Higher partial waves in femtoscopy

Femtoscopy is recently gaining more attention as a new approach complementary to scattering experiments for constraining hadron–hadron interactions. We discuss the effect of higher partial waves on the two-particle correlation function, which has been neglected in traditional formulae used in the femtoscopy analyses. We consider the partial-wave expansion of the scattering wave function in the Koonin–Pratt formula to give the correction to the correlation function by a sum of the contributions from each partial wave. We also generalize the Lednický–Lyuboshitz formula, which was originally derived for the s -wave interaction, to include higher partial waves. We find a compact representation of the generalized Lednický–Lyuboshitz formula given by the backward scattering amplitude f ( θ = π ) and the Fourier–Laplace transform of the relative source function, which gives an insight into the structure of the Lednický–Lyuboshitz formula and its relation to the optical theorem. We numerically demonstrate the significance of higher partial waves with resonances using the square potential well. Also, the generalized Lednický–Lyuboshitz formula turned out to be broken for higher partial waves, which indicates the importance of the centrifugal force with the higher partial waves.