# Sum Rule of Femtoscopic Correlation Function

## TL;DR

This paper refines a sum rule for femtoscopic correlation functions, resolving divergence issues by considering differences of functions, enabling better testing of theoretical models against experimental data.

## Contribution

It introduces an improved sum rule for correlation functions by addressing divergence problems through combining multiple functions, enhancing its practical applicability.

## Key findings

- The improved sum rule works well for Coulomb correlation functions.
- It can test the accuracy of approximate correlation function models.
- The approach is demonstrated with neutron-proton correlation functions.

## Abstract

A correlation function of two particles with small relative velocities obeys a sum rule - the momentum integral of the function is determined due to the completeness of quantum states of the particles. The original sum rule derived in 1995 suffered from a serious problem: the momentum integral was ultraviolet divergent in physically interesting cases. We resolve the problem by considering the sum rule not of a single correlation function but of a sum or difference of two appropriately chosen correlation functions. The improved sum rule is shown to work well for the exact Coulomb correlation functions. We argue that the sum rule can be used to test an accuracy and range of applicability of correlation functions computed in approximate models. The neutron-proton correlation function is discussed as an example.