Internal structure of the $T_{cc}(3875)^+$ from its light-quark mass dependence

TL;DR

This study uses a chiral effective field theory to analyze how the $T_{cc}(3875)^+$ state evolves with changing light-quark masses, providing insights into its molecular nature and the effects of pion exchange.

Contribution

It introduces a method to connect lattice QCD results at different pion masses with experimental data, incorporating three-body dynamics and one-pion exchange effects.

Findings

The $T_{cc}$ pole trajectory is consistent with a hadronic-molecule scenario.

Explicit one-pion exchange significantly affects the pole position for $m_  230$ MeV and above.

The approach successfully predicts the $T_{cc}$ behavior across varying pion masses.

Abstract

We employ a chiral effective field theory-based approach to connect $DD^*$ scattering observables at the physical and variable pion masses accessible in lattice QCD simulations. We incorporate all relevant scales associated with three-body $DD\pi$ dynamics and the left-hand cut induced by the one-pion exchange for pion masses higher than the physical one, as required by analyticity and unitarity. By adjusting the contact interactions to match experimental data at the physical pion mass and lattice finite-volume energy levels at $m_{\pi} = 280$ MeV, we predict the trajectory of the $T_{cc}$ pole as a function of the pion mass, finding it consistent with the hadronic-molecule scenario. In particular, we find that the explicit treatment of the one-pion exchange has a pronounced effect on the pole trajectory for $m_\pi \gtrsim 230$ MeV by pushing it into the complex energy plane.