Lattice study on a tetraquark state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math> in the HAL QCD method

Abstract

We study a doubly bottomed tetraquark state $(bb\overline{u}\overline{d})$ with quantum number $I({J}^{P})=0({1}^{+})$, denoted by ${T}_{bb}$, in lattice QCD with the nonrelativistic QCD (NRQCD) quark action for $b$ quarks. Employing ($2+1$)-flavor gauge configurations at $a\ensuremath{\approx}0.09\text{ }\text{ }\mathrm{fm}$ on ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattices, we have extracted the coupled-channel potential between $\overline{B}{\overline{B}}^{*}$ and ${\overline{B}}^{*}{\overline{B}}^{*}$ in the HAL QCD method, which predicts an existence of a bound ${T}_{bb}$ below the $\overline{B}{\overline{B}}^{*}$ threshold. By extrapolating results at ${m}_{\ensuremath{\pi}}\ensuremath{\approx}410$, 570, 700 MeV to the physical pion mass ${m}_{\ensuremath{\pi}}\ensuremath{\approx}140\text{ }\text{ }\mathrm{MeV}$, we obtain a binding energy with its statistical error as ${E}_{\text{binding}}^{(\mathrm{single})}=155(17)\text{ }\text{ }\mathrm{MeV}$ and ${E}_{\text{binding}}^{(\mathrm{coupled})}=83(10)\text{ }\text{ }\mathrm{MeV}$, where ``coupled'' means that effects due to virtual ${\overline{B}}^{*}{\overline{B}}^{*}$ states are included through the coupled channel potential, while only a potential for a single $\overline{B}{\overline{B}}^{*}$ channel is used in the analysis for ``single.'' A comparison shows that the effect from virtual ${\overline{B}}^{*}{\overline{B}}^{*}$ states is quite sizable to the binding energy of ${T}_{bb}$. We estimate systematic errors to be $\ifmmode\pm\else\textpm\fi{}20\text{ }\text{ }\mathrm{MeV}$ at most, which are mainly caused by the NRQCD approximation for $b$ quarks.

Topics & Concepts