The curvature of the chiral phase transition line for small values of ${\mu }_B$

Abstract

We present preliminary results from an ongoing calculation to determine the curvature of the chiral phase transition line in the chiral limit along the light-light, light-strange and strange-strange chemical potential directions. We do this by studying the appropriate $\mu$-derivatives of the chiral condensate as a function of the quark mass and comparing them to the scaling predictions of $3d$-$O(N)$ theory. We work at a fixed lattice spacing, $N_{\tau }=6$ and at four different quark masses $m_{\pi }\approx$ 140, 110, 90 and 80 MeV. For the light quark curvature, we obtain a value 0.03$⩽{\kappa }_{ll}⩽$0.11. We also find that both strange and light-strange curvatures are around an order of magnitude smaller. Currently, the light-strange curvature is the least constrained curvature and could have either sign, though our results seem to prefer a slightly negative value.

Comments: Contribution to the proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, Kobe Japan