Speaker
Description
The chiral phase transition in (2+1)-flavor QCD is expected to be of second order, if the breaking of axial anomaly remains sufficiently strong at the chiral phase transition temperature $T_c$ [1]. This observation is supported by the lattice QCD calculations [2]. However, the FRG model calculations suggest that the scaling window may be small [3], within which the universal scaling relations hold true and remain valid. Furthermore, whether or not the $U_A\,(1)$ symmetry gets effectively restored at $T=T_c\,\,$ remains to be controversial. These suggest that a more detailed analysis of universal critical behaviour close to $T=T_c\,\,$ is needed, as well as one also requires a direct determination of the relevant universality class for the chiral phase transition [1,4] in (2+1)-flavor QCD.
In this talk, we present new results from a study of the scaling behaviour of an improved order parameter $M=M_\ell-H\,\chi_\ell\,\,$ for chiral symmetry restoration in the light $2$-flavor sector of (2+1)-flavor QCD. Here $M_\ell\,\,$ and $\chi_\ell\,\,$ are multiplicatively renormalised light quark chiral condensate and chiral susceptibility respectively, with $H=m_\ell\,/\,m_s\,\,$ being the light-to-strange quark mass ratio.
We construct ratios of $M$ for two different values of the light quark mass, $m_\ell$ (or $H$ equivalently) at $T\,$ close to $T_c\,$. In the scaling region, we find a unique intersection point for these ratios at $T=T_c$ , which allows us not only to determine $T_c\,\,$ but also the underlying universality class of the chiral phase transition, from the knowledge of the critical exponent $\delta$ .
The approach followed here in this work, will allow one to further constrain the influence of axial anomaly on the universal critical behaviour in (2+1)-flavor QCD. It also provides a new way of determining the chiral phase transition temperature $T_c\,$, which strengthens the upper bound on the temperature range, within which a critical end point in QCD for non-vanishing chemical potential values can possibly be found in heavy-ion experiments.
[1] R. D. Pisarski and F. Wilczek, Phys. Rev. D 29 (1984) 338
[2] H. T. Ding et al. [HotQCD], Phys. Rev. Lett. 123 (2019) 062002
[3] J. Braun et al., Phys. Rev. D 102 (2020) 056010
[4] A. Pelissetto and E. Vicari, Phys. Rev. D 88 (2013) 105018
