Quark mass dependence of a QCD critical point and structure of the Columbia plot

Abstract We study the quark-mass dependence of the QCD critical point at varying bare up/down quark masses with fixed strange quark mass. We explore the corresponding second-order critical surface in the three-dimensional Columbia plot and study the extension of the associated crossover hyperplane at real and imaginary baryon chemical potential. To this end, we employ a by now well-tested combination of lattice Yang–Mills theory and a (truncated) version of Dyson–Schwinger equations at $$N_{f}=2+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> quark flavours. We find evidence for a positive curvature of the second-order surface at (large) real chemical potential and a crossover region for imaginary chemical potential. Our results support the notion of a tricritical point at finite chemical potential in the chiral limit.