Femtoscopy correlation functions and hadron-hadron scattering amplitudes in presence of Coulomb potential

Abstract: This work addresses the incorporation of Coulomb interactions into femtoscopy correlation functions (CFs) used to probe hadron interactions. Combining strong contact potentials with Coulomb effects, the derived scattering amplitudes and wave functions are used to compute CFs, accounting for both interactions coherently. Next, we analyze the nature of the corrections due to the finite range of the strong interaction, closely linked to off-shell effects, and propose an approximate method to account for them. We show how these corrections turn out to be essential to accurately extract the strong hadron-hadron scattering amplitudes from CF data. We compare the obtained expressions for the CFs with those reported in previous theoretical frameworks. Also, using proton-proton systems as a case study, we obtain a good comparison of our results with previous realistic theoretical calculations and with accurate recent data from the ALICE experiment. The framework enables precise CF calculations without numerical solution of the Schr\"odinger equation, offering a practical tool for femtoscopy analyses involving charged hadrons. In addition, the scheme allows for an easy connection with scattering amplitudes obtained from Effective Field Theories.