DOES THE RUBAKOV EFFECT EXIST IN AN SU(2) MODEL

In an SU(2) spontaneously broken gauge theory with a Higgs triplet, the mass effect of an iosspin 1/2 fermion on the fernlion-nlonopole bound states is discussed. It is shown that when the direct coupling betrveen fermion and Higgs field approaches zero, but the Dirac mass remalns finiteness, the necessary condition of the fermion-monopole bound state cannot be satisfied. This result means that the Rubakov effect is absent for SU(2) monopole because of the Dirac mass.     

在SU(2)模型中费密子的质量与Rubakov效应

在自发破缺的具有Higgs三重态的SU(2)规范理论中,讨论了同位旋1/2的费密子的质量对费密子-磁单极束缚态的影响。结果表明,当费密子与Higgs场之间的直接耦合趋于零,但狄拉克质量保持固定时,费密子-磁单极束缚态的必要条件必不被满足。这个结果意味着对于SU(2)模型由于狄拉克质量效应,Rubakov效应不存在。 关键词：     

Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos

In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed. Received: 15 March 1999 / Published online: 22 October 1999     

Axial-vector anomaly for Dirac-Kähler fermions on the lattice

The axial-vector current of Dirac-Kähler fermions on the lattice is studied. We consider a U(1) gauge theory in two dimensions as well as an SU(N) gauge theory in four dimensions. Using a short-distance expansion of the fermion propagator in an external gauge field, we show that the correct anomaly is reproduced in the continuum limit.     

SU(3)L×U(1)X Model and a New Candidate for Dark Matter

We consider a gauge model based on SU(3)_L×U(1)_X symmetry. In the model each lepton family contains a new neutral fermion (N-Particle). We calculate the lifetime of the N-particle and estimate the value of its mass. We show that the N-particle can act as dark matter particle.     

Chiral symmetry breakdown,anomaly, and the PCAC relation on a lattice

Lattice fermion formulation is investigated using a solvable model which resembles quantum chromodynamics. CP₂^N?1 models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the $\text{1}\text{N}$ expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) apparently occurs in this model, and the “pion” mass is calculated. From the above results, it is shown that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied.     

Bounds on the number and masses of quarks and leptons

We assume weak, electromagnetic and strong interactions to be asymptotically divergent, and to become strong at very large energies, of the order of the Plank mass. In this picture, the “low-energy” couplings (i.e. in the 10² GeV region) must be near the infrared stable point, and this allows us to put bounds on the number of elementary fermions (quarks and leptons). Similar assumptions on the Higgs couplings give bound on the fermion and on the Higgs boson masses. We consider the cases where weak and electromagnetic interactions are described by the gauge groups SU(2) ? U(1) or SU(2)_R ? U(1). The weak neutral current mixing angle is computed in both cases.     

An SU(5) model with hierarchical fermion masses and a phantom axion

We present an SU(5) model with hierarchical fermion structure and without strong CP violation. The Peccei-Quinn U(1) symmetry we need is tied to the symmetry needed to produce the observed fermion mass spectrum. It is spontaneously broken at 10¹⁵ GeV which makes the axion almost unobservable.     

Parity doubling and SU(2)LxSU(2)R restoration in the hadron spectrum

We construct the most general nonlinear representation of chiral SU(2)LxSU(2)R broken down spontaneously to the isospin SU(2), on a pair of hadrons of same spin and isospin and opposite parity. We show that any such representation is equivalent, through a hadron field transformation, to two irreducible representations on two hadrons of opposite parity with different masses and axial-vector couplings. This implies that chiral symmetry realized in the Nambu-Goldstone mode does not predict the existence of degenerate multiplets of hadrons of opposite parity nor any relations between their couplings or masses.     

VACUUM OF 2+1 DIMENSIONAL SU(2) LGT WITH FERMIONS AND SPONTANEOUS CHIRAL SYMMETRY BREAKING

By incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state,the vacuum structure of 2+1 dimensional SU(2) LGT with fermions is studied.We calculate the fermion condensate <ψψ>,and obtain a good scaling behavior.

     

THE CHIRAL SU(2)L SU(2)R σ-MODEL WITH MASSIVE π MESONS

The chiral SU(2)_L SU(2)_R σ-Model with both spontaneous and dynamical symmetry breaking is investigated and massive π mesons are obtained.The physical mechanism of how π mesons acquire mass is discussed.     

THE WILSON LOOP EXPECTATION VALUES IN 2-AND 3-DIMENSIONAL su(2) LGT

An improved Monte Carlo scheme is applied to the computation of the expectation values of nxm Wilson loops in both 2-and 3-dimensional SU(2) lattice gauge theories.The results are compared with those simulated by the discrete group Y₁₂₀ and the exact results in two dimensions.     

Proton decay in locally supersymmetric GUT

Proton decay is studied in the supergravity model with “the hidden sector” as the source of supersymmetry breaking. Each dimension-five operator is found to accompany ΔB ≠ 0 four-scalar interactions. The Higgs fermion exchange for loop diagrams at low energies can be as important as the gauge fermion exchange, if the associated Yukawa coupling is significant as suggested by the radiatively induced SU(2) × U(1) breaking mechanism. The experimental bound for p → K⁰μ⁺ gives the lower bound of the order of 10¹⁶ GeV for the mass of the baryon-number violating Higgs particle.     

Neutrino masses in the supersymmetric SU(3)C⊗SU(3)L⊗U(1)X model with right-handed neutrinos

The R-symmetry formalism is applied for the supersymmetric SU(3)_C⊗SU(3)_L⊗U(1)_X (3-3-1) model with right-handed neutrinos. For this kind of models, we study the generalization of the MSSM relation among R-parity, spin and matter parity. Discrete symmetries for the proton stable in this model are imposed, and we show that in such a case it is able to give leptons masses at only the tree level contributions required. A simple mechanism for the mass generation of the neutrinos is explored. We show that at the low-energy effective theory, the neutrino spectrum contains three Dirac fermions, one massless and two degenerate in mass. At the energy level where the mixing among them with the neutralinos is turned on, neutrinos obtain Majorana masses and correct the low-energy effective result which naturally gives rise to an inverted hierarchy mass pattern. This mass spectrum can fit the current data with minor fine-tuning. Consistent values for masses of the charged leptons are also given. In this model, the MSSM neutralinos and charginos can be explicitly identified in terms of the new constraints on masses which is not as in a supersymmetric version of the minimal 3-3-1 model. PACS 11.30.Er; 14.60.Pq; 14.60.-z; 12.60.Jv     

Absence of species doubling in finite-element quantum electrodynamics

In this Letter, it will be demonstrated explicitly that the finite-element formulation of quantum electrodynamics is free from fermion doubling. We do this by (1) examining the lattice fermion propagator and using it to compute the one-loop vacuum polarization on the lattice, and (2) by an explict computation of vector and axial-vector current anomalies for an arbitrary rectangular lattice in the Schwinger model. There it is shown that requiring that the vector current be conserved necessitates the use of a square lattice, in which case the axial-vector current is anomalous.     

Fermion masses in grand unified theories: Effective Yukawa terms

It is argued that effective non-renormalizable terms of the type recently proposed by Ellis and Gaillard can give rise to large contributions to the fermion masses. The combined effect of this kind of term and the usual Yukawa couplings could explain the observed hierarchy of fermion masses. Two toy-models based on the gauge groups SU (5)×SU(2) _H and SO(10)×SU(2) _H (where SU(2) _H is a gauged “horizontal” symmetry) are shown in which one can obtain some interesting mass relations previously obtained under very different assumptions.     

Early unification and the Weinberg angle in the SU(4)4 grand unified model

In the framework of the grand unified gauge group SU(4)⁴ we discuss possibilities to reconcile the low unification scale (10⁵?10⁷ GeV) with the acceptable value of sin²θ_w. We consider various specific models which differ by the values of the intermediate mass scale, the choice of the fermion multiplets and by the embedding of the electroweak group SU(2) into SU(4)⁴. The class of theories with early unification and correct sin²θ_w is constructed. They all predict new non-sequential fermions which are SU(2)_L,R singlets and have unconventional electric charges. Cosmological implications of such theories are discussed and it is argued that new particles may well account for the positive results of searches for fractional charge in terrestrial matter.     

FUNDAMENTAL PROBLEMS OF SU(2)t WZW MODELS

In this paper,we give a solution to fundamental problems of Wess-Zumino-Witten model for the case j₃=1 and the method of solving the fundamental problems for the general case.We find also the explicit connection between the crossing matrix of SU(2)_t WZW model and the braid matrix of SL(2,q) quantum group,the latter is just the quantum Racah coefficent.     

An SU (3)_L×U(1)_X Electroweak Model

We studied an SU(3)_L×U(1)_X electroweak model. By requiring M2z1-M2w/ cos²θw to be less than experimental value we abtain a lower bound on M_Z′ The relation between M_Z′ and M_U (M_V) then gives a lower bound on M_U (M_V). We further consider the K_L－K_S mass difference due to Z′ exchange and obtain stronger lower bounds on M_Z′ and M_U (M_V).     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.