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In this paper, the first femtoscopic analysis of pion-kaon correlations atthe LHC is reported. The analysis was performed on the Pb-Pb collision data at$\sqrt{s_{\rm{NN}}}$ = 2.76 TeV recorded with the ALICE detector. Thenon-identical particle correlations probe the spatio-temporal separationbetween sources of different particle species as well as the average sourcesize of the emitting system. The sizes of the pion and kaon sources increasewith centrality, and pions are emitted closer to the centre of the systemand/or later than kaons. This is naturally expected in a system with strongradial flow and is qualitatively reproduced by hydrodynamic models. ALICE dataon pion-kaon emission asymmetry are consistent with (3+1)-dimensional viscoushydrodynamics coupled to a statistical hadronization model, resonancepropagation, and decay code THERMINATOR 2 calculation, with an additional timedelay between 1 and 2 fm$/c$ for kaons. The delay can be interpreted asevidence for a significant hadronic rescattering phase in heavy-ion collisionsat the LHC.

Pion-kaon femtoscopy and the lifetime of the hadronic phase in Pb$-$Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV