Roberge-Weiss endpoint and chiral symmetry restoration in $N_f = 2+1$ QCD

TL;DR

This study explores the relationship between the Roberge-Weiss endpoint transition and chiral symmetry restoration in 2+1 flavor QCD, finding evidence they coincide in the chiral limit, with the transition remaining second order in the 3D Ising class.

Contribution

It provides the first finite size scaling analysis of the Roberge-Weiss endpoint in 2+1 flavor QCD near the chiral limit, suggesting a possible coincidence of the two transitions.

Findings

Transition remains second order in the 3D Ising universality class.

Results are consistent with the Roberge-Weiss and chiral transitions coinciding in the chiral limit.

Critical scaling of the chiral condensate supports the transition's universality class.

Abstract

We investigate the fate of the Roberge-Weiss endpoint transition and its connection with the restoration of chiral symmetry as the chiral limit of $N_f = 2+1$ QCD is approached. We adopt a stout staggered discretization on lattices with $N_t = 4$ sites in the temporal direction; the chiral limit is approached maintaining a constant physical value of the strange-to-light mass ratio and exploring three different light quark masses, corresponding to pseudo-Goldstone pion masses $m_\pi \simeq 100, 70$ and 50 MeV around the transition. A finite size scaling analysis provides evidence that the transition remains second order, in the 3D Ising universality class, in all the explored mass range. The residual chiral symmetry of the staggered action also allows us to investigate the relation between the Roberge-Weiss endpoint transition and the chiral restoration transition as the chiral limit is approached: our results, including the critical scaling of the chiral condensate, are consistent with a coincidence of the two transitions in the chiral limit; however we are not able to discern the symmetry controlling the critical behavior, because the critical indexes relevant to the scaling of the chiral condensate are very close to each other for the two possible universality classes (3D Ising or O(2)).