Towards the chiral phase transition in the Roberge-Weiss plane

TL;DR

This paper investigates the nature of phase transitions in QCD with imaginary chemical potential, showing that the RW endpoint is second order and belongs to the Z(2) universality class, with implications for chiral symmetry restoration.

Contribution

It provides a finite size scaling analysis demonstrating the second order nature of the RW endpoint and its universality class in (2+1)-flavor QCD with physical strange quark mass.

Findings

The RW endpoint is second order for light quark masses above a threshold.

The chiral condensate behaves like an energy operator in the effective spin model.

Critical temperatures for RW and chiral transitions coincide at the RW plane.

Abstract

We discuss the interplay between chiral and center sector phase transitions that occur in QCD with an imaginary quark chemical potential $\mu=i(2n+1) \pi T/3$. Based on a finite size scaling analysis in (2+1)-flavor QCD using HISQ fermions with a physical strange quark mass and a range of light quark masses, we show that the endpoint of the line of first-order Roberge-Weiss (RW) transitions between center sectors is second order for light quark masses $m_l\ge m_s/320$, and that it belongs to the $3$-d, $Z(2)$ universality class. The operator for the chiral condensate behaves like an energy-like operator in an effective spin model for the RW phase transition. As a consequence, for any non-zero value of the quark mass, the chiral condensate will have an infinite slope at the RW phase transition temperature, $T_{RW}$. Its fluctuation, the disconnected chiral susceptibility, behaves like the specific heat in $Z(2)$ symmetric models and diverges in the infinite volume limit at the RW phase transition temperature $T_{RW}$ for any non-zero value of the light quark masses. Our analysis suggests the critical temperatures for the RW phase transition and the chiral phase transition coincide in the RW plane. On lattices with temporal extent $N_\tau=4$, we find in the chiral limit $T_{\chi}=T_{RW}=195(1)~$MeV.