The curvature of the critical surface (m_ud,m_s)^{crit}(mu): a progress report

Understand

At zero chemical potential mu, the order of the temperature-driven quark-hadron transition depends on the quark masses m_{u,d} and m_s.

• Along a critical line bounding the region of first-order chiral transitions in the (m_{u,d},m_s) plane, this transition is second order.
• When the chemical potential is turned on, this critical line spans a surface, whose curvature at mu=0 can be determined without any sign or overlap problem.
• Our past measurements on N_t=4 lattices suggest that the region of quark masses for which the transition is first order shrinks when mu is turned on, which makes a QCD chiral critical point at small mu/T unlikely.