Nature of the chiral phase transition of two flavor QCD from an imaginary chemical potential with HISQ fermions

The nature of the thermal phase transition of two flavor QCD in the chiral limit has an important implication for the QCD phase diagram. We carry out lattice QCD simulations in an attempt to address this problem. Simulations are conducted with a Symanzik-improved gauge action and the Highly Improved Staggered Quark fermion action. Within the imaginary chemical potential formulation, five different quark masses, $am=0.020$, 0.018, 0.015, 0.013, 0.010, and four different lattice volumes, Nₛ=8, 12, 16, 20, with temporal extent Nₜ=4 are used to explore the scaling behavior. At each of the quark masses, the Binder cumulants of the chiral condensate on different lattice volumes approximately intersect at one point. We find that at the intersection point the Binder cumulant B₄(am,aμc) is around 3, which deviates from the $Z(2)$ universality class value 1.604. However, based on the expectations of $Z(2)$ criticality, the fitting result only with the data from the largest lattice volume Nₛ=20 agrees well with earlier result [Phys. Rev. D 90, 074030 (2014). This fact implies that, although the finite cutoff effects could be reduced with Highly Improved Staggered Quark fermions even on Nₜ=4 lattices, larger lattices with spatial extent Nₛ>=20 for such studies are needed to control finite volume effects.