SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking (_χSB) in SU(2) lattice gauge theory with quarks in the $\text{l =}\text{1}\text{2}\text{, l = 1, l =}\text{3}\text{2}$, and l = 2 representations of the color group. We perform Monte Carlo evaluations of $\text{〈}\text{ψ}\text{ψ〉}$ in the quenched approximation and extract the relevant length scales for _χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain $\text{T}{}_{\mathrm{l\; =\; 1}}\text{/T}{}_{\mathrm{l}}\text{=}\text{1}\text{2}\text{～ 8}$. Our results for the higher representations, $\text{l =}\text{3}\text{2}\text{and}\text{l = 2}$, are consistent with Casimir scaling and give C₂g_mom² ～ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between _χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.     

Chiral SU4 × SU4 symmetry breaking and the Cabibbo angle

The structure of chiral SU₄ × SU₄ symmetry breaking, in the limit of exact chiral SU₂ × SU₂ symmetry, is related to the Cabibbo angle, thus leading to a satisfactory determination of the Cabibbo angle in terms of the kaon and D-meson masses and decay constants.     

Meson wave functions and SU(3) symmetry breaking

The wave functions of the pseudoscalar and vector mesons (K, ?, K¹, ?) are found using the QCD sum rules and are used for the calculation of the heavy quarkonium two-particle decay widths.     

SU(4) flavor symmetry breaking in D-meson couplings to light hadrons

The European Physical Journal A - This work presents a simple method to determine the significant partial wave contributions to experimentally determined observables in pseudoscalar meson...     

SU(3) symmetry breaking and superfluidity of hadronic matter

We associate SU(3) breaking of strong interactions with superfluidity of hadronic matter. At high energies and large transverse momenta a phase transition occurs and SU(3) becomes an exact symmetry.     

Dynamical symmetry breaking in the SU (2) gauge theory

Properties of vacua of the SU(2) gauge theory containing massless and massive fermions are investigated within the one-loop approximation. As a result of a condensation of composite scalar made of gauge fields, some gauge fields acquire a mass and the original SU(2) gauge symmetry is suggested to breake down to U (1). We evaluate the effective potential for the constant magnetic field and then extract the so-called dielectric permeability κ from it. The phase is called paramagnetism for positive κ, perfect paramagnetism for vanishing κ and ferromagnetism for negative κ. The choice of a favorable phase is determined by the value of the coupling constant and the number and the mass of fermions. The perfect paramagnetic phase is most precisely studied. It is shown that solitons with non-zero charges carry divergent energies. Then, the electric flux around the charge is shown to be squeezed into a string in that phase.     

SU(3) symmetry breaking in charmed baryon decays

We explore the breaking effects of the SU(3) flavor symmetry in the singly Cabibbo-suppressed anti-triplet charmed baryon decays of \(\mathbf{B}_c\rightarrow \mathbf{B}_n M\), with \(\mathbf{B}_c=(\Xi _c^0,\Xi _c^+,\Lambda _c^+)\) and \(\mathbf{B}_n(M)\) the baryon (pseudo-scalar) octets. We find that these breaking effects can be used to account for the experimental data on the decay branching ratios of \({\mathcal {B}}(\Lambda _c^+\rightarrow \Sigma ^{0} K^{+},\Lambda ^{0} K^{+})\) and \(R'_{K/\pi }={\mathcal {B}}(\Xi ^0_c \rightarrow \Xi ^- K^+)\)/\({\mathcal {B}}(\Xi ^0_c \rightarrow \Xi ^- \pi ^+)\). In addition, we obtain that \({\mathcal {B}}(\Xi _{c}^{0} \rightarrow \Xi ^{-} K^{+},\Sigma ^{-} \pi ^{+})=(4.6 \pm 1.7,12.8 \pm 3.1)\times 10^{-4}\), \({\mathcal {B}}(\Xi _c^0\rightarrow pK^-,\Sigma ^+\pi ^-)=(3.0 \pm 1.0, 5.2 \pm 1.6)\times 10^{-4}\) and \({\mathcal {B}}(\Xi _c^+\rightarrow \Sigma ^{0(+)} \pi ^{+(0)})=(10.3 \pm 1.7)\times 10^{-4}\), which all receive significant contributions from the breaking effects, and can be tested by the BESIII and LHCb experiments.     

SU(3) spin-orbit coupled fermions in an optical lattice

We propose a scheme to realize the SU(3)spin-orbit coupled three-component fermions in an one-dimensional optical lattice.The topological properties of the single-particle Hamiltonian are studied by calculating the Berry phase,winding number and edge state.We also investigate the effects of the interaction on the ground-state topology of the system,and characterize the interaction-induced topological phase transitions,using a state-of-the-art density-matrix renormalization-group numerical method.Finally,we show the typical features of the emerging quantum phases,and map out the many-body phase diagram between the interaction and the Zeeman field.Our results establish a way for exploring novel quantum physics induced by the SOC with SU(N)symmetry.     

SU(3) × SU(3) symmetry breaking in a simple model

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 ultra-violet divergences. The possibility of a spontaneous breakdown of the symmetry is described and the Goldstone theorem is verified in the one-loop approximation.     

Chiral symmetry on the lattice with Wilson fermions

The chiral properties of the continuum limit of lattice QCD with Wilson fermions are studied. We show that a partially conserved axial current can be defined, satisfying the usual current algebra requirements.A proper definition of the chiral symmetry order parameter, $\text{〈0|}\text{ψ}\text{ψ|0〉}$, is given, and the chiral properties of composite operators are investigated. The implications of our analysis to the lattice determination of non-leptonic weak amplitudes are also discussed.     

Spontaneous SU(2) symmetry breaking in one-dimensional quantum antiferromagnet

We present a Bethe Ansatz based investigation of a one-dimensional (1D) Heisenberg spin chain in a real 3D crystal lattice. We have shown that due to an influence of the lattice distortion on a crystalline field of ligands of magnetic ions, a Heisenberg antiferromagnetic spin chain is unstable under the appearance of a magnetic anisotropy of the “easy-plane” type. The effects of an external magnetic field and nonzero temperature onto such a phase transition are studied. Received: 19 January 1998 / Revised: 16 March 1998 / Accepted: 17 March 1998     

Radiative gauge symmetry breaking in supersymmetric flipped SU(5)

The radiative breaking of the SU(5)×U(1) symmetry in the flipped SU(5) model recently proposed by Antoniadis et al. is studied using renormalization group techniques. It is shown that gaugino masses can only be the dominant source of supersymmetry breaking at the Planck scale if the U(1) gaugino mass M₁ is at least 10 times larger than the SU(5) gaugino mass M₅. If M₁≅M₅ at the Planck scale, non-vanishing trilinear soft breaking terms (“A-terms”) are needed already at the Planck scale. In both cases consequences for the sparticle spectrum at the weak scale are discussed.