On the existence of a phase transition for QCD with three light quarks

We report full QCD simulations on a ${16}^3$×4 lattice. For two degenerate flavors no finite-temperature phase transition is found for quark masses of ma=0.01 and 0.025, where a is the lattice spacing, while for three degenerate flavors a first-order transition is easily seen for ma=0.025. Nature, with nearly massless up and down quarks and one heavier strange quark, lies between these two cases. For ${\mathit{m}}_{\mathit{u},}$da=0.025 and ${\mathit{m}}_{\mathit{s}}$a=0.1 we find that ${\mathit{m}}_{\mathit{K}}$/${\mathit{m}}_{\mathrm{\rho }}$=0.46(1) and that no transition occurs, calling into question the existence of a QCD phase transition.