QCD phase transition in the chiral limit

Abstract: We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{\rm MeV}\lesssim m_\pi\lesssim 163~{\rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV. We also present some preliminary calculations on interplay of effective $U_A(1)$ restoration and chiral phase transition towards chiral limit.