Regularizing thermo and magnetic contributions within nonrenormalizable theories

TL;DR

This paper proposes a regularization scheme for thermo and magnetic effects in nonrenormalizable theories, improving physical consistency of thermomagnetic observables in the Polyakov--Nambu--Jona-Lasinio model.

Contribution

It introduces a novel regularization method that isolates divergences and applies it to the PNJL model, enhancing the physical reliability of thermomagnetic predictions.

Findings

More consistent thermomagnetic behavior observed with the new scheme.

Naive regularization leads to unphysical results at high temperatures.

The scheme improves agreement with expected physical properties.

Abstract

The importance of implementing a proper regularization procedure in order to treat thermo and magnetic contributions within nonrenormalizable theories is investigated. Our study suggests that potential divergences should be isolated into the vacuum and purely magnetic contributions and then regularized while the convergent thermomagnetic contributions should be integrated over the full momentum range. This prescription is illustrated by applying the proper time formalism to the two flavor Polyakov--Nambu--Jona-Lasinio model, whose magnetic field dependent coupling has been recently determined. Observables such as the pressure, magnetization, speed of sound squared, and specific heat evaluated within our scheme are compared with results furnished by other three possible prescriptions. We show that these quantities display a thermomagnetic behavior which is physically more consistent when our scheme is adopted. In particular, we demonstrate that naively regulating the (entangled) vacuum, magnetic and thermomagnetic contributions leads to physically inconsistent results especially at the high temperature domain.