Inclusion of heavy spin effects in the $u d \bar{b} \bar{b}$ $I(J^{P})=0(1^{-})$ four-quark channel in the Born-Oppenheimer approximation

TL;DR

This study refines previous lattice QCD analyses of a $u d ar{b} ar{b}$ tetraquark by including heavy quark spin effects, but finds no evidence of a resonance in the coupled channel approach.

Contribution

It introduces heavy quark spin effects into the Born-Oppenheimer approximation for the $u d ar{b} ar{b}$ tetraquark, expanding the analysis to coupled channels.

Findings

No tetraquark resonance found in the refined coupled channel analysis.

Heavy quark spin effects do not produce a bound state or resonance.

Varying potentials and quark masses did not reveal resonance signals.

Abstract

We refine our previous study of a $u d \bar{b} \bar{b}$ tetraquark resonance with quantum numbers $I(J^{P})=0(1^{-})$, which is based on antiheavy-antiheavy lattice QCD potentials, by including heavy quark spin effects via the mass difference of the $B$ and the $B^{*}$ meson. This leads to a coupled channel Schr\"odinger equation, where the two channels correspond to $BB$ and $B^{*}B^{*}$, respectively. We search for $\mbox{T}$ matrix poles in the complex energy plane, but do not find any indication for the existence of a tetraquark resonance in this refined coupled channel approach. We also vary the antiheavy-antiheavy potentials as well as the $b$ quark mass to further understand the dynamics of this four-quark system.