# Critical end points in (2+1)-flavor QCD with imaginary chemical potential

## TL;DR

This study investigates the critical quark mass in (2+1)-flavor QCD with imaginary chemical potential using the HISQ action, finding no evidence of first order transitions at low quark masses and suggesting a possible coincidence of RW and chiral transitions in the chiral limit.

## Contribution

The paper provides new results using the HISQ action in the RW plane, showing the absence of first order transitions at low quark masses and exploring the relation between RW and chiral transitions.

## Key findings

- No evidence of first order transitions at lowest quark masses with HISQ.
- Chiral observables are sensitive to the RW transition.
- RW and chiral transitions may coincide in the chiral limit.

## Abstract

We present here the results from an ongoing determination of the critical quark mass in simulations of (2+1)-flavor QCD with an imaginary chemical potential. Studies with unimproved actions found the existence of a critical quark mass value at which the crossover transition ends on a second order phase transition and becomes first order for smaller values of the quark mass for the case of both vanishing and imaginary chemical potential. We use the Highly Improved Staggered Quark (HISQ) action and perform calculations in the Roberge-Weiss (RW) plane, where the value of the critical mass is expected to be largest. The lowest quark mass value used in our simulation corresponds to the pion mass $m_\pi$, down to $40$ MeV. Contrary to calculations performed with unimproved actions we find no evidence for the occurrence of first order transitions at the smallest quark mass values explored so far. Moreover we also show that the chiral observables are sensitive to the RW transition. Our results also indicate that the RW transition and chiral transition could coincide in the chiral limit.