# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Lattice study on a tetra-quark state $T_{bb}$ in the HALQCD method

Aug 9, 2022, 2:40 PM
20m
CP1-HSZ/Ground-0.010 - HS2 (CP1-HSZ)

### CP1-HSZ/Ground-0.010 - HS2

#### CP1-HSZ

450
Oral Presentation Hadron Spectroscopy and Interactions

### Speaker

Sinya Aoki (Yukawa Institute for Theoretical Physics, Kyoto University)

### Description

We study a doubly-bottomed tetra-quark state $(bb\bar{u}\bar{d})$ with quantum number $I(J^P)=0(1^+)$, denoted by $T_{bb}$, in lattice QCD with the NRQCD quark action for $b$ quarks.
Employing $(2+1)$-flavor gauge configurations at $a \approx 0.09$ {fm} on $32^3\times 64$ lattices, we have extracted the coupled channel HAL QCD potential between $\bar{B}\bar{B}^*$ and $\bar{B}^* \bar{B}^*$, which predicts an existence of a bound $T_{bb}$ below the $\bar{B}\bar{B}^*$ threshold.
By extrapolating results at $m_\pi\approx 410,\, 570,\, 700$ {MeV} to the physical pion mass $m_\pi\approx140$ {MeV}, we obtain a biding energy with its statistical error as $E_{\rm binding}^{\rm (single)} = 155(17)$ MeV and $E_{\rm binding}^{\rm (coupled)} = 83(10)$ MeV, where "coupled" means that effects due to virtual $\bar{B}^* \bar{B}^*$ states are included through the coupled channel potential, while only a potential for a single $\bar{B}\bar{B}^*$ channel is used in the analysis for single".
A comparison shows that the effect from virtual $\bar{B}^* \bar{B}^*$ states is quite sizable to the binding energy of $T_{bb}$. We estimate systematic errors to be $\pm 20$ MeV at most, which are mainly caused by the NRQCD approximation for $b$ quarks.

### Primary authors

Sinya Aoki (Yukawa Institute for Theoretical Physics, Kyoto University) Mr Takafumi Aoki (Yukawa Institute for Theoretical Physics, Kyoto University)