Exploring QCD phase diagram at vanishing baryon density on the lattice

I report on the current status of QCD phase diagram at vanishing baryon density. I focus on the QCD phase diagram with three degenerate quark flavor using Highly Improved Staggered Quarks on $N_τ=6$ lattices. No evidence of a first order phase transition in the pion mass window of $80\lesssim m_π \lesssim 230$MeV is found. The pion mass at the critical point where the chiral first order phase transition ends is estimated to be $m^c_π \lesssim 45$ MeV.

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