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

Rajiv V Gavai,Sayantan Sharma

doi:10.1016/j.physletb.2015.07.036

Rajiv V Gavai, Sayantan Sharma

Open Access

https://doi.org/10.1016/j.physletb.2015.07.036

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Abstract

Quark number susceptibility on the lattice, obtained by merely adding a μN term with μ 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 exists 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.

Highlights

The phase diagram of the strongly interacting matter described by Quantum Chromodynamics (QCD) has been a subject of intense research in the recent years
We show that no further divergences are observed once the free theory divergence is subtracted from the quark number susceptibilities
The higher order quark number susceptibilities needed for locating the critical point using the Taylor expansion approach are easier to compute in the linear case as well

Summary

Introduction

The phase diagram of the strongly interacting matter described by Quantum Chromodynamics (QCD) has been a subject of intense research in the recent years. Introducing the chemical potential by a μN-term, where N is the corresponding conserved charge, leads to both much fewer terms and lesser cancellations at the same m [17], thereby reducing the computational cost up to 60% at eighth order; more savings ought to accrue by going to even higher orders Will this improve the precision of the location of the critical point but more precise Taylor coefficients and more terms in the Taylor expansion can potentially lead to a better control of the QCD equation of state at finite baryon density which will be needed for the analysis of the heavy-ion data from the beam energy scan at RHIC as well as the future experiments at FAIR and NICA. We discuss its possible consequences and the extensions to higher order QNS

Thermodynamics of non-interacting fermions

Continuum free fermions

Quenched results on the lattice

Findings

Summary