Effects of strangeness on the chiral pseudocritical line

Within a $2+1$ flavor Nambu–Jona-Lasinio model, we calculate the curvature coefficients and check them against available lattice QCD estimations. With the observation that the flavor mixing due to the 't Hooft determinant term significantly affects the ${\kappa }_2^S$, we explore the effect of ${\mu }_S$ on the $T-{\mu }_B$ crossover lines. With the novel determination of negative ${\kappa }_2^B$ at large ${\mu }_S$, we advocate the importance of studying the same in lattice QCD.