$T_{cc}^+$ via the plane wave approach and including diquark-antidiquark operators

TL;DR

This paper develops a novel lattice QCD approach using plane waves and diquark-antidiquark operators to better analyze the $T_{cc}^+$ state, overcoming limitations of traditional methods near the left-hand cut.

Contribution

It introduces a combined plane-wave and effective-field-theoretic method with diquark-antidiquark operators to improve spectral resolution in lattice QCD studies of $T_{cc}^+$.

Findings

Inclusion of diquark-antidiquark operators impacts the energy spectrum.

The method is more effective at larger heavy quark masses.

Results suggest improved understanding of the $T_{cc}^+$ state.

Abstract

The determination of the $DD^{*}$ scattering amplitude from lattice QCD is complicated by long-range interactions. In particular, the L\"uscher method is no longer applicable in the kinematical region close to the left-hand cut. We tackle this problem by adopting plane-wave and effective-field-theoretic methods, which also address partial wave mixing. In addition, we incorporate a diquark-antidiquark interpolator in the operator basis (along with the relevant scattering operators) in order to achieve a better resolution of the energy spectrum. Results show that inclusion of it already has some impact at physical charm quark mass, although it is more significant for larger heavy quark masses, in line with expectations.