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

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 $32^3times 64$ lattices. The potential predicts an existence of a bound $T_{bb}$ below the $bar{B}bar{B}^*$ threshold. At the physical pion mass $m_piapprox140$ {MeV} extrapolated from $m_piapprox 410, , 570, , 700$ {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.