supposed that: a) the spherically symmetric solution is a field distribution of the classical ``quark'' and in this sense it is similar to the Coulomb potential; b) the cylindrically symmetric solution describes a classical field ``string'' (flux tube) between two ``quarks''. It is noticed that these solutions are typically for the classical $SU(3)$ Yang - Mills theory in contradiction to monopole that is an exceptional solution. This allows to conclude that the confining properties of the classical $SU(3)$ Yang - Mills theory are general properties of this theory.
Skyrmions from SU(3) harmonic maps and their quantization
Kopeliovich, V B; Zakrzewski, W J
2000-01-01
Static properties of SU(3) multiskyrmions with baryon number up to 6(classical masses and momenta of inertia) are estimated. The calculations arebased on the recently suggested generalization of the SU(2) rational mapansaetze applied to the SU(3) model. Both SU(2) embedded skyrmions and genuineSU(3) solutions are considered, and it is shown that although, at the classicallevel, the energy of embeddings is lower, the quantum corrections can alterthis conclusion. This correction to the energy of lowest state, bilinear in theWess-Zumino (WZ) term, is presented for the most general case as a convolutionof the inverse tensor of inertia and the components of the WZ-term.
Transport coefficients from SU(3) Polyakov linear-σ model
In the mean field approximation, the grand potential of SU(3) Polyakov linear-σ model (PLSM) is analyzed for the order parameter of the light and strange chiral phase-transitions, σl and σs, respectively, and for the deconfinement order parameters φ and φ*. Furthermore, the subtracted condensate Δl,s and the chiral order-parameters Mb are compared with lattice QCD calculations. By using the dynamical quasiparticle model (DQPM), which can be considered as a system of noninteracting massive quasiparticles, we have evaluated the decay width and the relaxation time of quarks and gluons. In the framework of LSM and with Polyakov loop corrections included, the interaction measure Δ/T4, the specific heat cv and speed of sound squared cs2 have been determined, as well as the temperature dependence of the normalized quark number density nq/T3 and the quark number susceptibilities χq/T2 at various values of the baryon chemical potential. The electric and heat conductivity, σe and κ, and the bulk and shear viscosities normalized to the thermal entropy, ζ/s and η/s, are compared with available results of lattice QCD calculations.
Exact solutions to D=2 Supersymmetric Yang-Mills Quantum Mechanics with SU(3) gauge group
Korcyl, Piotr
2009-01-01
In this article we present the cut Fock space approach to the D=d+1=2, Supersymmetric Yang-Mills Quantum Mechanics (SYMQM). We start by briefly introducing the main features of the framework. We concentrate on those properties of the method which make it a convenient set up not only for numerical calculations but also for analytic computations. In the main part of the article a sample of results are discussed, namely, analytic and numerical analysis of the D=2, SYMQM systems with SU(2) and SU(3) gauge symmetry.
Finite-temperature study of eight-flavor SU(3) gauge theory
Schaich, David; Rinaldi, Enrico
2015-01-01
We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \\lesssim 20$ on lattice volumes as large as $48^3 \\times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.
Is SU(3) Chiral Perturbation Theory an Effective Field Theory?
Holstein, Barry R.
1998-01-01
We argue that the difficulties associated with the convergence properties of conventional SU(3) chiral perturbation theory can be ameliorated by use of a cutoff, which suppresses the model-dependent short distance effects in such calculations.
Soliton Solution of SU(3) Gauge Fields at Finite Temperature
WANG Dian-Fu; SONG He-Shan
2005-01-01
@@ Starting from a soliton model of SU(3) gauge fields, we investigate the behaviour of the model at finite temperature. it is found that colour confinement at zero temperature can be melted away under high temperatures.
Flux tubes and coherence length in the SU(3) vacuum
Cea, Paolo; Cosmai, Leonardo; Cuteri, Francesca; Papa, Alessandro
2013-01-01
An estimate of the London penetration and coherence lengths in the vacuum of the SU(3) pure gauge theory is given downstream an analysis of the transverse profile of the chromoelectric flux tubes. Within ordinary superconductivity, a simple variational model for the magnitude of the normalized order parameter of an isolated vortex produces an analytic expression for magnetic field and supercurrent density. In the picture of SU(3) vacuum as dual superconductor, this expression provides us with...
Intermediate Symmetries in the Spontaneous Breaking of Supersymmetric SO(10)
Buccella, F.; Savoy, C. A.
We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU(3) ⊗ SU(2) ⊗ U(1) for the most physically interesting cases of SU(5) or flipped SU(5) ⊗ U(1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU(5) symmetry there is at most one singlet of the residual symmetry in each SO(10) irreducible representation. We also point out on more general grounds in supersymmetric GUTs that some intermediate symmetries can be exactly realized and others can only be approximated by fine-tuning. In the first category, there could occur some tunneling between the vacua with exact and approximate intermediate symmetry. The flipped SU(5) ⊗ U(1) symmetry improves the unification of gauge couplings if (B-L) is broken by ∥(B-L)∥ =1 scalars yielding right-handed neutrino masses below 1014 GeV.
Intermediate Symmetries in the Spontaneous Breaking of Supersymmetric SO(10)
Buccella, F
2002-01-01
We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU(3)xSU(2)xU(1) for the most physically interesting cases of SU(5) or flipped SU(5)xU(1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU(5) symmetry there is at most one singlet of the residual symmetry in each SO(10) irreducible representation. We also point out on more general grounds in supersymmetric GUT's that some intermediate symmetries can be exactly realized and others can only be approximated by fine-tuning. In the first category, there could occur some tunneling between the vacua with exact and approximate intermediate symmetry. The flipped SU(5)xU(1) symmetry improves the unification of gauge couplings if (B-L) is broken by (B-L)=1 scalars yielding right handed neutrino masses below 10^{14} GeV}.
Heavy quark solitons strangeness and symmetry breaking
Momen, A; Subbaraman, A; Momen, Arshad; Schechter, Joseph; Subbaraman, Anand
1994-01-01
We discuss the generalization of the Callan-Klebanov model to the case of heavy quark baryons. The light flavor group is considered to be $SU(3)$ and the limit of heavy spin symmetry is taken. The presence of the Wess-Zumino-Witten term permits the neat development of a picture , at the collective level, of a light diquark bound to a ``heavy" quark with decoupled spin degree of freedom. The consequences of $SU(3)$ symmetry breaking are discussed in detail. We point out that the $SU(3)$ mass splittings of the heavy baryons essentially measure the ``low energy" physics once more and that the comparison with experiment is satisfactory.
Heavy quark solitons: Strangeness and symmetry breaking
We discuss the generalization of the Callan-Klebanov model to the case of heavy quark baryons. The light flavor group is considered to be SU(3) and the limit of heavy spin symmetry is taken. The presence of the Wess-Zumino-Witten term permits the neat development of a picture, at the collective level, of a light diquark bound to a ''heavy'' quark with decoupled spin degree of freedom. The consequences of SU(3) symmetry breaking are discussed in detail. We point out that the SU(3) mass splitting of the heavy baryons essentially measure the ''low energy'' physics once more and that the comparison with experiment is satisfactory
Glueball-like screening masses in pure SU(3) at finite temperatures
We investigate the finite-temperature excitation spectrum in the gluon sector of SU(3) pure gauge theory through measurements of screening masses in correlations of loop operators. We develop the classification of such operators under the symmetry group of the ''z-slice''. In the confined phase of the theory, we find that the spectrum dynamically realises the zero-temperature symmetries. We observe a large thermal shift of the 0++ glueball mass. In the deconfined phase, the spectrum distinguishes between operators coupling to electrically and magnetically polarised gluon fields. The former yields a screening mass equal to the Wilson-line screening mass; the latter a method for the measurement of the magnetic mass in the high-temperature limit. (orig.)
The SU(3) Nambu-Jona-Lasinio soliton in the collective quantization formulation
On grounds of a semibosonized Nambu-Jona-Lasinio model, which has SU(3)RxSU(3)L symmetry in the chiral limit, mass splittings for spin 1/2 and spin 3/2 baryons are studied in the presence of an explicit chiral-symmetry-breaking strange-quark mass. To this aim these strangeness-carrying baryons are understood as SU(3)-rotational excitations of an SU(2)-embedded soliton solution. Therefore, within the framework of collective quantization, the fermion determinant with the strange-quark mass is expanded up to the second order in the flavor rotation velocity and up to the first order in this quark mass. Besides, the strange and non-strange moments of inertia, which have some counterparts within the Skyrme model, some so-called anomalous moments of inertia are obtained. These can be related to the imaginary part of the effective euclidian action and contain among others the anomalous baryon current. This is shown in a gradient expansion up to the first non-vanishing order. Together with the Σ-commutator these are the solitonic ingredients of the collective hamiltonian, which is then diagnonalized by means of strict perturbation theory in the strange-quark mass and by the Yabu-Ando method. Both methods yield very good results for the masses of the spin 1/2 and 3/2 baryons. The former one reproduces some interesting mass formulas of Gell-Mann, Okubo and of Guadagnini and the latter one is able to describe the mass splittings up to a few MeV. (orig.)
Mass Formulas Derived by Symmetry Breaking and Prediction of Masses on Heavy Flavor Hadrons
Chang, Yi-Fang
2008-01-01
The base is the Lagrangian of symmetry and its dynamical breaking or Higgs breaking. When the soliton-like solutions of the scalar field equations are substituted into the spinor field equations, in the approximation of non-relativity we derive the Morse-type potential, whose energy spectrum is the GMO mass formula and its modified accurate mass formula. According to the symmetry of s-c quarks, the heavy flavor hadrons which made of u,d and c quarks may be classified by SU(3) octet and decuplet. Then some simple mass formulas are obtained, from this we predict some masses of unknown hadrons.
Symmetry and Phase Transitions in Nuclei
Phase transitions in nuclei have received considerable attention in recent years, especially after the discovery that, contrary to expectations, systems at the critical point of a phase transition display a simple structure. In this talk, quantum phase transitions (QPT), i.e. phase transitions that occur as a function of a coupling constant that appears in the quantum Hamiltonian, H, describing the system, will be reviewed and experimental evidence for their occurrence in nuclei will be presented. The phase transitions discussed in the talk will be shape phase transitions. Different shapes have different symmetries, classified by the dynamic symmetries of the Interacting Boson Model, U(5), SU(3) and SO(6). Very recently, the concept of Quantum Phase Transitions has been extended to Excited State Quantum Phase Transitions (ESQPT). This extension will be discussed and some evidence for incipient ESQPT in nuclei will be presented. Systems at the critical point of a phase transition are called 'critical systems'. Approximate analytic formulas for energy spectra and other properties of 'critical nuclei', in particular for nuclei at the critical point of the second order U(5)-SO(6) transition, called E(5), and along the line of first order U(5)-SU(3) transitions, called X(5), will be presented. Experimental evidence for 'critical nuclei' will be also shown. Finally, the microscopic derivation of shape phase transitions in nuclei within the framework of density functional methods will be briefly discussed.(author)
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces
SU(3) Approach to Hypernuclear Interactions and Spectroscopy
Lenske, H; Gaitanos, T
2016-01-01
The $SU(3)$ meson exchange approach to interactions within the baryon octet and nuclear density functional theory are used to derive an \\emph{ab initio} description of hypernuclear interactions. The density dependence of interactions is recast into a DFT with density dependent interaction vertices. The field-theoretical structure is retained by expressing the vertices as functionals of the matter field operators. Applications to infinite hypermatter and neutron star matter are discussed. A new approach is presented allowing to determine in-medium coupling constants out of the $NN$-vertex functionals, obtained e.g. by DBHF theory, for the full baryon octet by exploiting $SU(3)$ relations.
Flux tubes and coherence length in the SU(3) vacuum
Cea, Paolo; Cuteri, Francesca; Papa, Alessandro
2013-01-01
An estimate of the London penetration and coherence lengths in the vacuum of the SU(3) pure gauge theory is given downstream an analysis of the transverse profile of the chromoelectric flux tubes. Within ordinary superconductivity, a simple variational model for the magnitude of the normalized order parameter of an isolated vortex produces an analytic expression for magnetic field and supercurrent density. In the picture of SU(3) vacuum as dual superconductor, this expression provides us with the function that fits the chromoelectric field data. The smearing procedure is used in order to reduce noise.
Flux tubes and coherence length in the SU(3) vacuum
Cea, P.; Cosmai, L.; Cuteri, F.; Papa, A.
An estimate of the London penetration and coherence lengths in the vacuum of the SU(3) pure gauge theory is given downstream an analysis of the transverse profile of the chromoelectric flux tubes. Within ordinary superconductivity, a simple variational model for the magnitude of the normalized order parameter of an isolated vortex produces an analytic expression for magnetic field and supercurrent density. In the picture of SU(3) vacuum as dual superconductor, this expression provides us with the function that fits the chromoelectric field data. The smearing procedure is used in order to reduce noise.
Quark and lepton generations: CP-violation and rare processes in SUSY SU(3)HV-gauge horizontal model
In this paper, the current state of the generation mixing and CP-violation problems is discussed from the standpoint of the hypothetical existence of SUSY - SU(3)HV-gauge horizontal symmetry. The behaviour of the estimates for the horizontal symmetry breaking scale showed certain regularities depending on particular symmetry breaking schemes and generation mixing mechanisms (different anzatzes for quark and lepton mass matrices with 3 and 4 generations have been discussed). Supersymmetry is supposed to be important for: the hierarchy problem, certain useful constraints on Yukawa couplings, the super-Higgs effect in the case of a broken local horizontal symmetry, the estimates of the gauge coupling constants gH and the restrictions on the horizontal gaugino masses. 24 refs
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
String tension in SU(3) lattice gauge theory
Wilson loop expectation values have been determined in SU(3) lattice gauge theory without fermions using Monte Carlo methods and considering lattices up to 104 sites. A heat bath technique has been developed in order to enhance the statistical independence of successive lattice configurations. (author)
Parida, M K; Das, C R; Purkayastha, B; 10.1140/epjc/s2003-01180-x
2003-01-01
In a class of SUSY SO(10) with SU(2)/sub L/*SU(2)/sub R/*U(1)/sub B-L /*SU(3)/sub C/ (g/sub 2L/ not= g/sub 2R/) intermediate gauge symmetry, we observe that the prediction on the unification mass (M /sub U/) is unaffected by Planck-scale-induced gravitational and intermediate-scale threshold effects, although the intermediate scale (M/sub I/) itself is subject to such corrections. In particular, without invoking the presence of additional lighter scalar degrees of freedom but including plausible and reasonable threshold effects, we find that interesting solutions for neutrino physics corresponding to M/sub I/ approximately= 10/sup 10/-10/sup 13/ GeV and M/sub U/ approximately= (5-6) * 10/sup 17/ GeV are permitted in the minimal models. The possibilities of low-mass right-handed gauge bosons corresponding to M/sub I/ approximately= 1-10 TeV consistent with the CERN-LEP data are pointed out in a number of models in which threshold effects are included using effective mass parameters. (39 refs).
Kotb, M.
2016-07-01
In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES' s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to 150-162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. 156Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.
An algebraic method for solving the SU(3) Gauss law
Salmela, A
2003-01-01
A generalisation of existing SU(2) results is obtained. In particular, the source-free Gauss law for SU(3)-valued gauge fields is solved using a non-Abelian analogue of the Poincare lemma. When sources are present, the colour-electric field is divided into two parts in a way similar to the Hodge decomposition. Singularities due to coinciding eigenvalues of the colour-magnetic field are also analysed.
Fixed point SU(3) gauge actions: scaling properties and glueballs
We present a new parametrization of a SU(3) fixed point (FP) gauge action using smeared ('fat') gauge links. We report on the scaling behaviour of the FP action on coarse lattices by means of the static quark-antiquark potential, the hadronic scale r0, the string tension σ and the critical temperature Tc of the deconfining phase transition. In addition, we investigate the low lying glueball masses where we observe no scaling violations within the statistical errors
Using Wilson flow to study the SU(3) deconfinement transition
Datta, Saumen; Lytle, Andrew
2015-01-01
We explore the use of Wilson flow to study the deconfinement transition in SU(3) gauge theory. We use the flowed Polyakov loop as a renormalized order parameter for the transition, and use it to renormalize the Polyakov loop. We also study the flow properties of the electric and magnetic gluon condensates, and demonstrate that the difference of the flowed operators shows rapid change across the transition point.
Dark Matter from a Classically Scale-Invariant $SU(3)_X$
Karam, Alexandros
2016-01-01
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra $SU(3)_X$ gauge factor gets completely broken by the vevs of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic $Z_2\\times Z_2'$ discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.
$SU(3)_{c} X SU(4)_{L} X U(1)_{x}$ model for three families
Sanchez, Luis A; Ponce, W A; Sanchez, Luis A.; Perez, Felipe A.; Ponce, William A.; 10.1140/epjc/s2004-01851-0
2004-01-01
An extension of the Standard Model to the local gauge group $SU(3)_c\\otimes SU(4)_L\\otimes U(1)_X$ as a three-family model is presented. The model does not contain exotic electric charges and we obtain a consistent mass spectrum by introducing an anomaly-free discrete $Z_2$ symmetry. The neutral currents coupled to all neutral vector bosons in the model are studied. By using experimental results from the CERN LEP, SLAC Linear Collider and atomic parity violation we constrain the mixing angle between two of the neutral currents in the model and the mass of the additional neutral gauge bosons to be $-0.0032\\leq\\sin\\theta\\leq 0.0031$ and $0.67 \\hbox{TeV}\\leq M_{Z_2} \\leq 6.1$ TeV at 95% C.L., respectively.
Zuker, A P; Nowacki, F; Lenzi, S
2014-01-01
It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from $^{56}$Ni to $^{96}$Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei $^{72}$Kr and $^{84}$Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones,
The evolution of gauge couplings and the Weinberg angle in 5 dimensions for an SU(3) gauge group
Khojali, Mohammed Omer; Deandrea, Aldo
2016-01-01
We test in a simplified 5-dimensional model with SU(3) gauge symmetry, the evolution equations of the gauge couplings of a model containing bulk fields, gauge fields and one pair of fermions. In this model we assume that the fermion doublet and two singlet fields are located at fixed points of the extra-dimension compactified on an $S^{1}/Z_{2}$ orbifold. The gauge coupling evolution is derived at one-loop in 5-dimensions, for the gauge group $G = SU(3)$, and used to test the impact on lower energy observables, in particular the Weinberg angle. The gauge bosons and the Higgs field arise from the gauge bosons in 5 dimensions, as in a gauge-Higgs model. The model is used as a testing ground as it is not a complete and realistic model for the electroweak interactions.
Improved constraints on chiral SU(3) dynamics from kaonic hydrogen
Ikeda, Yoichi; Weise, Wolfram
2011-01-01
A new improved study of K^- - proton interactions near threshold is performed using coupled-channels dynamics based on the next-to-leading order chiral SU(3) meson-baryon effective Lagrangian. Accurate constraints are now provided by new high-precision kaonic hydrogen measurements. Together with threshold branching ratios and scattering data, these constraints permit an updated analysis of the complex barK N and pi Sigma coupled-channels amplitudes and an improved determination of the K^- p scattering length, including uncertainty estimates.
A simplified SO(6,2) model of SU(3)
A new realization is obtained of the representation of so(6,2) which has been shown recently by Flath and Biedenharn, and also by Bracken and MacGibbon, to define a model of SU(3). In contrast to the realization in terms of six pairs of boson operators used previously, which involved cubic expressions, the new realization involves only quadratic expressions in eight pairs of boson operators, and is manifestly hermitian. Properties of this new ''oscillator realization'', and in particular its advantages over the old realization, are discussed briefly. It is deduced that the representation of so(6,2) is integrable to a unitary group representation. (orig.)
Gauge origin of discrete flavor symmetries in heterotic orbifolds
Florian Beye
2014-09-01
Full Text Available We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kähler modulus T. Using this mechanism it is shown that the Δ(54 non-Abelian discrete symmetry group originates from a SU(3 gauge symmetry, whereas the D4 symmetry group is obtained from a SU(2 gauge symmetry.
Höllwieser, Roman
2015-01-01
We apply the relative weights method to extract an effective Polyakov line action, at finite chemical potential, from an underlying $SU(3)$ lattice gauge theory with dynamical fermions. The center-symmetry breaking terms in the effective theory are fit to a form suggested by the hopping-parameter expansion, and the effective action is solved at finite chemical potential by a mean field approach. We present preliminary results for one-link staggered fermions with mass $ma=1.0$ and Wilson gauge action at $\\beta=5.4$ on $L^3\\times4$ lattices with $L=16$.
This paper concludes our efforts in describing SU(3)-Yang-Mills theories at different couplings/temperatures in terms of effective Polyakov-loop models. The associated effective couplings are determined through an inverse Monte Carlo procedure based on novel Schwinger-Dyson equations that employ the symmetries of the Haar measure. Because of the first-order nature of the phase transition we encounter a fine-tuning problem in reproducing the correct behavior of the Polyakov-loop from the effective models. The problem remains under control as long as the number of effective couplings is sufficiently small
Deconfinement and chiral symmetry restoration in an SU(3) gauge theory with adjoint fermions
We analyze the finite temperature phase diagram of QCD with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions show that the deconfinement and chiral phase transitions occur at two distinct temperatures. While the deconfinement transition is first-order at Td we find evidence for a continuous chiral transition at a higher temperature Tc ≅ 8 Td. We observe a rapid change of bulk thermodynamic observables at Td which reflects the increase in the number of degrees of freedom. However, these show little variation at Tc, where the fermion condensate vanishes. We also analyze the potential between static fundamental and adjoint charges in all three phases and extract the corresponding screening masses above Td
Reig, Mario; Vaquera-Araujo, C A
2016-01-01
Here we propose a realistic $\\mathrm{SU(3)_c \\otimes SU(3)_L \\otimes U(1)_X}$ electroweak gauge model with enlarged Higgs sector. The scheme allows for the natural implementation of a type-II seesaw mechanism for Dirac neutrinos, while charged lepton and quark masses are reproduced with natural flavor conservation in the scalar sector. The new $\\mathrm{SU(3)_c \\otimes SU(3)_L \\otimes U(1)_X}$ energy scale characterizing neutrino mass generation could be accessible to the current LHC experiments.
$SU(3)_{C}\\otimes SU(3)_{L}\\otimes U(1)_{X}$ models in view of the 750 GeV diphoton signal
Martinez, R; Sierra, C F
2016-01-01
We analyze the recent diphoton signal reported by ATLAS and CMS collaborations in the context of the $SU(3)_{C}\\otimes SU(3)_{L}\\otimes U(1)_{X}$ anomaly free models , with a 750 GeV scalar candidate which can decay into two photons. This models may explain the 750GeV signal by means of one loop decays to $\\gamma\\gamma$ through both charged vector and charged Higgs bosons, as well as top-, bottom- and electron-like exotic particles that arise naturally from the condition of anomalies cancellation of the $SU(3)_{C}\\otimes SU(3)_{L}\\otimes U(1)_{X}$ models.
Disoriented chiral condensate dynamics with the SU(3) linear sigma model
The SU(3) extension of the linear sigma model is employed to elucidate the effect of including strangeness on the formation of disoriented chiral condensates. By means of a Hartree factorization, approximate dispersion relations for the 18 scalar and pseudoscalar meson species are derived and their self-consistent solution makes it possible to trace out the thermal path of the two order parameters as well as delineate the region of instability within which spontaneous pair creation becomes possible. The results depend significantly on the employed sigma mass, with the highest values yielding the largest regions of instability. An approximate solution of the equations of motion for the order parameter in scenarios emulating uniform scaling expansions show that even with a rapid quench only the pionic modes grow unstable. Nevertheless, the rapid and oscillatory relaxation of the order parameters leads to enhanced production of both pions and (to a lesser degree) kaons. copyright 1999 The American Physical Society
Superdeformations and fermion dynamical symmetries
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU3 of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU3 fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU3 symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting γ-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs
Bilarge neutrino mixing and μ-τ permutation symmetry for two-loop radiative mechanism
The presence of approximate electron number conservation and μ-τ permutation symmetry of S2 is shown to naturally provide bilarge neutrino mixing. First, the bimaximal neutrino mixing together with Ue3=0 is guaranteed to appear owing to S2, and then, the bilarge neutrino mixing together with |Ue3|2. The observed mass hierarchy of Δm·2 atm2 is subject to another tiny violation of the electron number conservation. This scenario is realized in a specific model based on SU(3)LxU(1)N with two-loop radiative mechanism for neutrino masses. The radiative effects from heavy leptons contained in lepton triplets generate the bimaximal structure, and those from charged leptons, which break S2, generate the bilarge structure together with vertical bar Ue3 vertical bar 2 symmetry is extended to a discrete Z8 symmetry, which also ensures the absence of a one-loop radiative mechanism
Topological susceptibility near Tc in SU(3 gauge theory
Guang-Yi Xiong
2016-01-01
Full Text Available Topological charge susceptibility χt for pure gauge SU(3 theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χt with values decreasing from (188(1 MeV4 to (67(3 MeV4 as the temperature increased from zero temperature to 1.9Tc which demonstrates the existence of topological excitations far above Tc. The 4th order cumulant c4 of topological charge, as well as the ratio c4/χt is also investigated. Results of c4 show step-like behavior near Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
IR fixed points in SU(3 gauge theories
K.-I. Ishikawa
2015-09-01
Full Text Available We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the SU(3 gauge theories with Nf fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cutoff, which we cannot remove in the conformal field theories in sharp contrast to the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for Nf=16,12,8 and Nf=7 and indeed identify the location of the IR fixed points in all cases.
Topological susceptibility near Tc in SU(3) gauge theory
Xiong, Guang-Yi; Zhang, Jian-Bo; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping
2016-01-01
Topological charge susceptibility χt for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χt with values decreasing from (188 (1) MeV) 4 to (67 (3) MeV) 4 as the temperature increased from zero temperature to 1.9Tc which demonstrates the existence of topological excitations far above Tc. The 4th order cumulant c4 of topological charge, as well as the ratio c4 /χt is also investigated. Results of c4 show step-like behavior near Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
IR fixed points in $SU(3)$ gauge Theories
Ishikawa, K -I; Nakayama, Yu; Yoshie, Y
2015-01-01
We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the $SU(3)$ gauge theories with $N_f$ fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cut-off, which we cannot remove in the conformal field theories in sharp contrast with the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for $N_f=16, 12, 8 $ and $N_f=7$ and indeed identify the location of the IR fixed points in all cases.
SU(3) breaking in hyperon transition vector form factors
We present a calculation of the SU(3)-breaking corrections to the hyperon transition vector form factors to O(p4) in heavy baryon chiral perturbation theory with finite-range regularisation. Both octet and decuplet degrees of freedom are included. We formulate a chiral expansion at the kinematic point Q2=-(MB1-MB2)2, which can be conveniently accessed in lattice QCD. The two unknown low-energy constants at this point are constrained by lattice QCD simulation results for the Σ-→n and Ξ0→Σ+ transition form factors. Hence we determine lattice-informed values of f1 at the physical point. This work constitutes progress towards the precise determination of vertical stroke Vus vertical stroke from hyperon semileptonic decays.
Strange magnetic moments of octet baryons under SU(3) breaking
CAO Lu; WANG Biao; CHEN Hong
2012-01-01
Magnetic moments of octet baryons are parameterized to all orders of the flavor SU(3) breaking with the irreducible tensor technique in order to extract the contribution of each flavor quark to the magnetic moments of the octet baryons.The not-yet measured magnetic moment of Σ0 is predicted to be 0.649 μN.Our parameterized forms for the magnetic moments are explicitly flavor-dependent,and hence each flavor component of the magnetic moments can be evaluated directly via the flavor projection operator.It is fouud that the strange magnetic moment of the nucleon is suppressed due to the small isoscalar anomalous magnetic moment of the nucleon.In particular,the strange magnetic form factor of the nucleon turns out to be positive,(G(s)N) (0) =0.428 μN,which is consistent with recent data.
SU(3) breaking in hyperon transition vector form factors
Shanahan, P.E.; Thomas, A.W.; Young, R.D.; Zanotti, J.M. [ARC Centre of Excellence in Particle Physics at the Terascale, Adelaide (Australia); Centre for the Subatomic Structure of Matter (CSSM), Adelaide, SA (Australia); Adelaide Univ., SA (Australia). Dept. of Physics; Cooke, A.N.; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2015-08-15
We present a calculation of the SU(3)-breaking corrections to the hyperon transition vector form factors to O(p{sup 4}) in heavy baryon chiral perturbation theory with finite-range regularisation. Both octet and decuplet degrees of freedom are included. We formulate a chiral expansion at the kinematic point Q{sup 2}=-(M{sub B{sub 1}}-M{sub B{sub 2}}){sup 2}, which can be conveniently accessed in lattice QCD. The two unknown low-energy constants at this point are constrained by lattice QCD simulation results for the Σ{sup -}→n and Ξ{sup 0}→Σ{sup +} transition form factors. Hence we determine lattice-informed values of f{sub 1} at the physical point. This work constitutes progress towards the precise determination of vertical stroke V{sub us} vertical stroke from hyperon semileptonic decays.
Chiral symmetry and chiral-symmetry breaking
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed
Efficacy of the SU(3) scheme for ab initio large-scale calculations beyond the lightest nuclei
Dytrych, T; Launey, K D; Draayer, J P; Vary, J P; Langr, D; Saule, E; Caprio, M A; Catalyurek, U; Sosonkina, M
2016-01-01
We report on the computational characteristics of ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We examine the computational complexity of the current implementation of the SA-NCSM approach, dubbed LSU3shell, by analyzing ab initio results for 6Li and 12C in large harmonic oscillator model spaces and SU(3)-selected subspaces. We demonstrate LSU3shell's strong-scaling properties achieved with highly-parallel methods for computing the many-body matrix elements. Results compare favorably with complete model space calculations and significant memory savings are achieved in physically important applications. In particular, a well-chosen symmetry-adapted basis affords memory savings in calculations of states with a fixed total angular momentum in large model spaces while exactly preserving translational invariance.
Symmetries and Symmetry Breaking
Van Oers, W T H
2003-01-01
In understanding the world of matter, the introduction of symmetry principles following experimentation or using the predictive power of symmetry principles to guide experimentation is most profound. The conservation of energy, linear momentum, angular momentum, charge, and CPT involve fundamental symmetries. All other conservation laws are valid within a restricted subspace of the four interactions: the strong, the electromagnetic, the weak, and the gravitational interaction. In this paper comments are made regarding parity violation in hadronic systems, charge symmetry breaking in two nucleon and few nucleon systems, and time-reversal-invariance in hadronic systems.
Moduli in General $SU(3)$-Structure Heterotic Compactifications
Svanes, Eirik Eik
2014-01-01
In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compact part of space-time $X$ is a six-dimensional manifold of what we refer to as a heterotic $SU(3)$-structure. We show that this system can be put in terms of a holomorphic operator $\\bar D$ on a bundle $\\mathcal{Q}=T^*X\\oplus\\mathrm{End}(TX)\\oplus\\mathrm{End}(V)\\oplus TX$, defined by a series of extensions. We proceed to compute the infinitesimal deformation space of this structure, given by $T\\mathcal{M}=H^{(0,1)}(\\mathcal{Q})$, which constitutes the infinitesimal spectrum of the four-dimensional theory. In doing so, we find an over counting of moduli by $H^{(0,1)}(\\mathrm{End}(TX))$, which can be reinterpreted as $\\mathcal{O}(\\alpha')$ field redefinitions. We next consider non-maximally symmetric domain wall compactifications of the form $M_{10}=M_3\\times Y$, where $M...
Hadronization in the SU(3) Nambu - Jona-Lasinio model
Rehberg, P
1995-01-01
The hadronization process for quarks combining into two mesons, q\\bar q\\to MM' at temperature T is described within the SU(3) Nambu- Jona-Lasinio model with finite current quark masses. Invariant matrix elements, cross-sections and transition rates are calculated to leading order in a 1/N_c expansion. Four independent classes, u\\bar d, u\\bar s, u\\bar u and s\\bar s\\to hadrons are analysed, and the yield is found to be dominated by pion production. Threshold behaviour is determined by the exothermic or endothermic nature of the processes constituting the hadronization class. A strong suppression of transition rates is found at the pionic Mott temperature T_{M\\pi}=212 MeV, at which the pion becomes a resonant state. The mean time for hadronization is calculated to be 2-4 fm/c near the Mott temperature. The calculation of strangeness changing processes indicates that hadronization accounts for a 1% increase in the absolute value of the kaon to pion ratio at T=150 MeV.
Theory of broken gauge symmetry of families
A theoretical scheme is considered, based on the gauge spontaneously-broken SU(3)H symmetry of families. The generation of quark and lepton masses is induced by their mixing with hypothetical superheavy fermions, providing a relationship of the observed mass hierarchy and mixing of quarks and leptons with the structure of horizontal symmetry breaking. The model predicts the existance of invisible axion, being simultaneously familon and Majoron, as well as the existence of neutrino Majorana mass hierarchy
Clusters and the quasi-dynamical symmetry
The possible role of the quasi-dynamical symmetry in nuclear clusterization is discussed. Two particular examples are considered: i) the phases and phase-transitions of some algebraic cluster models, and ii) the clusterization in heavy nuclei. The interrelation of exotic (superdeformed, hyperdeformed) nuclear shapes and cluster-configurations are also investigated both for light, and for heavy nuclei, based on the dynamical and quasi-dynamical SU(3) symmetries, respectively
Properties of single cluster structure of $d^*(2380)$ in chiral SU(3) quark model
Lü, Qi-Fang; Dong, Yu-Bing; Shen, Peng-Nian; Zhang, Zong-Ye
2016-01-01
The structure of $d^*(2380)$ is re-studied with the single cluster structure in the chiral SU(3) quark model which has successfully been employed to explain the scattering and binding behaviors of baryonic systems. The mass and width are explicitly calculated with two types of trial wave functions. The result shows that the $(0s)^6 [6]_{orb}$ configuration is easy to convert to the configuration with the same $[6]_{orb}$ symmetry but $2\\hbar \\omega$ excitation back and forth, however, it is seldom to turn into a two-cluster configuration with a (1s) relative motion in between. The resultant mass and width are about $2394$MeV and $25$MeV, respectively, and the stable size is about $0.75fm$, which are consistent with both the results in the two-cluster configuration calculation and the data measured by the COSY collaboration. It seems that the observed $d^*$ is a six-quark dominated exotic state with a spherical shape and breath mode in the coordinate space. Moreover, if $d^*$ does have $2\\hbar \\omega$ excitati...
Scalar-Quark Systems and Chimera Hadrons in SU(3)_c Lattice QCD
Iida, H; Takahashi, T T
2007-01-01
Light scalar-quarks \\phi (colored scalar particles or idealized diquarks) and their color-singlet hadronic states are studied with quenched SU(3)_c lattice QCD in terms of mass generation in strong interaction without chiral symmetry breaking. We investigate ``scalar-quark mesons'' \\phi^\\dagger \\phi and ``scalar-quark baryons'' \\phi\\phi\\phi which are the bound states of scalar-quarks \\phi. We also investigate the bound states of scalar-quarks \\phi and quarks \\psi, i.e., \\phi^\\dagger \\psi, \\psi\\psi\\phi and \\phi\\phi\\psi, which we name ``chimera hadrons''. All the new-type hadrons including \\phi are found to have a large mass even for zero bare scalar-quark mass m_\\phi=0 at a^{-1}\\simeq 1GeV. We find that the constituent scalar-quark and quark picture is satisfied for all the new-type hadrons. Namely, the mass of the new-type hadron composed of m \\phi's and n \\psi's, M_{{m}\\phi+{n}\\psi}, satisfies M_{{m}\\phi+{n}\\psi}\\simeq {m} M_\\phi +{n} M_\\psi, where M_\\phi and M_\\psi are the constituent scalar-quark and quark...
Empirical Example of Nucleus with Transitional Dynamical Symmetry X(5)
张大立; 赵惠英
2002-01-01
By analysing the energy spectrum, E2 transition rates and branching ratios, it is shown explicitly that the nucleus 150Nd provides an empirical example with X(5) symmetry at the critical point of the transition from U(5) to SU(3) symmetry.
Creation and annihilation operators for SU(3) in an SO(6,2) model
Creation and annihilation operators are defined which are Wigner operators (tensor shift operators) for SU(3). While the annihilation operators are simply boson operators, the creation operators are cubic polynomials in boson operators. Together they generate under commutation the Lie algebra of SO(6,2). A model for SU(3) is defined. The different SU(3) irreducible representations appear explicitly as manifestly covariant, irreducible tensors, whose orthogonality and normalisation properties are examined. Other Wigner operators for SU(3) can be constructed simply as products of the new creation and annihilation operators, or sums of such products. (author)
SU(3) magnet: finite-gap integration on the lowest genus curve
We consider the integrable system of isotropic SU(3) Landau-Lifshits equation as a Hamiltonian system on a coadjoint orbit of the SU(3) loop group. We connect the mentioned equation with an isotropic SU(3) magnet because it describes the mean fields of magnetic and quadrupole moments in a spin-1 lattice. For the system of isotropic SU(3) Landau-Lifshits equation we perform separation of variables in Sklyanin's manner, and integrate in the lowest finite gap where the spectral curve is elliptic
An approach to permutation symmetry for the electroweak theory
Jora, R; Schechter, J; Jora, Renata; Nasri, Salah; Schechter, Joseph
2006-01-01
The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry ($S_3$) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the $S_3$ holds to first approximation, somewhat in the manner of the old SU(3) flavor symmetry of the three flavor quark model. We discuss the nature of the perturbations which are the analogs of the Gell-Mann Okubo perturbations in the above case but confine our attention for the most part to the $S_3$ invariant model. We postulate that the $S_3$ invariant mass spectrum consists of non zero masses for the $(\\tau,b,t)$ and zero masses for the other charged fermions but approximately degenerate masses for the three neutrinos. The mixing matrices are assumed to be trivial f...
Quantum mechanics. Symmetries. 5. corr. ed.
The volume quantum mechanics treats the as elegant as mighty theory of the symmetry groups and their application in quantum mechanics and the theory of the elementary particles. By means of many examples and problems with worked-out solutions the application of the fundamental principles to realistic problems is elucidated. The themes are symmetries in quantum mechanics, representations of the algebra of the angular momentum operators as generators of the SO(3) group. fundamental properties of Lie groups as mathematical supplement, symmetry groups and their physical meaning, thr isospin group, the hypercharge, quarks and the symmetry group SU(3), representations of the permutation group and Young diagrams, group characters as mathematical supplement, charm and the symmetry group SU(4), Cartan-Weyl claasification as mathematical supplement, special discrete symmetries, dynamical symmetries and the hydrogen atom, non-compact Lie groups as mathematical supplement, a proof of Racah's theorem.
The SU(3)/Z_3 QCD(adj) deconfinement transition via the gauge theory/"affine" XY-model duality
Anber, Mohamed M; Poppitz, Erich
2012-01-01
Earlier, two of us and M. Unsal [arXiv:1112.6389] showed that some 4d gauge theories, compactified on a small spatial circle of size L and considered at temperatures 1/beta near deconfinement, are dual to 2d "affine" XY-spin models. We use the duality to study deconfinement in SU(3)/Z_3 theories with n_f>1 massless adjoint Weyl fermions, QCD(adj) on R^2 x S^1_beta x S^1_L. The"affine" XY-model describes two "spins" - compact scalars taking values in the SU(3) root lattice, with nearest-neighbor interactions and subject to an "external field" preserving the topological Z_3^t and a discrete Z_3^chi subgroup of the chiral symmetry of the 4d gauge theory. The equivalent Coulomb gas representation of the theory exhibits electric-magnetic duality, which is also a high-/low-temperature duality. A renormalization group analysis suggests - but is not convincing, due to the onset of strong coupling - that the self-dual point is a fixed point, implying a continuous deconfinement transition. Here, we study the nature of ...
Notes on TQFT wire models and coherence equations for SU(3) triangular cells
Coquereaux, R; Schieber, G
2010-01-01
After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.
Algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
Belliard, S; Ragoucy, E; Slavnov, N A
2012-01-01
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of XXX SU(3)-invariant Heisenberg chain.
The role of SU(2) 3n-j coefficients in SU(3)
The irreducible representations of the group SU(3) may be given completely in terms of the 3-j, 6-j, and 9-j coefficients of SU(2). More remarkably these same coefficients, and the 12-j coefficients as well, enter into the description of a large class of Clebsch-Gordan (C-G) coefficients for the group SU(3), this occurrence going beyond that in the well-known group-subgroup reduction SU(3)↓U(2). The problem of determining the SU(3) irreducible representations and its C-G coefficients is reviewed, and it is shown how the SU(2) quantities enter into the SU(3) problem in special cases
Spinor Structure and Internal Symmetries
Varlamov, V. V.
2015-10-01
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.
Strong coupling and quasispinor representations of the SU(3) rotor model
We define a coupling scheme, in close parallel to the coupling scheme of Elliott and Wilsdon, in which nucleonic intrinsic spins are strongly coupled to SU(3) spatial wave functions. The scheme is proposed for shell-model calculations in strongly deformed nuclei and for semimicroscopic analyses of rotations in odd-mass nuclei and other nuclei for which the spin-orbit interaction is believed to play an important role. The coupling scheme extends the domain of utility of the SU(3) model, and the symplectic model, to heavy nuclei and odd-mass nuclei. It is based on the observation that the low angular-momentum states of an SU(3) irrep have properties that mimic those of a corresponding irrep of the rotor algebra. Thus, we show that strongly coupled spin-SU(3) bands behave like strongly coupled rotor bands with properties that approach those of irreducible representations of the rigid-rotor algebra in the limit of large SU(3) quantum numbers. Moreover, we determine that the low angular-momentum states of a strongly coupled band of states of half-odd integer angular momentum behave to a high degree of accuracy as if they belonged to an SU(3) irrep. These are the quasispinor SU(3) irreps referred to in the title. (orig.)
Karsch, F.; Laermann, E.; Lütgemeier, M.
1994-01-01
We establish a close relation between the spatial string tension of the (3+1)-dimensional $SU(3)$ gauge theory at finite temperature ($\\sigma_s$) and the string tension of the 3-dimensional $SU(3)$ gauge theory ($\\sigma_3$) which is similar to what has been found previously for $SU(2)$. We obtain $\\sqrt{\\sigma_3} = (0.554 \\pm 0.004) g_3^2$ and $\\sqrt{\\sigma_s} = (0.586 \\pm 0.045)g^2(T) T$, respectively. For temperatures larger than twice the critical temperature results are consistent with a ...
On SU(3) effective models and chiral phase-transition
Tawfik, Abdel Nasser
2015-01-01
The sensitivity of Polyakov Nambu-Jona-Lasinio (PNJL) model as an effective theory of quark dynamics to chiral symmetry has been utilized in studying the QCD phase-diagram. Also, Poyakov linear sigma-model (PLSM), in which information about the confining glue sector of the theory was included through Polyakov-loop potential. Furthermore, from quasi-particle model (QPM), the gluonic sector of QPM is integrated to LSM in order to reproduce recent lattice calculations. We review PLSM, QLSM, PNJL and HRG with respect to their descriptions for the chiral phase-transition. We analyse chiral order-parameter M(T), normalized net-strange condensate Delta_{q,s}(T) and chiral phase-diagram and compare the results with lattice QCD. We conclude that PLSM works perfectly in reproducing M(T) and Delta_{q,s}(T). HRG model reproduces Delta_{q,s}(T), while PNJL and QLSM seem to fail. These differences are present in QCD chiral phase-diagram. PLSM chiral boundary is located in upper band of lattice QCD calculations and agree we...
Charge independence and charge symmetry
Miller, G A; Miller, Gerald A; van Oers, Willem T H
1994-01-01
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed.
Charge independence and charge symmetry
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed. (author). 145 refs., 3 tabs., 11 figs
△△ Dibaryon Structure in Extended Chiral SU(3) Quark Model
DAI Lian-Rong
2005-01-01
@@ The structure of △△ dibaryon is studied in the extended chiral SU(3) quark model in which vector meson exchanges are included. The effect of the vector meson fields is very similar to that of the one-gluon exchange (OGE) interaction. Both in the chiral SU(3) quark model and in the extended chiral SU(3) quark model, the resultant mass of the △△ dibaryon is lower than the threshold of the △△ channel but higher than that of the△Nπ channel.
Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs
Evans, David E
2009-01-01
We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except $\\mathcal{E}_4^{(12)}$ proposed by di Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be computed for the corresponding integrable statistical mechanical models and provide the framework for studying corresponding braided subfactors to realise all the SU(3) modular invariants as well as a framework for a new SU(3) planar algebra theory.
Quasi-integrable deformations of the SU(3) Affine Toda theory
Ferreira, L. A.; Klimas, P.; Zakrzewski, Wojtek J.
2016-05-01
We consider deformations of the SU(3) Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only asymptotically, i.e. in the process of the scattering of two solitons these charges do vary in time, but they return, after the scattering, to the values they had prior to the scattering. This phenomenon, which we have called quasi-integrability, is related to special properties of the two-soliton solutions under space-time parity transformations. Some properties of the AT solitons are discussed, especially those involving interesting static multi-soliton solutions. We support our analytical studies with detailed numerical ones in which the time evolution has been simulated by the 4th order Runge-Kutta method. We find that for some perturbations the solitons repel and for the others they form a quasi-bound state. When we send solitons towards each other they can repel when they come close together with or without `flipping' the fields of the model. The solitons radiate very little and appear to be stable. These results support the ideas of quasi-integrability, i.e. that many effects of integrability also approximately hold for the deformed models.
A 125 GeV Scalar Boson and SU(N_{TC})\\otimes SU(3)_{{}_{L}}\\otimes U(1)_{{}_{X}} models
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Natale, A. A.
2013-01-01
We verify that SU(N)_{{}_{TC}}\\otimes SU(3)_{{}_{L}}\\otimes U(1)_{{}_{X}} models, where the gauge symmetry breaking is totally dynamical and promoted by the non-Abelian technicolor (TC) group and the strong Abelian interactions, are quite constrained by the LHC data. The theory contains a T quark self-energy involving the mixing between the neutral gauge bosons, which introduces the coupling between the light and heavy composite scalar bosons of the model. We determine the lightest scalar bos...
Quarks and the Poincare group: SU(6) x SU(3) as a classification group for baryons
The description of baryons as a three quark system results in an irreducible unitary representation of the Poincare group. Starting from this description collinear baryon states can be classified within the SU(6) x SU(3) group. (WL)
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
Kremer, Christoph
2016-01-27
The first part of this thesis revolves around symmetries in the sd-IBA-1. A region of approximate O(6) symmetry for the ground-state band, a partial dynamical symmetry (PDS) of type III, in the parameter space of the extended consistent-Q formalism is identified through quantum number fluctuations. The simultaneous occurrence of a SU(3) quasi dynamical symmetry for nuclei in the region of O(6) PDS is explained via the β=1, γ=0 intrinsic state underlying the ground-state band. The previously unrelated concepts of PDS and QDS are connected for the first time and many nuclei in the rare earth region that approximately satisfy both symmetry requirements are identified. Ground-state to ground-state (p, t) transfer reactions are presented as an experimental signature to identify pairs of nuclei that both exhibit O(6) PDS. In the second part of this thesis inelastic electron scattering off {sup 96}Zr is studied. The experiment was performed at the high resolution Lintott spectrometer at the S-DALINAC and covered a momentum-transfer range of 0.28 - 0.59 fm{sup -1}. Through a relative analysis using Plane Wave Born Approximation (PWBA) the B(E2;2{sup +}{sub 2}→0{sup +}{sub 1}) value is extracted without incurring the additional model dependence of a Distorted Wave Born Approximation (DWBA). By combining this result with known multipole mixing ratios and branching ratios all decay strengths of the 2{sup +}{sub 2} state are determined. A mixing calculation establishes very weak mixing (V{sub mix}=76 keV) between states of the ground-state band and those of the band build on top of the 0{sup +}{sub 2} state which includes the 2{sup +}{sub 2} state. The occurrence of these two isolated bands is interpreted within the shell model in terms of type II shell evolution.
A new procedure for constructing basis vectors of SU(3)⊃SO(3)
Pan, Feng; Yuan, Shuli; Launey, Kristina D.; Draayer, Jerry P.
2016-08-01
A simple and effective algebraic angular momentum projection procedure for constructing basis vectors of SU (3) ⊃ SO (3) ⊃ SO (2) from the canonical U (3) ⊃ U (2) ⊃ U (1) basis vectors is outlined. The expansion coefficients are components of the null-space vectors of a projection matrix with, in general, four nonzero elements in each row, where the projection matrix is derived from known matrix elements of the U (3) generators in the canonical basis. The advantage of the new procedure lies in the fact that the Hill-Wheeler integral involved in the Elliott's projection operator method used previously is avoided, thereby achieving faster numerical calculations with improved accuracy. Selected analytical expressions of the expansion coefficients for the SU (3) irreps [n13 ,n23 ], or equally, (λ , μ) = (n13 -n23 ,n23) with λ and μ the SU (3) labels familiar from the Elliott model, are presented as examples for n23 ≤ 4. Explicit formulae for evaluating SO (3)-reduced matrix elements of SU (3) generators are derived. A general formula for evaluating the SU (3) ⊃ SO (3) Wigner coefficients is given, which is expressed in terms of the expansion coefficients and known U (3) ⊃ U (2) and U (2) ⊃ U (1) Wigner coefficients. Formulae for evaluating the elementary Wigner coefficients of SU (3) ⊃ SO (3), i.e., for the SU (3) coupling [n13 ,n23 ] ⊗ [ 1 , 0 ], are explicitly given with some analytical examples shown to check the validity of the results. However, the Gram-Schmidt orthonormalization is still needed in order to provide orthonormalized basis vectors.
Non-Kaehler SYZ mirror symmetry
Lau, Siu-Cheong; Yau, Shing-Tung
2014-01-01
We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric $SU(3)$ systems with Ramond-Ramond fluxes, and generalized them to higher dimensions. We show that Fourier-Mukai transform provides the mirror map between these Type IIA and Type IIB supersymmetric systems in the semi-flat setting. This is concretely exhibited by nilmanifolds.
Diffeomorphism symmetry in quantum gravity models
Dittrich, Bianca
2008-01-01
We review and discuss the role of diffeomorphism symmetry in quantum gravity models. Such models often involve a discretization of the space-time manifold as a regularization method. Generically this leads to a breaking of the symmetries to approximate ones, however there are incidences in which the symmetries are exactly preserved. Both kind of symmetries have to be taken into account in covariant and canonical theories in order to ensure the correct continuum limit. We will sketch how to identify exact and approximate symmetries in the action and how to define a corresponding canonical theory in which such symmetries are reflected as exact and approximate constraints.
Intermediate Symmetries in the Spontaneous Breaking of Supersymmetric SO(10)
Buccella, F.; Savoy, C.A.
2002-01-01
We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU(3)xSU(2)xU(1) for the most physically interesting cases of SU(5) or flipped SU(5)xU(1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU(5) symmetry there is at most one singlet of the residual symmetry in each SO(10) irreducible representation. We also point out on more genera...
Lepton-flavor-changing processes and CP violation in the SU(3)cxSU(3)LxU(1)X model
By extending the electroweak gauge group to SU(3)LxU(1)Y, the SU(3)cxSU(3)LxU(1)X (3-3-1) dilepton gauge bosons Y which do not respect individual lepton family number. We point out that, in addition to family diagonal couplings such as Y-e-e that change the lepton family number by two uinits, dileptons may also have family nondiagonal couplings such as Y-μ-e. The latter coupling violates lepton family number by a single unit and manifests itself via lepton-flavor-changing decays such as μ→3e and μ→eγ. The family nondiagonal interaction can be CP violating and typically generates an extremely large leptonic electric dipole moment. We demonstrate a natural mechanism for eliminating both single unit lepton-flavor violation and large leptonic CP violation. Although we focus on the 3-3-1 model, our results are applicable to other dilepton models as well, including SU(15) grand unification
Z-Z' Mixing and Z-Mediated FCNCs in SU(3)_C x SU(3)_L x U(1)_X Models
Buras, Andrzej J; Girrbach-Noe, Jennifer
2014-01-01
Most of the existing analyses of FCNC processes in the 331 models, based on the gauge group SU(3)_C x SU(3)_L x U(1)_X, take only into account tree-level exchanges of a new heavy neutral gauge boson Z'. However due to the Z-Z' mixing also corresponding contributions from Z boson are present that are usually neglected. We calculate the impact of these contributions on Delta F=2 processes and rare K, B_s and B_d decays for different values of a parameter beta, which distinguishes between various 331 models and for different fermion representations under the SU(3)_L group. We find a general expression for the Z-Z' mixing in terms beta, M_Z, M_Z' and tan(bar{beta}), familiar from 2 Higgs Doublet models, that differs from the one quoted in the literature. We study in particular the models with beta=+-n/sqrt{3} with n=1,2 which have recently been investigated by us in the context of new data on B_{s,d}->mu^+ mu^- and B_d->K^*(K)mu^+ mu^-. We find that these new contributions can indeed be neglected in the case of D...
AdS/dCFT one-point functions of the SU(3) sector
de Leeuw, Marius; Mori, Stefano
2016-01-01
We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU(3) sub-sector of the defect CFT dual to the D3-D5 probe brane system with background gauge field flux, k, valid for k=2. The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU(3) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU(2) counterpart, the one-point function formula for the SU(3) sub-sector is of determinant type. We discuss the the differences with the SU(2) case and the challenges in extending the present formula beyond k=2.
The Polyakov loop and its correlators in higher representations of SU(3) at finite temperature
Huebner, K.A.
2006-09-15
We have calculated the Polyakov loop in representations D=3,6,8,10,15,15',24,27 and diquark and baryonic Polyakov loop correlation functions with fundamental sources in SU(3) pure gauge theory and 2-flavour QCD with staggered quarks and Q anti Q-singlet correlation functions with sources in the fundamental and adjoint representation in SU(3) pure gauge theory. We have tested a new renormalisation procedure for the Polyakov loop and extracted the adjoint Polyakov loop below T{sub c}, binding energy of the gluelump and string breaking distances. Moreover, we could show Casimir scaling for the Polyakov loop in different representations in SU(3) pure gauge theory above T{sub c}. Diquark antitriplet and baryonic singlet free energies are related to the Q anti Q-singlet free energies by the Casimir as well. (orig.)
The Polyakov loop and its correlators in higher representations of SU(3) at finite temperature
We have calculated the Polyakov loop in representations D=3,6,8,10,15,15',24,27 and diquark and baryonic Polyakov loop correlation functions with fundamental sources in SU(3) pure gauge theory and 2-flavour QCD with staggered quarks and Q anti Q-singlet correlation functions with sources in the fundamental and adjoint representation in SU(3) pure gauge theory. We have tested a new renormalisation procedure for the Polyakov loop and extracted the adjoint Polyakov loop below Tc, binding energy of the gluelump and string breaking distances. Moreover, we could show Casimir scaling for the Polyakov loop in different representations in SU(3) pure gauge theory above Tc. Diquark antitriplet and baryonic singlet free energies are related to the Q anti Q-singlet free energies by the Casimir as well. (orig.)
Lattice study for conformal windows of SU(2) and SU(3) gauge theories with fundamental fermions
Huang, Cynthia Y -H; Lin, C -J David; Ogawa, Kenji; Ohki, Hiroshi; Ramos, Alberto; Rinaldi, Enrico
2015-01-01
We present our investigation of SU(2) gauge theory with 8 flavours, and SU(3) gauge theory with 12 flavours. For the SU(2) case, at strong bare coupling, $\\beta \\lesssim 1.45$, the distribution of the lowest eigenvalue of the Dirac operator can be described by chiral random matrix theory for the Gaussian symplectic ensemble. Our preliminary result indicates that the chiral phase transition in this theory is of bulk nature. For the SU(3) theory, we use high-precision lattice data to perform the step-scaling study of the coupling, $g_{{\\rm GF}}$, in the Gradient Flow scheme. We carefully examine the reliability of the continuum extrapolation in the analysis, and conclude that the scaling behaviour of this SU(3) theory is not governed by possible infrared conformality at $g_{{\\rm GF}}^{2} \\lesssim 6$.
The Spectrum of the Baryon Masses in a Self-consistent SU(3) Quantum Skyrme Model
Jurciukonis, Darius; Regelskis, Vidas
2012-01-01
The semiclassical SU(3) Skyrme model is traditionally considered as describing a rigid quantum rotator with the profile function being fixed by the classical solution of the corresponding SU(2) Skyrme model. In contrast, we go beyond the classical profile function by quantizing the SU(3) Skyrme model canonically. The quantization of the model is performed in terms of the collective coordinate formalism and leads to the establishment of purely quantum corrections of the model. These new corrections are of fundamental importance. They are crucial in obtaining stable quantum solitons of the quantum SU(3) Skyrme model, thus making the model self-consistent and not dependent on the classical solution of the SU(2) case. We show that such a treatment of the model leads to a family of stable quantum solitons that describe the baryon octet and decuplet and reproduce the experimental values of their masses.
Dynamical symmetries of the shell model
The applications of spectrum generating algebras and of dynamical symmetries in the nuclear shell model are many and varied. They stretch back to Wigner's early work on the supermultiplet model and encompass important landmarks in our understanding of the structure of the atomic nucleus such as Racah's SU(2) pairing model and Elliot's SU(3) rotational model. One of the aims of this contribution has been to show the historical importance of the idea of dynamical symmetry in nuclear physics. Another has been to indicate that, in spite of being old, this idea continues to inspire developments that are at the forefront of today's research in nuclear physics. It has been argued in this contribution that the main driving features of nuclear structure can be represented algebraically but at the same time the limitations of the symmetry approach must be recognised. It should be clear that such approach can only account for gross properties and that any detailed description requires more involved numerical calculations of which we have seen many fine examples during this symposium. In this way symmetry techniques can be used as an appropriate starting point for detailed calculations. A noteworthy example of this approach is the pseudo-SU(3) model which starting from its initial symmetry Ansatz has grown into an adequate and powerful description of the nucleus in terms of a truncated shell model. (author)
Dynamical symmetries of the shell model
Van Isacker, P
2000-07-01
The applications of spectrum generating algebras and of dynamical symmetries in the nuclear shell model are many and varied. They stretch back to Wigner's early work on the supermultiplet model and encompass important landmarks in our understanding of the structure of the atomic nucleus such as Racah's SU(2) pairing model and Elliot's SU(3) rotational model. One of the aims of this contribution has been to show the historical importance of the idea of dynamical symmetry in nuclear physics. Another has been to indicate that, in spite of being old, this idea continues to inspire developments that are at the forefront of today's research in nuclear physics. It has been argued in this contribution that the main driving features of nuclear structure can be represented algebraically but at the same time the limitations of the symmetry approach must be recognised. It should be clear that such approach can only account for gross properties and that any detailed description requires more involved numerical calculations of which we have seen many fine examples during this symposium. In this way symmetry techniques can be used as an appropriate starting point for detailed calculations. A noteworthy example of this approach is the pseudo-SU(3) model which starting from its initial symmetry Ansatz has grown into an adequate and powerful description of the nucleus in terms of a truncated shell model. (author)
The Polyakov loop and its correlators in higher representations of SU(3) at finite temperature
Hübner, Kay A.
2006-01-01
We have calculated the Polyakov loop in representations D=3,6,8,10,15a,15s,24,27 and diquark and baryonic Polyakov loop correlation functions with fundamental sources in SU(3) pure gauge theory and 2-flavour QCD with staggered quarks and Qbar Q-singlet correlation functions with sources in the fundamental and adjoint representation in SU(3) pure gauge theory. We have tested a new renormalisation procedure for the Polyakov loop and extracted the adjoint Polyakov loop below T_c, binding energy ...
SU(3)-instantons and G2, Spin (7)-heterotic string solitons
Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. A formula for the Riemannian scalar curvature is obtained. Nonconformally flat solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 6, 7 and 8. A Riemannian metric with holonomy contained in G2 arose from our solution and Hitchin's flow equations, which seems to be new. Compact examples of SU(3), G2 and Spin(7) instanton satisfying the anomaly cancellation conditions are presented. (author)
Bosonization of the generalized SU(3) Nambu-Jona-Lasinio model in the 1/N expansion
The present work consists in a 1/N expansion of extended version of the SU(3) Nambu-Jona-Lasinio model in the context of the Functional Integral. The gap equations, meson propagators, triangle diagram, etc, appear quite naturally as different orders in the expansion. The new features of this approach is the inclusion of high order corrections in the 1/N leading orders, which have never included in the previous one. The method also allows for the construction of a chiral Lagrangian of interacting mesons based on the SU(3) NJL model, here obtained for the first time. (author)
Unconstrained SU(2) and SU(3) Yang-Mills classical mechanics
A systematic study of contraints in SU(2) and SU(3) Yang-Mills classical mechanics is performed. Expect for the SU(2) case with spatial angular momenta they turn out to be nonholonomic. The complete elimination of the unphysical gauge and rotatinal degrees of freedom is achieved using Dirac's constraint formalism. We present an effective unconstrained formulation of the general SU(2) Yang-Mills classical mechanics as well as for SU(3) in the subspace of vanishing spatial angular momenta that is well suited for further explicit dynamical investigations. (orig.)
$\\Delta(27)$ family symmetry and neutrino mixing
Varzielas, Ivo de Medeiros
2015-01-01
The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry. In this paper the family symmetry is the non-Abelian discrete group $\\Delta(27)$, a subgroup of $SU(3)$ with triplet and anti-triplet representations. Different frameworks are constructed in which the mixing follows from combining fermion mass terms with the vacuum structure enforced by the discrete symmetry. Mass terms for the fermions originate from familon triplets, anti-triplets or both. Vacuum alignment for the family symmetry breaking familons follows from simple invariants.
We calculate the glueball mass spectrum in the SU(3) lattice regularized gauge theory. We find four light glueballs: the 0++, 2++, 0-+, and, most interestingly from the experimental point of view, the oddball 1-+. We calculate the 0++ and 2++ masses over a range of β values and find that both states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature. (orig.)
Macroscopic limit of the microscopic SU(3)containsSO(3) integrity basis interaction
It is shown that a fourth degree SU(3)containsSO(3) integrity basis interaction, encountered in both fermion and boson theories of nuclear structure, maps onto an axially symmetric rotor Hamiltonian for a special linear combination of the third (LQL) and fourth (LQQL) order scalar operators
Monte Carlo Renormalization Group study for SU(3) lattice gauge theory
A special Monte Carlo Renormalization Group method, the so-called ratio method is discussed. Possible systematic error of the method is investigated, and a systematic improvement is proposed based on perturbation theory. The method is applied to determine the β-function of 4 dimensional SU(3) pure gauge theory
Invariant Differential Operators for Non-Compact Lie Groups: the Reduced SU(3,3) Multiplets
Dobrev, V K
2013-01-01
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary representations for $n\\leq 4$, and the reduced ones for $n=2$. Here we give the reduced multiplets for the algebra $su(3,3)$.
SU (3) realization of the rigid asymmetric rotor within the IBM
It is shown that the spectrum of the asymmetric rotor can be realized quantum mechanically in terms of a system of interacting bosons. This is achieved in the SU(3) limit of the interacting boson model by considering higher-order interactions between the bosons. The spectrum corresponds to that of a rigid asymmetric rotor in the limit of infinite boson number. (author)
Splitting the spectral flow and the SU(3) Casson invariant for spliced sums
Boden, Hans U.; Himpel, Benjamin
2009-01-01
We show that the SU(3) Casson invariant for spliced sums along certain torus knots equals 16 times the product of their SU(2) Casson knot invariants. The key step is a splitting formula for su(n) spectral flow for closed 3–manifolds split along a torus....
London penetration depth and coherence length of SU(3) vacuum flux tubes
Cea, Paolo; Cosmai, Leonardo; Cuteri, Francesca; Papa, Alessandro
2014-01-01
The transverse profile of the chromoelectric field generated by a quark-antiquark pair in the SU(3) vacuum is analysed within the dual superconductor scenario, then the London penetration depth and coherence length are extracted. The color field is determined on the lattice through a connected correlator of two Polyakov loops measured on smeared configurations.
Weak-coupling universality in SU(3) mixed actions: Theory versus high-statistics simulation
Predictions of weak-coupling universality and high-statistics simulations on the string tension of SU(3) do disagree beyond the statistical error. This disagreement is larger for the conventional two-loop universality formula than for the self-consistent large-N expression. Various ways out are suggested
The spin-orbit interaction and SU(3) generators in superdeformation
We found that the effect of the spin-orbit coupling force becomes smaller for the parity doublet levels and for some other levels around superdeformation. This is because of the strongly deformed quadrupole field, which indicates the L-S coupling scheme is recovered for these level. These levels can be described by SU(3) group with eight generators and Casimir operator. (orig.)
Fortran MPI Checkerboard Code for SU(3) Lattice Gauge Theory II
Berg, Bernd A.; Wu, Hao
2009-01-01
We study the performance of MPI checkerboard code for SU(3) lattice gauge theory as function of the number of MPI processes, which run in parallel on an identical number of CPU cores. Computing platforms explored are a small PC cluster at FSU and the Cray at NERSC.
Family symmetry, fermion mass matrices and cosmic texture
The observed replication of fermions in three families is undoubtedly a reflection of a deeper symmetry underlying the standard model. In this paper we investigate one very elementary possibility, that physics above the grand unification scale is described by the symmetry group G x SU(3)fam with G a gauged grand unified group, and SU(3)fam a global family symmetry. The breaking of this symmetry at the GUT scale produces global texture, providing a mechanism for structure formation in the universe, and sets strong constraints on the low energy fermion mass matrix. With the addition of a 45 Higgs and certain assumptions about the relative strength of Higgs couplings, the simplest SU(5) theory yields an eight-parameter form for the fermion mass matrices, which we show is consistent with the thirteen observable masses and mixing angles. We discuss the natural suppression of flavour-changing neutral currents (FCNCs) and emphasise the rich low energy Higgs sector. With minor assumptions, the theory unifies consistently with the recent LEP data. We consider the extension to G = SO(10), where some simplification and further predictiveness emerges. Finally we discuss the dynamics of SU(3)fam texture and show that the known constraints on unification ''predict'' a GUT symmetry-breaking scale of the order required for cosmic structure formation, and by the recent detection of cosmic microwave anisotropy by COBE. (orig.)