Lattice study on a tetraquark state $T_{bb}$ in the HAL QCD method

TL;DR

This study uses lattice QCD with HAL QCD method to predict a bound doubly-bottomed tetraquark state $T_{bb}$ with a binding energy around 83 MeV, highlighting the importance of coupled channel effects.

Contribution

First lattice QCD calculation of the $T_{bb}$ tetraquark using HAL QCD method with coupled channel analysis and NRQCD for $b$ quarks.

Findings

Predicts a bound $T_{bb}$ below the $ar{B}ar{B}^*$ threshold.

Coupled channel effects significantly influence the binding energy.

Estimated binding energy is approximately 83 MeV with systematic uncertainties.

Abstract

We investigate a doubly-bottomed tetraquark state $T_{bb}$ $(bb \bar{u}\bar{d})$ with quantum number $I(J^P)=0(1^+)$ in $(2+1)$-flavor lattice QCD. Using the Non-Relativistic QCD (NRQCD) quark action for $b$ quarks, we have extracted the coupled channel potential between $\bar{B}\bar{B}^*$ and $\bar{B}^* \bar{B}^*$ in the HAL QCD method at $a \approx 0.09$ {fm} on $32^3\times 64$ lattices. The potential predicts an existence of a bound $T_{bb}$ below the $\bar{B}\bar{B}^*$ threshold. At the physical pion mass $m_\pi\approx140$ {MeV} extrapolated from $m_\pi\approx 410,\, 570,\, 700$ {MeV}, a binding energy with its statistical error is given by $E_{\rm binding}^{\rm (coupled)} = 83(10)$ MeV from a coupled channel analysis where effects due to virtual $\bar{B}^* \bar{B}^*$ states are included through the coupled channel potential, while we obtain $E_{\rm binding}^{\rm (single)} = 155(17)$ MeV only from a potential for a single $\bar{B}\bar{B}^*$ channel. This difference indicates that the effect from virtual $\bar{B}^* \bar{B}^*$ states is sizable to the binding energy of $T_{bb}$. Adding $\pm 20$ MeV as empirical systematic error caused by the NRQCD approximation for $b$ quarks, our estimate of the $T_{bb}$ binding energy becomes $83(10)(20)$ MeV.