Comparison of integral equations used to study $T_{cc}^+$ for a stable $D^*$

TL;DR

This paper compares three formalisms used to study $DD^*$ scattering related to the $T_{cc}^+$ tetraquark, analyzing their differences, similarities, and how they can be reconciled in simplified models.

Contribution

It provides a detailed comparison of RFT, LS, and BRH formalisms for $DD^*$ scattering, clarifying their relations and technical aspects.

Findings

Differences between methods can be minimized by adjusting short-range couplings.

Conditions under which RFT and BRH reduce to LS are derived.

Technical issues in the RFT approach are addressed.

Abstract

We perform a detailed comparison between three formalisms used in recent studies of $DD^*$ scattering, which aim to understand the properties of the doubly-charmed tetraquark, $T_{cc}^+(3875)$. These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baiao Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.