Higher partial waves in femtoscopy

TL;DR

This paper investigates the impact of higher partial waves on femtoscopy correlation functions, extending existing formulas to include these effects and demonstrating their significance through numerical examples.

Contribution

It generalizes the Lednicky-Lyuboshitz formula to incorporate higher partial waves and provides a compact representation linking it to the scattering amplitude and source function.

Findings

Higher partial waves significantly affect correlation functions with resonances.

The generalized formula reveals the importance of centrifugal forces for higher partial waves.

The traditional Lednicky-Lyuboshitz formula breaks down for higher partial waves.

Abstract

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 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 Lednicky-Lyuboshitz formula, which was originally derived for the s-wave interaction, for higher partial waves. We find a compact representation of the generalized Lednicky-Lyuboshitz formula given by the backward scattering amplitude $f(\theta = \pi)$ and the Fourier-Laplace transform of the relative source function, which gives an insight into the structure of the Lednicky-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 Lednicky-Lyuboshitz formula turned out to be broken for higher partial waves, which suggests the importance of the centrifugal force for the higher partial waves.