A chiral SU(2)L⊗SU(2)R gauge model on the lattice

An explicitly chiral symmetric SU(2)_L⊗SU(2)_R model with a scalar doublet and a mirror pair of fermion doublets is investigated in lattice perturbation theory.     

Structure of σ model in [1, 1] representation of SU(2) ⊗ SU(2) group

The spontaneous breakdown of symmetry of the-model in the [1, 1] representation of SU(2) SU(2) group is investigated. It is shown that the spontaneous breakdown is realized in all cases of squared mass ² in mass term in the Lagrangian ( ²>0, ²=0, ²<0), unlike the-model in [1/2, 1/2] representation, in which the spontaneous breakdown only for the case ²<0 manifests itself. Further, different but equivalent methods of obtaining the nonlinear realization for pions in the frame of an extended in such a way-model are demonstrated. Finally, it is sketched, that the obtained results can be generalized to all [N/2,N/2] representations of SU(2) SU(2) chiral group.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.On leave of absence from theDept. of Theoretical Physics, Comenius University, Bratislava, Czechoslovakia.     

Green function renormalization in SU(2)L ⊗ U(1) four-fermion model

Using the Dyson-Schwinger equation, the four-fermion Green functions in one-loop approximation to the SU(2)_L U(1) four-fermion model are found, as well as corrections to them. An expression is obtained for the collective field propagator in the one-loop approximation, and its regularization is performed. In the model under consideration, collective excitations are identified with a massless Goldstone field and a massive scalar field. It is shown that as a result of the reconstruction of the vacuum, one fermion (the analog of the neutrino) is massless, while the other (the analog of the electron), massive.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 19–23, January, 1984.     

AnSU(2)l ⊗SU(2)r symmetric Yukawa model in the symmetric phase

The lattice regularizedSU(2)l ?SU(2)r symmetric scalar fermion model with explicit mirror fermions is investigated in the phase with unbroken symmetry. In the present work numerical Monte Carlo calculations with dynamical fermions are performed on 4³·8 and 4³·16 lattices near the expected perturbative Gaussian fixed point. The bare Yukawa coupling of the mirror fermion is fixed at zero. Global symmetries of the model are discussed, and the numerical results are supported by lattice perturbation theory.     

Lepton-flavor-violating pion decay π+→μ−νμ e + e + and SU(3)C ⊗ SU(3)L ⊗ U(1)N model

Within the minimal SU(3)_C ? SU(3)_L ? U(1)_N model, the lepton-flavor-violating decay π⁺→μ^?ν_μ e ⁺ e ⁺ is calculated without directly invoking lepton mixing. The branching ratio for this rare pion-decay mode is found to be much smaller than the current experimental upper limit. If the anomalous interactions are discarded, this result coincides with the result of the previous calculation.     

Spontaneous SU(2) symmetry violation in the SU(2) L × SU(2) R × SU(4) electroweak model

A new approach to electroweak (EW) composite scalars is developed starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure SU(2) _L × SU(2) _R × SU(4), where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios.     

SU(4)⊙SU(2)⊙SU(1)统一模型

本文提出一种SU(4)⊙SU(2)⊙SU(1)统一模型. 在此模型中, 层子和轻子放于同一个多重态中, 所以它们有耦合, 但这种耦合不会导致质子衰变, 只对高能散射有效应. 此模型预言了有两种中性中间玻色子, 还算得了sin²θ_w=0.25, 并可使中微子有合理的质量.     

Inclusion of fermions in the locally SU(2) ⊗ U(1)-invariant model with dynamical symmetry breaking

It is shown that dynamic symmetry breaking in the locally SU(2) U(1)-invariant model with mixed inclusion of fermions in a four-fermion interaction leads to a situation in which one collective scalar field, representing the sum of all generations of fermion-antifermion pairs, acts as the total (one-loop) effective Lagrangian. Mass formulas are found for the scalar field and gauge vector fields. The effective Lagrangian obtained coincides in form with the standard Lagrangian in the Glashow-Weinberg-Salam theory of electroweak interactions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 41–45, July, 1991.     

Chiral SU(2)×SU(2) model with infrared quark confinement

An SU(2)×SU(2) chiral quark model describing the properties and interaction of pions and scalar and vector mesons is considered. The confinement of quarks is introduced in the model by means of an infrared cut-off in the one-loop quark diagrams. This cutoff gives rise to the elimination of the unphysical thresholds of the quark-antiquark pair production. The π-a ₁ transitions are taken into account. The model conserves all low-energy theorems. The masses of mesons and the widths of the decays ρ → 2π and σ → 2π are calculated.     

SU(2)×SU(2)格点手征模型的进一步研究

本文利用变分─累积展开方法将SU(2)×SU(2)格点手征模型的自由能展开到第五级,分别用主值法和聚点法(accumulation point)确定变分参数,结果表明后者能得到与蒙特卡罗模拟更为一致的内能和比热曲线.     

SU(4)⊕SU(2)⊕U(1)统一模型

本文提出一种SU(4)SU(2)U(1)统一模型。在此模型中,层子和轻子放于同一个多重态中,所以它们有耦合,但这种耦合不会导致质子衰变,只对高能散射有效应。此模型预言了有两种中性中间玻色子,还算得了sin~2θ_w=0.25,并可使中微子有合理的质量。     

β FUNCTION FOR SU(2)×SU(2) CHIRAL MODEL ON 2-DIMENSIONAL RANDOM TRIANGLE LATTICE

The β function behavior for SU(2)×SU(2) chiral model on 2-dimensional random triangle lattice has been studied with Monte Carlo renormalization group method.Its behavior is similar to that of the 4-dimensional SU(2) gauge theory.However,it is smoother from weak to strong coupling regions.There is no nonperturbative peak structure.The asymptotic scaling starts beyond β=1.6.     

SU(mn) SU(m)×SU(n)单粒子母分系数

本文利用置换群CG系数计算了五个粒子以内的所有SU(mn) SU(m)×SU(n)单粒子母分系数.     

Entanglement Conditions for Mixed SU(2) and SU(1, 1) Systems

We derive a class of inequalities for detecting entanglement in the mixed SU(2) and SU(1,?1) systems based on the Schrödinger-Robertson indeterminacy relations in conjugation with the partial transposition. These inequalities are in general stronger than those based on the usual Heisenberg uncertainty relations for detecting entanglement. Furthermore, based on the complete reduction from SU(2) and SU(1,?1) systems to bosonic systems, we derive some entanglement conditions for two-mode systems. We also use the partial reduction to obtain some inequalities in the mixed SU(2) (or SU(1,?1)) and bosonic systems.     

SU(2)×SU(2) ELECTROWEAK THEORY IN LEP 1 DATA ON Z PARTICLE PRODUCTION

Recent data obtained by LEP1 are discussed and their potential implication for the existence of a Z particle. This letter advocates that this fits within the basic tenet of an SU(2)×SU(2) extended theory of the standard model of electroweak interactions. This extended electroweak model is motivated by nonabelian electrodynamics that provides an effective calculus for nonlinear optics.     

二维随机格点SU(2)×SU(2)自旋系统的Monte-Carlo模拟

本文对8×8, 9×9和10×10三种二维随机格点阵的SU(2)×SU(2)手征模型进行了Monte-Carlo(M-C)模拟, 得到了链作用形式的内能和比热结果. 计算结果表明: 当β≥1.0以后, 系统进入过渡区, 但无明显的连续相变迹象; 其统计涨落则由于有限体积引起的边界效应而致. 结果与四维随机格点的SU(2)理论这Monte Carlo计算基本一致^[5,6]. 从而我们相信, 在新的随机格点形式下, 亦可能存在4维SU(N)规范理论和2维SU(N)×SU(N)自旋系统的一致性.     

On superstring-inspired SU(3) × SU(2) × (U(1))2 models with SO(10) unification

Alternative compactification of the heterotic superstring can give rise to a residual four-dimensional SO(10) gauge symmetry for the observable sector. We consider a model with gauge group SU(3) × SU(2) × (U(1))², resulting from the Hosotani breaking of SO(10), study its further gauge symmetry breaking and calculate the particle spectrum. We find that all breakings can occur close to the weak scale; the top mass lies preferentially between 40 and 60 GeV, the second Z boson mass is O(200–400) GeV. The sparticle spectrum is quite heavy, apart possibly from a light chargino, whose mass can be as light as O(30) GeV.     

SU(mn)SU(m)×SU(n)单粒子母分系数

本文利用置换群CG系数计算了五个粒子以内的所有SU(mn)SU(m)×SU(n)单粒子母分系数。