The QCD chiral phase transition for different numbers of quark flavours

Abstract

We present results from a comprehensive study of the location of the chiral critical surface, which separates regions of first-order chiral transitions from analytic crossovers, in the bare parameter space of lattice QCD with unimproved staggered fermions. We study the theories with $N_f\in[2,8]$ and trace the chiral critical surface along diminishing lattice spacing, with $N_\tau=\{4,6,8\}$. This allows for an extrapolation to the lattice chiral limit, where the surface has to terminate in a tricritical line, employing known tricritical scaling relations. Knowing the phase structure in the lattice bare parameter space allows to draw conclusions for the approach to the continuum and chiral limits taken in the appropriate order. Our data provide evidence for the continuum chiral limit to feature a second-order transition for all $N_f\in[2,7]$. We perform an analogous scaling analysis with already published data from $N_f=3$ $O(a)$-improved Wilson fermions, which is also consistent with a second-order transition in the continuum. A modified Columbia plot reflecting those results is suggested.