Perturbative Yukawa theory at finite density: the role of masses and renormalization group flow at two loops

TL;DR

This paper analyzes Yukawa theory at finite density, focusing on how masses and renormalization group flow influence the equation of state up to two loops, with analytical calculations for arbitrary masses.

Contribution

It provides analytical two-loop integral calculations for Yukawa theory with arbitrary masses and explores the impact of flavor number on renormalization group flow.

Findings

Analytical expressions for two-loop integrals with arbitrary masses.

Insights into the flavor dependence of renormalization group flow.

Enhanced understanding of thermodynamics in dense fermionic systems.

Abstract

Yukawa theory at vanishing temperature provides (one of the ingredients for) an effective description of the thermodynamics of a variety of cold and dense fermionic systems. We study the role of masses and the renormalization group flow in the calculation of the equation of state up to two loops within the MSbar scheme. Two-loop integrals are computed analytically for arbitrary fermion and scalar masses, and expressed in terms of well-known special functions. The dependence of the renormalization group flow on the number of fermion flavors is also discussed.