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.     

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.     

Dynamical SU(3) symmetry breaking in the linear baryonic string model

A dynamical mechanism responsible for breaking of the SU(3) symmetry among various states from the s-u-d sector is proposed. In the case when SU(3) is dynamically maximally broken we obtain Λ_α - Λ_γ degeneracy and reproduce also other prominent features of the leading strange baryon trajectories.     

Dynamical symmetry breaking of extended gauge symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group G(LR)=SU(3)(c) x SU(2)(L) x SU(2)(R) x U(1)(B-L), and its extension to the Pati-Salam gauge group G(422)=SU(4)(PS) x SU(2)(L) x SU(2)(R). The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of G(LR) and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why G(LR) and G422 break to SU(3)(c) x SU(2)(L) x U(1)(Y), and why this takes place at a scale (approximately 10(3) TeV) large compared to the electroweak scale, but much smaller than a GUT scale.     

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     

Universality in SU(2) lattice gauge theory

A method of resumming perturbation theory is used to re-analyze previous Monte Carlo data of Bhanot and Dashen. We find no inconsistency with universality. There appears to be a relatively large region where Monte Carlo studies can reliably be done.     

Dynamical symmetry breaking in SO(4n+2) and E(6) gauge theories

We find that SO(4n+2) and E(6) gauge theories with fermions in the complex spinor representation (and no scalar fields at all) undergo dynamical breaking of the gauge symmetry, according to the rules of Raby, Dimopoulos, and Susskind.     

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.     

Dynamical rearrangement of SU(3) symmetry

The dynamical rearrangement of the SU(3) group is studied in connection with a 2-dimensional analogy of Holstein-Primakoff transformation. Infrared effect and low energy theorems are considered.     

Finite temperature SU(2) lattice gauge theory

We discuss SU(2) lattice gauge theories at non-zero temperature and prove several rigorous results including i) the absence of confinement for sufficiently high temperature in the pure gauge theory, and ii) the absence of spontaneous chiral symmetry breaking for sufficiently high temperature in the theory with massless fundamental representation fermions.     

Finite tension strings in SU(2) gauge theory

The second-order field equations of the SU(2) Higgs model are studied and a new class of string solutions is obtained. The tension is finite and scale-dependent and the strings are of minus one unit flux.     

Proof of chiral symmetry breaking in lattice gauge theory

Using the method of infrared bounds and partial-integration formulas, we prove that there is a chiral phase transition in four-dimensional strongly coupled lattice gauge theory with gauge group U(N) and staggered fermions for all N5.     

SU(N) gauge fields with spherical symmetry

A method to construct spherically symmetricSU(N) gauge fields and an invariant classification are presented. For the groupSU(3) the ansätze are completely elaborated. The corresponding sourcelessSU(3)-Yang-Mills equations are discussed.     

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.