Pion-kaon femtoscopy in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV modeled in (3+1)D hydrodynamics coupled to Therminator 2 and the effect of delayed kaon emission

Abstract: Non-identical particle femtoscopy measures the size of the system emitting particles ("radius") in heavy-ion collisions as well as the difference between mean emission space-time coordinates of two particle species ("emission asymmetry"). The system created in such collisions at the LHC behaves collectively and its dynamics is well described by hydrodynamic models. A significant emission asymmetry between pions and kaons, coming from collective flow, enhanced by contribution from flowing resonances is predicted. We present calculations within the (3+1)D viscous hydrodynamic model coupled to statistical hadronization code Therminator 2, corresponding to Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. We obtain femtoscopic radii and emission asymmetry for pion-kaon pairs as a function of collision centrality. The radii grow linearly with cube root of particle multiplicity density. The emission asymmetry is negative and comparable to the radius, indicating that pions are emitted closer to the center of the system and/or later than kaons. Recent ALICE Collaboration measurements of identical kaon femtoscopy shows that kaons are emitted, on average, 2.1~fm/$c$ later than pions. We modify our calculation by introducing such delay and find that the system source size is only weakly affected. In contrast the pion-kaon emission asymmetry is directly sensitive to such delays and the modified calculation shows significantly lower values of asymmetry. Therefore we propose the measurement of the pion-kaon femtoscopic correlation function as a sensitive probe of the time delays in particle emission.