Curvature of the chiral phase transition line from the magnetic equation of state of (2+1)-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge ($B, S$) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energy-like scaling variable that enters the parametrization of the MEoS, allows to explore the variation of $T_c(\mu_B,\mu_S) = T_c ( 1 - (\kappa_2^B \hat{\mu}_B^2 + \kappa_2^S \hat{\mu}_S^2 + 2\kappa_{11}^{BS} \hat{\mu}_B \hat{\mu}_S))$ along different lines in the $(\mu_B,\mu_S)$ plane. On lattices with fixed cut-off in units of temperature, $aT=1/8$, we find $\kappa_2^B=0.015(1)$, $\kappa_2^S=0.0124(5)$ and $\kappa_{11}^{BS}=-0.0050(7)$. We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10\% larger than along the strangeness neutral line. The latter differs only by about $3\%$ from the curvature on a line of vanishing strange quark chemical potential, $\mu_s=0$. We also show that close to the chiral limit the strange quark mass contributes like an energy-like variable in scaling relations for pseudo-critical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, $T_c(m_s)= T_c(m_s^{\rm phy}) (1 - 0.097(2) (m_s-m_s^{\rm phys})/m_s^{\rm phy}+{\cal O}((\Delta m_s)^2)$.