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We investigate the phase structure of QCD with 3 degenerate quark flavors asfunction of the degenerate quark masses at vanishing baryon number density. Weuse the Highly Improved Staggered Quarks on lattices with temporal extent$N_{t}=6$ and perform calculations for six values of quark masses, which in thecontinuum limit correspond to pion masses in the range $80~{\rm MeV} \lesssimm_{\pi} \lesssim 230~$MeV. By analyzing the volume and temperature dependenceof the chiral condensate and chiral susceptibility we find no direct evidencefor a first order phase transition in this range of pion mass values. Relyingon the universal scaling behaviors of the chiral observables near ananticipated chiral critical point, we estimate an upper bound for the criticalpion mass, $m_\pi^c \lesssim$ 50 MeV, below which a region of first orderchiral phase transition is favored.

Chiral phase structure of three flavor QCD at vanishing baryon number density