Incorporating $DD\pi$ effects and left-hand cuts in lattice QCD studies of the $T_{cc}(3875)^+$

TL;DR

This paper extends a relativistic formalism to include $DD\pi$ interactions in lattice QCD, enabling better analysis of the $T_{cc}(3875)^+$ tetraquark and related systems by accounting for effects like left-hand cuts.

Contribution

It introduces a generalized three-particle finite-volume scattering formalism for $DD\pi$ systems, improving the analysis of lattice QCD data involving doubly-charmed tetraquarks.

Findings

Formalism valid below the left-hand cut in $D D^*$ scattering.

Applicable to lattice QCD studies of $T_{cc}(3875)^+$.

Addresses previous issues in finite-volume energy analysis.

Abstract

We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic $DD\pi$ systems in the charm $C=2$ sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark $T_{cc}(3875)^+$ is expected to manifest as a pole in the $DD \pi \to DD \pi$ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the $D^*$ is bound and, in particular, remains valid below the left-hand cut in $D D^*$ scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies.