Chiral Yukawa Model Research Articles

Higgs mass bounds from renormalization flow for a Higgs–top–bottom model

We study a chiral Yukawa model mimicking the Higgs-top-bottom sector of the standard model. We re-analyze the conventional arguments that relate a lower bound for the Higgs mass with vacuum stability in the light of exact results for the regularized fermion determinant as well as in the framework of the functional renormalization group. In both cases, we find no indication for vacuum instability nor meta-stability induced by top-fluctuations if the cutoff is kept finite but arbitrary. A lower bound for the Higgs mass arises for the class of standard bare potentials of \phi^4 type from the requirement of a well-defined functional integral (i.e., stability of the bare potential). This consistency bound can however be relaxed considerably by more general forms of the bare potential without necessarily introducing new meta-stable minima.

Reflection positivity of free overlap fermions

It is shown that free lattice fermions defined by overlap Dirac operator fulfill the Osterwalder-Schrader reflection positivity condition with respect to the link-reflection. The proof holds true in non-gauge models with interactions such as chiral Yukawa models.

Comparison of Boltzmann kinetics with quantum dynamics for a chiral Yukawa model far from equilibrium

Boltzmann equations are often used to describe the nonequilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of the Boltzmann and the Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by the Kadanoff-Baym equations is severely restricted in the case of the Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. In contrast to this standard Boltzmann equations cannot describe the process of quantum-chemical equilibration, and consequently also cannot feature the above separation of time scales.

Dynamical chiral symmetry breaking on the light front. II. The Nambu–Jona-Lasinio model

An investigation of dynamical chiral symmetry breaking on the light front is made in the Nambu--Jona-Lasinio model with one flavor and N colors. The analysis of the model suffers from extraordinary complexity due to the existence of a ``fermionic constraint,'' i.e., a constraint equation for the bad spinor component. However, to solve this constraint is of special importance. In classical theory, we can exactly solve it and then explicitly check the property of ``light-front chiral transformation.'' In quantum theory, we introduce a bilocal formulation to solve the fermionic constraint by the $1/N$ expansion. Systematic $1/N$ expansion of the fermion bilocal operator is realized by the boson expansion method. The leading (bilocal) fermionic constraint becomes a gap equation for a chiral condensate and thus if we choose a nontrivial solution of the gap equation, we are in the broken phase. As a result of the nonzero chiral condensate, we find an unusual chiral transformation of fields and nonvanishing of the light-front chiral charge. A leading-order eigenvalue equation for a single bosonic state is equivalent to a leading-order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wave functions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.

Dynamical chiral symmetry breaking on the light front: DLCQ approach

Dynamical chiral symmetry breaking in the DLCQ method is investigated in detail using a chiral Yukawa model closely related to the Nambu-Jona-Lasinio model. By classically solving three constraints characteristic of the light-front formalism, we show that the chiral transformation defined on the light front is equivalent to the usual one when bare mass is absent. A quantum analysis demonstrates that a nonperturbative mean-field solution to the ``zero-mode constraint'' for a scalar boson (sigma) can develop a nonzero condensate while a perturbative solution cannot. This description is due to our identification of the ``zero-mode constraint'' with the gap equation. The mean-field calculation clarifies unusual chiral transformation properties of fermionic field, which resolves a seemingly inconsistency between triviality of the null-plane chiral charge Q_5|0>=0 and nonzero condensate. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the PCAC relation and nonconservation of Q_5 in the broken phase.

Lattice chirality

The external fermion propagator and the internal fermion propagator in the overlap are given by different matrices. A generic problem (formulated by Pelissetto) faced by all chiral, non-local, propagators of Rebbi type is avoided in this manner. Nussinov-Weingarten-Witten mass inequalities are exactly preserved. I sketch how to obtain simple lattice chiral Yukawa models and simple expressions for covariant currents. Going beyond my oral presentation, I have added to the write-up several comments on Niedermayer's talk.

Monte-Carlo study of the Δϱ parameter

We present results concerning a lattice study of the electroweak ϱ-parameter. We have used an SU (2) × U (1) symmetric chiral Yukawa model built with Zaragoza fermions. The decoupling of the species doublers in this model is verified numerically. We find that the numerical data for Δϱ are well described by one-loop perturbation theory in the same finite volume and with the same finite cut-off. However, a finite cut-off can cause substantial deviations of Δϱ from the standard value, even in infinite volume.

Δ ρ in an SU(2)×U(1) chiral Yukawa model

We report on a simulation in progress of an SU(2) X U(1) fermion-Higgs model with two *non-degenerate* fermion doublets. The Zaragoza proposal for chiral lattice fermions is used; naive fermions are studied for comparison. The aims of this simulation are a non-perturbative study of the decoupling of species doublers, of triviality bounds on the Higgs and fermion masses and of the phenomenological quantity Delta-rho.

A class of chiral fermion models

We study the relation between the Roma and Zaragoza proposals for chiral fermions on the lattice. The fermion action in the Roma approach is shown to be equivalent to the one of the Zaragoza type. This result is used to perform a mean-field study of the phase diagram for chiral Yukawa models based on the Roma action. The phase diagram is compared with the one based on the Zaragoza model with the most local choice for the fermion interactions.

Ferrimagnetic phases in chiral Yukawa models.

We discuss the phase structure of chiral Yukawa models in the mean-field approximation. In particular, we examine under which conditions a ferrimagnetic phase appears, by calculating the slopes of possible second order phase transition lines near a critical point. Our results contrast with some statements which appeared in the literature recently.

Roma versus Zaragoza

The Roma and Zaragoza actions for chiral fermions on the lattice are shown to be essentially equivalent. The auxiliary fermion fields in the Roma model can be integrated out, and the resulting action is a special case of the Zaragoza approach. We use this result to perform a mean-field study of the phase diagram of chiral Yukawa models in the Roma formulation.

Phase diagram of a lattice SU(2) × SU(2) scalar-fermion model using the Zaragoza fermions

We present a calculation of the phase diagram of a SU(2) × SU(2) chiral Yukawa model with massless decoupled doublers, using a saddle point approach, both for small and large Yukawa coupling. Some preliminary MonteCarlo results are also known.

A better large N expansion for chiral Yukawa models

We consider the most general renormalizable chiral Yukawa model with SU(3) color replaced by SU( N c ), SU(2) L replaced by SU( N w ) and U(1) Y replaced by U (1) N w −1 in the limit N c → ∞, N w → ∞ with the ratio ρ= N w N c ≠ 0 , ∞ held fixed. Since for N w ⩾ 3 only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. The large N= N cN w expansion is expected to be no worse quantitatively in this model that in the purely scalar case and the N = ∞ limit is soluble even when the model is regularized non-perturbatively. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to m t ⩽ 1 itTeV.

Fermion mass and Yukawa coupling in lattice chiral Yukawa theory

We consider a chiral Yukawa model in which scalar and fermionic regulator fields appear in the Wilson-Yukawa coupling and all the physical fermion fields possess shift symmetry when the Yukawa coupling vanishes. With the fermionic hopping parameter expansion, it is shown that the fermion mass is proportional to the Higgs vacuum expectation value. It is also argued that the coupling of fermion to the external gauge field can be chiral if the hopping parameter of the scalar regulator field is taken to the critical value.

Massless decoupled doublers: Chiral Yukawa models and chiral gauge theories

We present a new method for regularizing chiral theories on the lattice. The arbitrariness in the regularization is used in order to decouple massless replica fermions. A continuum limit with only one fermion is obtained in perturbation theory and a Golterman-Petcher like symmetry related to the decoupling of the replicas in the non-perturbative regime is identified. In the case of Chiral Gauge Theories gauge invariance is broken at the level of the regularization, so our approach shares many of the characteristics of the Rome approach.

Mirror fermions in chiral gauge theories

Mirror fermions appear naturally in lattice formulations of the standard model. The phenomenological limits on their existence and discovery limits at future colliders are discussed. After an introduction of lattice actions for chiral Yukawa-models, a recent numerical simulation is presented. In particular, the emerging phase structure and features of the allowed region in renormalised couplings are discussed.

Chiral Yukawa models in the planar limit

We consider the most general renormalizable chiral Yukawa model with SU(3) color replaced by SU( N c), SU(2) L replaced by SU( N w) and U(1) Y replaced by U(1) N w−1 in the limit N c → ∞, N w → ∞ with the ϱ= N w N c ≠0 , ∞ held fixed. Since for N w⩾3 only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to m t⩽1 TeV.

1/ d estimates of boson and fermion masses and the critical lines for a U(1) L ⊗ U (1) R lattice Yukawa model

We find the phase diagram and calculate the boson and fermion masses of a chiral Yukawa model by applying the 1/ d expansion to the first subleading order in 1/ d. Most of the features found in numerical simulations are reproduced, including the increase of the fermion mass as the critical line is approached from the broken phase.

Chiral Yukawa models on the lattice and decoupling.

A new formulation on the lattice of a theory with a chiral fermion-scalar coupling and minimal field content is proposed. The arbitrariness in the regularization is used in order to decouple the replica fermions from the scalar. A continuum limit with just one fermion coupled to the scalar is obtained in perturbation theory and a Golterman-Petcher-like symmetry related to the decoupling of the replica fermions is identified.

Random walk approximation in a chiral Yukawa-model and global symmetries

The fermion propagator is investigated in a chiral Yukawa-model with explicit mirror fermions applying the random walk approximation to the hopping parameter expansion. It is shown that the globalSU(2)L⊗SU(2)R symmetry breaking due to the mass splitting within fermion doublets does influence the critical behaviour of the fermion spectrum in the continuum limit. In particular, in the case of a mirror pair of split doublets, whereSU(2)L⊕SU(2)R is broken toSU(2)L, no evidence is found for a dynamical spectrum doubling at infinitely strong bare Yukawa-couplings, in contrast to the case with degenerate doublets andSU(2)L⊗SU(2)R symmetry.