On the computation of one-loop amplitudes with external fermions in 4D heterotic superstrings

We present the technical tools needed to compute any one-loop amplitude involving external spacetime fermions in a four-dimensional heterotic string model à la Kawai-Lewellen-Tye. As an example, we compute the one-loop three-point amplitude with one “photon” and two external massive fermions (“electrons”). As a check of our computation, we verify that the one-loop contribution to the Anomalous Magnetic Moment vanishes if the model has spacetime supersymmetry, as required by the supersymmetric sum rules.     

Fermionic langevin equations without kernel and Zwanzinger's gauge fixing procedure

We study the compatibility of Zwanzinger's gauge fixing procedure and the Langevin equations without kernel for massive fermions from the renormalization theory point of view. The UV divergent part of the QED fermionic propagator is computed at the one-loop level. The problems encountered in its subtraction are analyzed.     

Exotic phases of finite temperature gauge theories

We calculate the phase diagrams at high temperature of SU(N) gauge theories with massive fermions by minimizing the one-loop effective potential. Considering fermions in the adjoint (Adj) representation at various N we observe a variety of phases when N_f2 Majorana flavours and periodic boundary conditions are applied to fermions. Also the confined phase is perturbatively accessible. For N=3, we add Fundamental (F) representation fermions with antiperiodic boundary conditions to adjoint QCD to show how the Z(3)-symmetry breaks in the confined phase.     

Lorentz violation from the Higgs portal

We study bounds and signatures of models where the Higgs doublet has an inhomogeneous mass or vacuum expectation value, being coupled to a hidden sector that breaks Lorentz invariance. This physics is best described by a low-energy effective Lagrangian in which the Higgs speed-of-light is smaller than c; such effect is naturally small because it is suppressed by four powers of the inhomogeneity scale. The Lorentz violation in the Higgs sector is communicated at tree level to fermions (via Yukawa interactions) and to massive gauge bosons, although the most important effect comes from one-loop diagrams for photons and from two-loop diagrams for fermions. We calculate these effects by deriving the renormalization-group equations for the speed-of-light of the Standard Model particles. An interesting feature is that the strong coupling dynamically makes the speed-of-light equal for all colored particles.     

Radiative decay of mesons and anomaly in 2+1 dimensions

In 2+1 space-time, we study the radiative decay of mesons with Yukawa couplings to two and four component fermions. In a four component theory, the electromagnetic current is free of parity odd radiative corrections; however an axialU(1) current is shown to develop a finite vacuum expectation value. Unlike even dimensions this anomaly is temperature dependent and does not play any role in the radiative decay. We calculate the effective action for the mesons and show that a finite kinetic term for these fields is induced at the one-loop level and vanishes as the temperature goes to infinity.     

Dynamical symmetry breaking in the SU (2) gauge theory

Properties of vacua of the SU(2) gauge theory containing massless and massive fermions are investigated within the one-loop approximation. As a result of a condensation of composite scalar made of gauge fields, some gauge fields acquire a mass and the original SU(2) gauge symmetry is suggested to breake down to U (1). We evaluate the effective potential for the constant magnetic field and then extract the so-called dielectric permeability κ from it. The phase is called paramagnetism for positive κ, perfect paramagnetism for vanishing κ and ferromagnetism for negative κ. The choice of a favorable phase is determined by the value of the coupling constant and the number and the mass of fermions. The perfect paramagnetic phase is most precisely studied. It is shown that solitons with non-zero charges carry divergent energies. Then, the electric flux around the charge is shown to be squeezed into a string in that phase.     

Mass bounds in a Z 2 scalar-fermion model

The lattice regularized Z ₂ scalar-fermion model using staggered fermions in four dimensions is investigated in the broken symmetry phase. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type of Yukawa interaction. Triviality upper bound and vacuum stability lower bound on the mass of the scalar particle are numerically estimated. Qualitative agreement between Monte Carlo data and one-loop perturbative results is obtained. Systematic errors of the upper bound are estimated. At strong Yukawa coupling, we see some quantitative disagreements due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.     

Algebraic algorithm for the computation of one-loop Feynman diagrams in lattice QCD with Wilson fermions

We describe an algebraic algorithm which allows us to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions.     

Left-right symmetry and finite one-loop Dirac neutrino mass

We present a modified version of the left-right symmetric model that includes a charged singlet scalar boson where the neutrino is massless at the tree level and acquires a smal and finite Dirac mass at the one-loop level. In the case if three families of fermions, it predicts m_ve=0 and the other two neutrinos are massive with v_τ lighter than v_v. The model also predicts large magnetic moments and v_μ→v_e+ψ decay rates. The new feature of the model is the inclusion of singlet charged heavy fermions which mix with the light quarks and leptons, leading to the existence of tree-level flavor-changing neutral currents, which can provide tests of the model.     

One-loop diagrams in lattice QCD with Wilson fermions

A large number of one-loop integrals emerging in a gauge perturbation theory on a lattice with Wilson fermions at r = 1 are evaluated with the use of the Burgio-Caracciolo-Pelissetto algorithm and the FORMpackage. In the bosonic case, an explicit analytical form of the recursion relations is presented.     

Thermodynamics of the System of Massive Dirac Fermions in a Uniform Magnetic Field

We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels,through which all thermodynamic quantities can be obtained.Making use of the Abel-Plana formula,these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable b=2eB/T~2.The zero-field magnetic susceptibility is expanded at zero mass,and the leading order term is logarithmic.We also calculate scalar,vector current,axial vector current and energy-momentum tensor of the system through ensemble average approach.Mass correction to chiral separation effect is discussed.For massless chiral fermions,our results recover the chiral magnetic effect for right-and left-handed fermions,as well as chiral separation effect.     

The sigma-model with Wilson lattice fermions

The σ-model with Wilson fermions is considered in one-loop lattice perturbation theory and in the hopping-parameter expansion at large bare couplings. Chiral-symmetry restoration in the large cut-off limit of perturbation theory is only possible if asymmetric counterterms are added to the lattice action. In the hopping-parameter expansion at infinitely large bare Yukawa coupling, dynamical parity doubling of the fermion occurs.     

Effective Lagrangian of SU（2） Yang—Mills Theory in the Presence of Fermions

We derive the one-loop effective action of SU(2) Yang-Mills theory in the presence of fermions in the low energy limit.This result is presented by separating the topological degrees,which describe the non-Abelian monopoles from the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2) Yang-Mills theory.     

Penguin and box diagrams in unitary gauge

We evaluate one-loop diagrams in the unitary gauge that contribute to flavor-changing neutral current (FCNC) transitions involving two and four fermions. Specifically, we deal with penguin and box diagrams arising within the standard model (SM) and in nonrenormalizable extensions thereof with anomalous couplings of the W boson to quarks. We show explicitly in the SM the subtle cancellation among divergences from individual unitary-gauge contributions to some of the physical FCNC amplitudes and derive expressions consistent with those obtained using R _ξ gauges in the literature. Some of our results can be used more generally in certain models involving fermions and gauge bosons which have interactions similar in form to those we consider.     

Gauge group breaking by Wilson loops

We examine the breaking of gauge symmetries by Wilson loops in the Hosotani-Toms model by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions. For anti-periodic fermions, all gauge groups remain unbroken. For periodic fermions, the groups G₂, F₄ and E₈ are broken by quantum corrections due to fermions in any irreducible representation, whereas E₆, E₇ and the classical groups only break if the fermion representation is in the same congruency class as the adjoint.     

Mass terms and mass renormalization for Susskind fermions

We discuss the symmetry properties of a geometrically motivated mass term giving different masses to the four flavours of Susskind fermions. Using this mass term we calculate the fermion self-energy in weak coupling perturbation theory at the one-loop level as well as the relation between the fermion masses on the lattice and in the continuum.     

General formulae for $f_1 \to f_2 \gamma$

At one-loop level the decay , where f₁ and f₂ are two spin-1/2 particles with the same electric charge, is mediated by a boson B and a spin-1/2 fermion F. The boson B may have either spin - interacting with the fermions through the Dirac matrices 1 and - or spin 1 - with V+A and V-A couplings to the fermions. I give general formulae for the one-loop electroweak amplitude of in all these cases. Received: 24 February 2003 / Revised version: 26 March 2003 / Published online: 2 June 2003     

Superconducting cosmic strings with coupled zero modes

The physics of fermion zero modes on bosonic superconducting strings is investigated. The charged field at the core couples left movers to right movers, giving an effective theory of massive fermions on the string world sheet. Despite their mass, the fermions still contribute to the bosonic current through the two-dimensional anomaly. Even when the Higgs field is neutral and there is no anomaly, the string remains superconducting provided the sum of the charges of the zero modes do not vanish. The mechanism is closely analogous to a theory of superconductivity proposed by Fröhlich.     

The sfermion-mass spectrum of the MSSM at the one-loop level

The sfermion-mass spectrum of the minimal supersymmetric standard model is investigated at the one-loop level. An on-shell scheme has been specified for renormalization of the basic breaking parameters of the sfermionic sector. Owing to SU(2)-invariance, the soft-breaking mass parameters of the left-chiral scalar fermions of each isospin doublet are identical. Thus, one of the sfermion masses of each doublet can be expressed in terms of the other masses and receives a mass shift at the one-loop level with respect to the lowest-order value, which can be of O(10 GeV). Both strong and electroweak contributions have been calculated for scalar quarks and leptons.Received: 26 June 2003, Revised: 24 September 2003, Published online: 7 November 2003