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.
Categories: hep-lat nucl-th