The isospin and compositeness of the $T_{cc}(3875)$ state

TL;DR

This study analyzes the $T_{cc}(3875)$ state using LHCb data, concluding it is a predominantly molecular $I=0$ state with minimal isospin breaking and no evidence for an $I=1$ state, based on a comprehensive fit.

Contribution

The paper introduces a general framework for analyzing the isospin and compositeness of the $T_{cc}(3875)$, demonstrating its molecular nature and quantifying channel probabilities and isospin breaking.

Findings

The $T_{cc}(3875)$ is predominantly a molecular state with about 69\% and 29\\% probabilities for $D^0 D^{*+}$ and $D^+ D^{*0}$ channels.

The state has isospin $I=0$ with very small isospin breaking effects.

No $I=1$ state is supported by the potential, consistent with experimental observations.

Abstract

We perform a fit to the LHCb data on the $T_{cc}(3875)$ state in order to determine its nature. We use a general framework that allows to have the $D^0 D^{*+}$, $D^+ D^{*0}$ components forming a molecular state, as well as a possible nonmolecular state or contributions from missing coupled channels. From the fits to the data we conclude that the state observed is clearly of molecular nature from the $D^0 D^{*+}$, $D^+ D^{*0}$ components and the possible contribution of a nonmolecular state or missing channels is smaller than 3\%, compatible with zero. We also determine that the state has isospin $I=0$ with a minor isospin breaking from the different masses of the channels involved, and the probabilities of the $D^0 D^{*+}$, $D^+ D^{*0}$ channels are of the order of 69\% and 29\% with uncertainties of 1\%. The differences between these probabilities should not be interpreted as a measure of the isospin violation. Due to the short range of the strong interaction where the isospin is manifested, the isospin nature is provided by the couplings of the state found to the $D^0 D^{*+}$, $D^+ D^{*0}$ components, and our results for these couplings indicate that we have an $I=0$ state with a very small isospin breaking. We also find that the potential obtained provides a repulsive interaction in $I=1$, preventing the formation of an $I=1$ state, in agreement with what is observed in the experiment.