PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Hadron Spectroscopy and Interactions
Lattice study on a tetraquark state $T_{bb}$ in the HAL QCD method
S. Aoki* and T. Aoki
Full text: pdf
Pre-published on: November 30, 2022
Published on: April 06, 2023
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.
DOI: https://doi.org/10.22323/1.430.0049
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