Importance of local tetraquark operators for $T_{cc}(3875)^+$

TL;DR

This study demonstrates that including local tetraquark operators in lattice QCD calculations significantly affects the energy spectrum and scattering phase shifts of the $T_{cc}(3875)^+$, highlighting their importance for accurate spectral analysis.

Contribution

The paper introduces a novel approach using distillation with position-space sampling to efficiently include local tetraquark operators in lattice QCD studies of the $T_{cc}$ spectrum.

Findings

Including local tetraquark operators causes significant shifts in energy levels.

The shifts impact the $DD^*$ scattering phase shifts derived from L"uscher analysis.

The method makes local tetraquark operators computationally feasible in distillation.

Abstract

The doubly charmed tetraquark $T_{cc}(3875)^+$ observed at LHCb has attracted considerable interest in recent years. To accurately determine its finite-volume spectrum, a variational analysis using a large basis of operators, including bilocal scattering operators, but also local tetraquark operators, should be employed. Using Wilson-clover fermions at the $SU(3)$-flavour-symmetric point, we investigated the importance of local tetraquark operators for the $T_{cc}$ spectrum by adding them to a large basis of bilocal $DD^*$ and $D^*D^*$ scattering operators. We performed this calculation using the distillation framework combined with a position-space sampling method that we recently developed. This method makes local tetraquark operators affordable in distillation. Upon including local tetraquark operators, we observe significant shifts in the estimates of several energy levels. Finally, we show the effect of these shifts on the $DD^*$ scattering phase shifts obtained from a single-channel $s$-wave L\"uscher analysis.