On higher-order corrections in a four-fermion Lifshitz model

TL;DR

This paper investigates a Lifshitz four-fermion model with z=3, revealing that two-loop Lorentz-violating corrections are significant, limiting the model's predictive power regarding particle propagation effects.

Contribution

It provides a detailed two-loop analysis of Lorentz-violating corrections in a renormalizable Lifshitz four-fermion model, highlighting limitations in its predictive capacity.

Findings

Two-loop corrections are quadratic in the cutoff.

Lorentz-violating effects are too large to be physical.

Model remains renormalizable with dynamical mass generation.

Abstract

We study a flavour-violating four-fermion interaction in the Lifshitz context, in 3+1 dimensions and with a critical exponent z=3. This model is renormalizable, and features dynamical mass generation, as well as asymptotic freedom. At one-loop, it is only logarithmically divergent, but the superficial degree of divergence of the two-point functions is 3. We calculate the two-loop corrections to the propagators, and show that, at this order, the Lorentz-violating corrections to the IR dispersion relation are quadratic in the cut off. Furthermore, these corrections are too important to represent a physical effect. As a consequence, the predictive power of the model in terms of Lorentz-violating effects in the propagation of particles is limited.