Eigenvalue spectra of QCD and the fate of UA(1) breaking towards the chiral limit

Olaf Kaczmarek,Sayantan Sharma,Lukas Mazur

doi:10.1103/physrevd.104.094518

Abstract

The finite temperature phase diagram of QCD with two massless quark flavors is not yet understood because of the subtle effects of anomalous $U_A(1)$ symmetry. In this work we address this issue by studying the fate of the anomalous $U_A(1)$ symmetry in $2+1$ flavor QCD just above the chiral crossover transition temperature $T_c$, lowering the light quark mass towards the chiral limit along line of constant physical strange quark mass. We use the gauge configurations generated using the Highly Improved Staggered Quark (HISQ) discretization on lattice volumes $32^3\times8$ and $56^3\times 8$ to study the renormalized eigenvalue spectrum of QCD with valence overlap Dirac operator. We have implemented new numerical techniques that have allowed us to measure about $100$-$200$ eigenvalues of the gauge ensembles with light quark masses $\gtrsim 0.6$ MeV. From a detailed analysis of the dependence of the renormalized eigenvalue spectrum and $U_A(1)$ breaking observables on the light quark mass, our study suggests $U_A(1)$ is broken at $T\gtrsim T_c$ even when the chiral limit is approached.

Highlights

Understanding the phase diagram of strongly interacting matter described by quantum chromodynamics (QCD) is one of the most challenging areas of contemporary research
In this work we address this issue by studying the fate of the anomalous UAð1Þ symmetry in 2 þ 1 flavor QCD just above the chiral crossover transition temperature Tc, lowering the light quark mass toward the chiral limit along the line of constant physical strange quark mass
In this work we report on the eigenvalue spectrum and the fate of anomalous UAð1Þ symmetry in the chiral symmetry restored phase of QCD on large volume Nτ 1⁄4 8 lattices as we approach the chiral limit along the line of constant physical strange quark mass

Summary

INTRODUCTION

Understanding the phase diagram of strongly interacting matter described by quantum chromodynamics (QCD) is one of the most challenging areas of contemporary research. Recent results on the topological susceptibility, which quantifies the UAð1Þ breaking in the chiral symmetry restored phase, shows a surprising trend for two-flavor QCD as a function of the quark mass. It vanishes at some critical value of the light quark mass [35,36]. We study the eigenvalue spectrum for QCD with HISQ fermions near Tc with a valence overlap Dirac operator and observe the dependence of the renormalized spectrum on light quark mass ml toward the chiral limit. We conclude by discussing the implications and a future outlook of our present work

NUMERICAL SETUP

Accelerating the overlap Dirac matrix diagonalization toward the chiral limit

EIGENVALUE SPECTRUM OF QCD WITH HISQ FERMIONS TOWARD THE CHIRAL LIMIT

QUANTIFYING UAð1Þ BREAKING IN THE CHIRAL LIMIT

CONCLUSIONS AND OUTLOOK