Effects Of Fermion Loops Research Articles

Fermions and Goldstone bosons in an asymptotically safe model

We consider a model in which Goldstone bosons, described by a SU(N) chiral nonlinear σ model, are coupled to an N-plet of colored fermions by means of a Yukawa interaction. We study the one-loop renormalization group flow and show that the non-Gaussian UV fixed point, which is present in the purely bosonic model, is lost because of fermion loop effects unless N is sufficiently large. We then add four-fermion contact interactions to the Lagrangian and show that in this case there exist several non-Gaussian fixed points. The strength of the contact interactions, predicted by the requirement that the theory flows towards a fixed point in the UV, is compared to the current experimental bounds. This toy model could provide an important building block of an asymptotically safe model of the weak interactions.

Fermion propagator in QED3 in the IR domain

We evaluate the fermion propagator in parity-conserving QED3 with N flavours, in the context of an IR domain approximation. This provides results which are non-perturbative in the loopwise expansion sense. We include fermion-loop effects, and show that they are relevant to the chiral symmetry breaking phenomenon, that can be understood in this context.

Quantum kinks: Solitons at strong coupling.

We examine solitons in theories with heavy fermions. These "quantum" solitons differ dramatically from semiclassical (perturbative) solitons because fermion loop effects are important when the Yukawa coupling is strong. We focus on kinks in a (1 + 1)-dimensional ${\ensuremath{\varphi}}^{4}$ theory coupled to fermions; a large-$N$ expansion is employed to treat the Yukawa coupling g nonperturbatively. A local expression for the fermion vacuum energy is derived using the WKB approximation for the Dirac eigenvalues. We find that fermion loop corrections increase the energy of the kink and (for large $g$) decrease its size. For large $g$, the energy of the quantum kink is proportional to $g$, and its size scales as $\frac{1}{g}$, unlike the classical kink; we argue that these features are generic to quantum solitons in theories with strong Yukawa couplings. We also discuss the possible instability of fermions to solitons.

Hadron masses in lattice QCD with internal fermion loops

Results are presented for light hadron and quark masses in lattice quantum chromodynamics with fermion vacuum polarization effects. A lattice of size 10×10×10×30 is used with a gauge coupling g 2=1.111 and n f=3. Previous qualitative results obtained with Wilson fermions on a smaller lattice at the same value of the coupling constant are confirmed and extended. The values for the hadron masses in units of the lattice spacing are significantly affected by the inclusion of three light fermion flavors, but the change can be reabsorbed to a large degree in a rescaling of the cutoff. For small quark mass the physical hadron mass estimates are comparable to the results with no loops and in reasonable agreement with phenomenology. Fermion loop effects on the other hand tend to change the dependence of the physical hadron masses on the quark mass, which in turn affects the estimates for the quark masses. These are found to be smaller than had previously been estimated. By considering heavy valence and light sea quarks, light quark masses are directly compared to the heavier quark masses.

Accelerated Langevin simulations of lattice QCD and other models

A fast algorithm is presented for simulating lattice field theories. The algorithm uses the Langevin equation and incorporates several innovations that greatly increase the speed and efficiency of the simulation. These innovations include the reduction of critical slowing down via Fourier acceleration and the use of a bilinear noise term to include the effects of fermion loops.

On fermion polarization effects in lattice gauge theories

The inclusion of internal fermion loop effects is discussed for the Wilson lattice fermions in SU(3) gauge theories with three flavors. The pseudofermion method is employed for taking into account the fermion determinant in the measure. Results with and without the fermion feedback are compared on a 4 × 4 × 4 × 16 lattice at β = 5.4 and 5.6. While for nonsinglet meson and baryon masses in lattice units the effects of fermion loops are significant, the results suggest that they can largely be accounted for by the change in the lambda parameter.

The quenched approximation in some two-dimensional field theories

We investigate the effect of suppressing closed fermion loops (the quenched approximation) in some (1 + 1)-dimensional field theories. In the Schwinger and Thirring models we find that effects of fermion loops on bound state masses can be absorbed in a rescaling of the coupling constant. In the Schwinger model an extra (decoupled) massless ghost appears and the order parameter 〈 ψψ〉 becomes infrared divergent. In an extension of the Schwinger model we compute effective lagrangians for the bound state spectrum in the quenched and unquenched case that look rather different.

Scale-scheme ambiguities in the Brodsky-Lepage-Mackenzie procedure

The recently proposed method of Brodsky, Lepage and Mackenzie for “eliminating scale ambiguities in perturbative QCD” yields different results in different renormalization schemes. We show that one cannot make a scheme-independent separation of fermion loop effects from other types of higher-order correction. The case of ϒ decay is discussed particularly.

Leptonic and hadronic corrections to mass and propagator ofW andZ bosons

Using the propagator formalism we establish more precisely the effects of fermion loops on the boson mass ratioMW2/MZ2 cos2 θ and on the energy dependence of the form factors associated to time-like or space-likeW, Z and γ exchanges. We calculate the corrections due to higher doublets of quarks including vector meson formation and to higher doublets of leptons for example a large number of neutrino types.