On curing the divergences in the quark number susceptibility

TL;DR

This paper addresses the divergence issue in lattice QCD when adding chemical potential linearly, proposing a subtraction method to achieve a finite continuum limit, validated through numerical tests on quenched quark number susceptibilities.

Contribution

It introduces a subtraction technique for divergences caused by chemical potential in lattice QCD, enabling a finite continuum limit.

Findings

Divergences are inherited from the continuum theory.

Subtraction method successfully removes divergences.

Finite continuum limit achieved in quenched simulations.

Abstract

Adding chemical potential $\mu$ linearly as $\mu N$ to the lattice QCD action, where $N$ is a conserved quark/baryon number, leads to a quadratic divergence as $a^{-2}$. We argue that it is inherited from the continuum theory and can be subtracted off on the lattice following a similar manner in the continuum. We test this idea for quenched quark number susceptibilities and demonstrate a finite continuum limit numerically.