Two- versus three-body approach to femtoscopic hadron-deuteron correlations

TL;DR

This paper compares two- and three-body methods for analyzing hadron-deuteron correlations, showing the conditions under which the simpler two-body approach is valid and deriving a formula for source radius extraction.

Contribution

It introduces a generalized three-body approach accounting for different source radii and derives a formula to relate two- and three-body correlation functions.

Findings

Two-body approach is valid for kaon-deuteron correlations with small sources.

Three-body approach is necessary for proton-deuteron correlations in small sources.

Derived a source radius formula connecting two- and three-body correlation functions.

Abstract

The three-body approach to hadron-deuteron correlations is shown to turn into a two-body approach if the three-particle hadron-deuteron wave function factorizes into the deuteron wave-function and the wave function of a hadron motion relative to the deuteron. Then, the hadron-deuteron correlation function is as in the two-body approach only the source radius somewhat changes. For this reason, as we argue, the two-body approach works well for kaon-deuteron correlations but it fails for proton-deuteron ones in case of small sources. Applying the three-body approach generalized to the case where the radius of the hadron source is different from the nucleon source radius, we derive the source radius formula which used in the two-body approach gives the correlation function as in the `factorized' three-body one. The formula is discussed in the context of existing and future experimental data.