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

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.