Phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential

Abstract

We determine the chiral phase transition line in $(2+1)$-flavor QCD for small values of the light quark chemical potential. We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. To do so we extend earlier studies of the magnetic equation of state in $(2+1)$-flavor QCD to finer lattice spacings, $aT=1/8$. We use these universal scaling properties of the chiral order parameter to extract the curvature of the transition line at two values of the cutoff, $aT=1/4$ and $1/8$. We find that cutoff effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain ${T}_{c}({\ensuremath{\mu}}_{q})/{T}_{c}(0)=1\ensuremath{-}0.059(2)(4)({\ensuremath{\mu}}_{q}/T{)}^{2}+\mathcal{O}({\ensuremath{\mu}}_{q}^{4})$.