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We study the splitting in the screening mass of pions and the $\eta$-mesonacross the chiral crossover. This splitting is determined by the 't Hooftdeterminant. We use results for the renormalisation group scale dependence ofthe 't Hooft determinant obtained within the functional renomalisation group inquenched QCD with two flavours. The scale dependence of the 't Hooftdeterminant is mapped to its temperature dependence with the help of aPolyakov-quark-meson model. As a result we obtain the temperature dependence ofthe splitting in the screening mass of pions and the $\eta$-meson.

Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover