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

Lattice study on a tetra-quark state Tbb in the HALQCD method

9 Aug 2022, 14:40

20m

CP1-HSZ/0.010 (CP1-HSZ) - HS2 (CP1-HSZ)

Oral Presentation Hadron Spectroscopy and Interactions Hadron Spectroscopy and Interactions

Speaker

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

Description

We study a doubly-bottomed tetra-quark state $(bb\overline{u}\overline{d})$ 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 $\overline{B}{\overline{B}}^{\ast }$ and ${\overline{B}}^{\ast }{\overline{B}}^{\ast }$, which predicts an existence of a bound $T_{bb}$ below the $\overline{B}{\overline{B}}^{\ast }$ threshold.
By extrapolating results at $m_{\pi }\approx 410,570,700$ {MeV} to the physical pion mass $m_{\pi }\approx 140$ {MeV}, we obtain a biding energy with its statistical error as $E_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}}^{(\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e})}=155(17)$ MeV and $E_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}}^{(\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{d})}=83(10)$ MeV, where "coupled" means that effects due to virtual ${\overline{B}}^{\ast }{\overline{B}}^{\ast }$ states are included through the coupled channel potential, while only a potential for a single $\overline{B}{\overline{B}}^{\ast }$ channel is used in the analysis for ``single".
A comparison shows that the effect from virtual ${\overline{B}}^{\ast }{\overline{B}}^{\ast }$ 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.

Presentation materials

Lattice20220809.pdf