Divergences in the quark number susceptibility : The origin and a cure

TL;DR

The paper investigates the quadratic divergence in lattice quark number susceptibility, demonstrating its origin in free fermions and proposing a subtraction method that simplifies higher-order susceptibility calculations in interacting theories.

Contribution

It introduces a straightforward subtraction technique to remove divergences in quark number susceptibility calculations on the lattice, applicable to both free and interacting theories.

Findings

Divergence exists even in free fermion theories with a cut-off regulator.

A subtraction method effectively removes the divergence in free lattice theories.

The divergence removal technique is successful in interacting theories, reducing computational effort.

Abstract

Quark number susceptibility on the lattice, obtained by merely adding a $\mu N$ term with $\mu$ as the chemical potential and $N$ as the conserved quark number, has a quadratic divergence in the cut-off $a$. We show that such a divergence already exist for free fermions with a cut-off regulator. While one can eliminate it in the free lattice theory by suitably modifying the action, as is popularly done, it can simply be subtracted off as well. Computations of higher order susceptibilities, needed for estimating the location of the QCD critical point, then need a lot fewer number of quark propagators at any order. We show that this method of divergence removal works in the interacting theory.