Search

We construct a charged vectorial field in the global limit of a U(1) chiral lattice gauge theory and, using the hopping parameter expansion, calculate its propagator. We show that the doubler modes are removed and that it is possible to tune a bare Yukawa-like coupling to obtain a finite mass for this field in the continuum limit. Related results are given for the propagators of chiral fermions.

We study the decoupling of doubler modes and the requisite tuning of the lattice fermion mass {ital am}{sub {ital f}}=0 (necessary for a finite {ital m}{sub {ital f}}/{ital m}{sub bosonic} in the continuum limit) for a formulation of the SU(2){times}U(1){sub {ital Y}} electroweak theory on the lattice.

Using a hopping parameter expansion, we demonstrate the decoupling of fermion doubler modes in the hypercharge U(1)Y lattice gauge theory. We also show analytically that it is possible to tune the bare Yukawa coupling to a value such that the fundamental physical fermion amf=0 (as is necessary in order to obtain a finite physical mass mf in the continuum limit), and we calculate this value. The appropriate special case of these results is compared with numerical simulations of the frozen-gauge limit of the U(1)Y theory, and good agreement is found. The role of the Yukawa coupling in a chiral lattice gauge theory is contrasted with that in a nonchiral Yukawa model.

The U (1) Y hypercharge sector of the standard electroweak theory is studied on the lattice. It is shown that, for fermions with both nonsinglet ψ L and ψ R , the doubler modes can be removed in the continuum limit while the masses of the physical fermions can be tuned appropriately. Data from simulations will be discussed and compared with recent analytic calculations.

It is conjectured that the lack of chiral gauge symmetry-preserving regulator is signalling a genuine quantum effect which breaks chiral gauge symmetries and generates masses for gauge bosons. This idea is applied to an SU(3) C ×SU(2) L ×U(1) Y model. It is shown that the dynamics of chiral fermions can generate masses for the W and Z bosons with the correct mass ratio. Chiral gauge theories without elementary scalars are found to be related to effective gauge theories with group element valued scalar fields. Furhtermore, massless fermions can exist in such theories.

Using analytic methods and dynamical fermion simulations, we study the properties of two nonperturbative continuum limits of a lattice Yukawa model with a real scalar field, at the (a) ferromagnetic-ferrimagnetic and (b) ferrimagnetic-antiferromagnetic phase boundaries. This work makes use of a new analytic result that the fermion mass vanishes identically in the antiferromagnetic phase.

We study the global limit of the hypercharge U(1){sub Y} sector of the standard lattice electroweak theory. We show that for fermions with both Y{sub R} = 0 and Y{sub R} {ne} 0 the doubler modes can be removed in the continuum limit while the physical fermion masses can be tuned to agree with physical values. 18 refs., 1 fig., 1 tab.

We determine the phase structure and properties of a 4D lattice model with a real scalar field interacting with staggered fermions via a local Yukawa interaction. For large bare Yukawa coupling, the phase diagram differs significantly from that for the model with a hypercubic Yukawa interaction; in particular, we find a new symmetric phase in which fermions are massive. We comment on implications for extracting regularization scheme-independent continuum physics from lattice scalar-fermion models.

Using a combination of analytic mean field techniques and hybrid Monte Carlo simulations, we determine the phase structure of a 4d Yukawa theory with a one-component scalar field interacting with two species of staggered lattice fermions. In a parametrization of the theory in terms of the Yukawa coupling γ and the nearest-neighbor scalar field coupling κ and quartic coupling λ, we find four different phases: (1) symmetric, disordered; (2) ferromagnetic; (3) antiferromagnetic; and (4) simultaneously ferromagnetically and antiferromagnetically ordered. To study the continuum limit of the model, we measure correlation functions and extract masses and renormalized scalar and Yukawa couplings close to the (second-order) phase boundary between phases (1) and (2). The current parametrization allows us to extend significantly previous studies of renormalized couplings and to probe a very large range of bare couplings in continuum parametrization. The renormalized Yukawa coupling γ R is always found to be ⪅1.5 for the range of bare coupling covered. The values of λ R are also bounded and exhibit only weak sensitivity to the bare λ. Comparisons are made with λ R values obtained in the pure 4d λo 4 theory.

Analytic and numerical studies of the lattice gauge theories with both Higgs and fermion fields are reported. A chiral transition is found in a wide class of such theories, both abelian and non-abelian. This transition separates each phase diagram into two regions, one with spontaneous chiral symmetry breaking and the other with explicit chiral symmetry. The transition is second order where probed. In models where Yukawa couplings are present, there exists a critical value of this coupling below which chiral transition still occurs. Some physical implications are noted.

We study the (zero-temperature) chiral transition in an SU(2) lattice gauge theory with I = 1 2 Higgs fields, and fermion fields with I = 1 2 and I = 0 , including Yukawa couplings. Using analytic methods in the strong gauge coupling limit, we demonstrate that (i) if at least one of the Yukawa couplings is sufficiently weak, this theory undergoes a spontaneous chiral symmetry breaking phase transition; (ii) this transition is removed when the Yukawa couplings are sufficiently strong. The transition is determined to be of second order, and approximate critical point calculations are given. Some implications for the continuum limit of the SU(2) model, and for electroweak interactions, are discussed.

Numerical evidence is found for the appearance of a massless vector state, the “photon”, in the broken phase of the lattice Georgi-Glashow model. Data is also presented for the lowest-lying scalar mass in the theory. Our simulations indicate that the transition between symmetric and broken phases is weakly first order for a wide range of couplings.

Properties of the phases in a gauge-Higgs model with SU(2)global ⊗ U(1)local symmetry are investigated using a variety of probes. These include studies of the low-lying spectrum and measurement of a quantity that is sensitive to the breaking of the global SU(2) symmetry and which provides useful information even on finite lattices. The strength of the effective gauge coupling and the ability (or lack thereof) of gauge interactions to induce chiral symmetry breaking is tested by evaluating 〈 ψ ψ〉 in the quenched approximation for singly-charged fermions.

We study the (zero-temperature) chiral transition in a U(1) gauge-Higgs-fermion theory with Yukawa couplings involving fermions of two different charges. Using analytic methods in the strong coupling limit, we find that for a range of sufficiently weak Yukawa couplings, this transition continues to exist and be of second-order, but is removed as the strength of the Yukawa coupling increases through a critical value. Some implications for the continuum limit of this model, and for electroweak interactions, are noted.

We study the chiral phase structure for SU(2) lattice gauge theory with an I = 12 Higgs field and I = 1 dynamical fermions. The order and location of the chiral transition for strong gauge coupling are in agreement with our previous analytic results. In the interior of the phase diagram, it is found that the chiral boundary lies above the line of transitions connecting to the O(4) critical point. This study elucidates the effect of fermion representation on the chiral transition and strengthens the basis for a possible explanation for the fact that the known weak nonsinglet fermions have I = 12.

We suggest a possible explanation, based on properties of the (zero-temperature) chiral transition in lattice gauge-Higgs theories, for why the known left-handed fermions have weak isospin 1 2 .

The two-generation SU(2) sector of the standard model with zero Yukawa couplings is studied on the lattice. The results from analytic studies and simulations with quenched fermions are reviewed. The methods and results of a Langevin simulation with dynamical fermions are presented. Implications for the strongly coupled standard model are mentioned.

Mass measurements are carried out in a lattice U(1) gauge-Higgs system with the Higgs fields transforming as a doublet under a global SU(2) symmetry. The model exhibits three distinct phases: Coulomb, Higgs and confining. Evidence is found for a massless vector state in the Coulomb phase, and massless Goldstone scalars in the Higgs phase. Also the behavior is studied of the massive states near the transitions between the Coulomb and Higgs phases and between the confining and Higgs phases.

The phase diagram of lattice SU(2) gauge theory with fundamental representation Higgs fields is probed by l= 1 2 and l =1 fermions. Quenched calculations of 〈 Ψ Ψ〉 l show two distinct regions characterized by broken or unbroken chiral symmetry. The location of the boundary between the two regions depends on the representation l of the fermions. For l= 1 2 fermions the presence is verified of Nambu-Goldstone bosons (“pions”) in the broken region and evidence is found for massless physical fermions in the chirally symmetric region. Effects of boundary conditions and the possibility of observing two particle cuts in finite lattice spectrum calculations are commented on also.

We study the implications of explicit lepton-number violating soft operators in a general low-energy effective theory with softly broken supersymmetry. Nonzero but relatively small VEVs of scalar neutrinos could exist. In the case where the VEVs of scalar neutrinos vanish, appreciable coefficients of the lepton-number violating soft operators are allowed. We also emphasize the role played by the mixing between the superpartners of the left- and right-handed leptons in the lepton family number violating process μ → eγ .

We consider the possibility that the lack of a chiral gauge symmetry-preserving regulator is signaling a genuine quantum effect which breaks the chiral gauge symmetry and generates mass for the gauge bosons. A nonperturbative analysis of an SU(3)C×SU(2)L×U(1)Y model regularized on a lattice is presented. Although both SU(2)L and U(1) Y symmetries in this model are broken in the regularized action, SU(3)C×U(1)Q symmetry can be maintained throughout the calculations. Using a hopping parameter expansion, the effective action for the gauge bosons is derived. Mass terms for the gauge bosons are generated, and the mass ratio of the gauge bosons is discussed.

We present an analytic study of the (zero-temperature) chiral symmetry-breaking phase transition in SU(2) lattice gauge-Higgs theory with fermions, relevant to the SU(2) sector of the standard electroweak theory. The transition is found to be second-order and the critical gauge-Higgs coupling is calculated in the limit of strong gauge coupling. New Monte Carlo measurements for quenched I = 1 2 fermions are presented and found to be in excellent agreement with the analytic results, which are not limited to the quenched approximation.

We report new results in three areas concerning the chiral transition in U(1) lattice gauge-Higgs theory with fermions. First, the case of a theory with two differently charged fermions simultaneously present is studied, and it is shown analytically that there are two associated continuous chiral phase transitions. Second, a general theorem is proved classifying the strong gauge-coupling behavior of any U(1) theory with a fermion and Higgs fields of arbitrary nonzero charges q f and q h : such a theory has a chiral transitions along the β g = 0 line if and only if q f is a nonzero multiple of q h . Third, new data is presented on the chiral transition with quenched fermions in the interiof of the phase diagram at small or zero gauge-Higgs coupling, completing our earlier mapping of the chiral phase boundary.

Using Monte Carlo methods, we study the (zero-temperature) chiral phase transition in 4D U(1) lattice gauge-Higgs theory with fermions of charge qf = 1 and 2. We report the first comparison between Monte Carlo data and analytic results (applicable at strong gauge coupling), and find very good agreement. In the interior of the phase diagram, the chiral transition is observed to coincide with the confinement-Higgs phase boundary for qf = 1 and to occur at larger βh for qf = 2.

We report the first measurements, with fully dynamical fermions, of the (zero-temperature) chiral symmetry-breaking phase transition in the SU (2) part of the standard SU(2)×U(1) electroweak lattice gauge theory. These are performed with a Langevin algorithm. Good agreement is found with the previous analytic strong gauge coupling results, regarding both the location and the order of the transition. The chiral boundary is also measured in the interior of the phase diagram and the phase structure with dynamical fermions is discussed.