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The finite temperature QCD transition for physical quark masses is acrossover. For smaller quark masses a first-order phase transition is expected.Using Symanzik improved gauge and stout improved fermion action for 2+1 flavourstaggered QCD we give estimates/bounds for the phase line separating thefirst-order region from the crossover one. The calculations are carried out ontwo different lattice spacings. Our conclusion for the critical mass is $m_0\lesssim 0.07 \cdot m_{phys}$ for $N_T=4$ and $m_0 \lesssim 0.12 \cdotm_{phys}$ for $N_T=6$ lattices.

The nature of the finite temperature QCD transition as a function of the quark masses