Bare Mass Term Research Articles

Four-dimensional lattice chiral gauge theories with anomalous fermion content

In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ``smoothness'' on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the St\"uckelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.

Baryons in massive Gross-Neveu models

Baryons in the large $N$ limit of ($1+1$)-dimensional Gross-Neveu models with either discrete or continuous chiral symmetry have long been known. We generalize their construction to the case where the symmetry is explicitly broken by a bare mass term in the Lagrangian. In the discrete symmetry case, the exact solution is found for arbitrary bare fermion mass, using the Hartree-Fock approach. It is mathematically closely related to polarons and bipolarons in conducting polymers. In the continuous symmetry case, a derivative expansion allows us to rederive a formerly proposed Skyrme-type model and to compute systematically corrections to the leading order description based on an effective sine-Gordon theory.

Partial gauge symmetry breaking via bare mass

We study gauge symmetry breaking patterns in supersymmetric gauge models defined on M4×S1. Instead of utilizing the Scherk–Schwarz mechanism, supersymmetry is broken by bare mass terms for gaugino and squarks. Though the matter content is the same, depending on the magnitude of the bare mass, the gauge symmetry breaking patterns are different. We present two examples, in one of which the partial gauge symmetry breaking SU(3)→SU(2)×U(1) is realized.

Effect of bare mass on the Hosotani mechanism

It is pointed out that the existence of bare mass terms for matter fields changes gauge symmetry patterns through the Hosotani mechanism. As a demonstration, we study an SU(2) gauge model with massive adjoint fermions defined on M4⊗S1. It turns out that the vacuum structure changes at certain critical values of mL, where m (L) stands for the bare mass (the circumference of S1). The gauge symmetry breaking patterns are different from models with massless adjoint fermions. We also consider a supersymmmetric SU(2) gauge model with adjoint hypermultiplets, in which the supersymmetry is broken by bare mass terms for the gaugino and squark fields instead of the Scherk–Schwarz mechanism.

MASSIVE YANG–MILLS THEORY IN ABELIAN GAUGES

We prove the perturbative renormalizability of pure SU(2) Yang–Mills theory in the Abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow us to preserve the standard form of the Slavnov–Taylor identities (but with modified BRST variations), mass terms for the diagonal gauge fields require the study of modified Slavnov–Taylor identities. We comment on the renormalization group equations, which describe the variation of the effective action with the different masses. Finite renormalized masses for the charged gauge fields, in the limit of vanishing bare mass terms, are possible provided a certain combination of wave function renormalization constants vanishes sufficiently rapidly in the infrared limit.

Simulations of Alice electrodynamics on a lattice

In this paper we present results of numerical simulations and some (analytical) approximations of a compact U(1)⋉ Z 2 lattice gauge theory, including an extra bare mass term for Alice fluxes. The subtle interplay between Alice fluxes and (Cheshire) magnetic charges is analysed. We determine the phase diagram and some characteristics of the model in three and four dimensions. The results of the numerical simulations in various regimes, compare well with some analytic approximations.

Lepton flavor violation in the supersymmetric standard model with vectorlike leptons

Lepton flavor violating processes are obtained from the mixing between ordinary leptons and vectorlike $\mathrm{SU}{(2)}_{L}$ doublet leptons which may originate in ${E}_{6}.$ The effects of this lepton mixing are, however, suppressed naturally by the hierarchy of the charged lepton masses. In the supersymmetric model, significant effects of lepton flavor violation may appear rather through slepton mixing, which is in the present case generated by radiative corrections with ordinary-exotic lepton couplings. We are especially interested in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ decay. In the model without the bare mass term of vectorlike leptons, the supersymmetric contributions are rather suppressed due to the approximate $\mathrm{U}{(1)}_{e}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{\ensuremath{\mu}}.$ It is, however, remarkable that they are substantially enhanced by ${\mathrm{tan}}^{6}\ensuremath{\beta}.$ Then, $\mathrm{Br}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma})$ might be comparable to the experimental bound for large tan \ensuremath{\beta}. In the model with the bare mass term, much larger contributions are obtained through slepton mixing. These investigations show that the supersymmetric effects on lepton flavor violation due to the vectorlike leptons can be observed in the near future experiments.

On the Effective Potential for Local Composite Operators

We show that the effective potential for local composite operators is a useful object in studying dynamical symmetry breaking by calculating the effective potential for the local composite operators ψψ and φ2 in the Gross–Neveu (GN) and O(N) models, respectively. Since the effective potential for local composite operators can be calculated by using the Cornwall–Jackiw–Tomboulis (CJT) effective potential in theory with additional bare mass terms, we show that divergences in the effective potential for local composite operators are the same as those in the CJT effective potential. We compare the results obtained with the results given by the auxiliary field method.

Lattice fermions and chiral symmetry

We propose a formulation of lattice fermions with one-sided differences that is hermitian, chirally symmetric (barring a bare mass term) and completely free of doubling. To obtain the axial anomaly in perturbation theory it was necessary to break chiral symmetry on the lattice only through a bare mass term for the physical fermion. The chiral limit may be taken once the continuum limit is reached. We comment on the role of the mass term with examples elsewhere in field theory.

Low energy properties of the heavy vector fermions and electroweak symmetry breaking.

We discuss the properties of the heavy vector fermions with bare Dirac mass terms and an SU(2)[times]SU(2) global symmetry in the Yukawa interaction Lagrangian. Using the heat kernel expansion method we calculate their contributions to the low energy observables. We argue that these heavy fermions may be responsible for a soft dynamical symmetry breaking through their condensation. We also discuss the possibility of considering ordinary fermions as one part of the vector fermions within our model.

Chiral aspon model: An alternative fully gauged model of CP violation.

A chiral aspon model is constructed which avoids problems with quantum gravity violation of continuous global symmetries. The model contains only gauged local symmetries spontaneous symmetry breaking, has no vectorlike fermions with bare mass terms, solves strong $\mathrm{CP}$ conservation, and has calculable weak $\mathrm{CP}$ violation. The model requires axigluons with mass locked to the aspon scale.

STOCHASTIC QUANTIZATION OF NAMBU-JONA-LASINIO MODEL

Stochastic quantizations of the Nambu-Jona-Lasinio model with and without the bare mass term are carried out. It is shown that, although the linear fermion Langevin equation is not chiral-invariant, one obtains the chiral-invariant effective potential in the equilibrium limit when the bare mass vanishes. Numerical solutions of the growing order parameter and two kinds of effective potentials, which take qualitatively different forms if the bare mass is nonvanishing, are presented.

Dark matter and the observability of the electroweak transition

In a recent paper, Dimopoulos et al. argued that the standard calculation of the abundance of a dark matter particle would not be affected by the electroweak transition. They considered a model with a fermion whose mass arises entirely through its interaction with the Higgs boson. I consider somewhat more complicated, but much more realistic, models, in which the dark matter particle may also be a scalar, in which a more realistic range of couplings is chosen, and in which the possibility of bare mass terms is included. It is shown that for almost all of parameter space, the electroweak transition will have a negligible effect; a (barely) significant effect arises only if the particle is a scalar with a huge coupling and a bare mass term in excess of 1300 GeV.

A technocolor model with softly broken flavor symmetry

I describe an explicit technicolor model in which the interactions that give rise to the quark and lepton masses are generated by the exchange of massive gauge bosons as in extended technocolor models but in which the gauge bosons couple the quarks and leptons not directly to the technifermions, but to heavy fermions. Quark and lepton masses arise from box diagrams. The masses of the heavy fermions in this model come both from bare fermion mass terms and from the renormalizable interactions of a set of spinless fields. The model has a softly broken flavor symmetry that realizes the GIM suppression of FCNC effects as in a CTSM model.

The Recovery of the Chiral Symmetry in Lattice Gross-Neveu Model

The recovery of the chiral symmetry is carefully analyzed in the lattice Gross-Neveu model with Wilson's fermion, by using the effective potential obtained in the large N limit. It turns out that we have to introduce two bare coupling constants for four-fermi interactions as well as the bare mass term in order to obtain the chiral symmetric theory in the continuum limit. A method is proposed to extract the genuine order parameter that scales in the continuum limit.

Canonical formalism and quantization of world-line in a curved background metric

After discussing three various approaches to the canonical formalism for a world-line in a curved background metric we develop a new covariant formalism. It is based on the Hamiltonian which, for τ=s, is equal to the proper mass and it generates translations in proper times. The resulting Poisson-bracket relations are equivalent to the geodesic equation. In the quantized theory the classical 4-velocity\(u^\mu \)is replaced by the operator\(\gamma ^\mu \) (Dirac matrices); the resulting Heisenberg equations are quantum analogue of the Papapetrou's equation for a spinning particle in a gravitational field. Our theory also predicts in a natural way the existence of an infinite bare mass term in the lagrangian for the Dirac (or Klein-Gordon) equation and thus provides a deeper understanding of the «renormalization» procedure.

On the s-wave interaction between massive fermions and a gut magnetic monopole

We follow closely the line of analysis of Rubakov and Callan on the S-wave strong interaction between magnetic monopoles and fermions. Our observation is that the inclusion of a bare mass term for the fermions modifies in a non perturbative fashion the two dimensional Action of the condensate field. It induces a repulsive barrier. The coefficient of transmission is not computed here.

Erratum: Classification of mass matrices and the calculability of the Cabibbo angle

We have analyzed all possible 2 x 2 mass matrices with two nonzero elements in an attempt to find which matrices yield a reasonable value of the Cabibbo angle upon diagonalization. We do not concern ourselves with the origin of these mass matrices (spontaneous symmetry breaking, bare-mass term, etc.). We find that, in the limit m/sub u//m/sub c/..-->..0, only four possible relationships exist between sin/sup 2/theta/sub C/ and the quark mass ratio m/sub d//m/sub s/, only one of which is reasonable for the usual value of m/sub d//m/sub s/ (approx.1/20). This limits the possible forms of the quark mass matrix to be two in number, both of which have been discussed previously in the literature.

Classification of mass matrices and the calculability of the Cabibbo angle

We have analyzed all possible 2 x 2 mass matrices with two nonzero elements in an attempt to find which matrices yield a reasonable value of the Cabibbo angle upon diagonalization. We do not concern ourselves with the origin of these mass matrices (spontaneous symmetry breaking, bare-mass term, etc.). We find that, in the limit m/sub u//m/sub c/..-->..0, only four possible relationships exist between sin/sup 2/theta/sub C/ and the quark mass ratio m/sub d//m/sub s/, only one of which is reasonable for the usual value of m/sub d//m/sub s/ (approx.1/20). This limits the possible forms of the quark mass matrix to be two in number, both of which have been discussed previously in the literature.

Asymptotic freedom, Higgs scalars, and dynamical symmetry breaking

For some spontaneously broken non-Abelian gauge theories with Higgs scalars we show that the symmetry is dynamically broken, i.e., the asymmetric bare-mass terms become zero in the limit of infinite cutoff. Also, Higgs scalars satisfy the compositeness criteria in terms of renormalization constants. (AIP)