Decays of fully beauty scalar tetraquarks to $B_q{\overline{B}}_q$ and $B_q^{*}{\overline{B}}_q^{*}$ mesons

Decays of the fully beauty four-quark structures $X_{4\mathrm{b}}$ and $T_{4\mathrm{b}}$ to $B$ meson pairs are investigated in the framework of the QCD three-point sum rule method. We model the scalar exotic mesons $X_{4\mathrm{b}}$ and $T_{4\mathrm{b}}$ as diquark-antidiquark systems composed of the axial-vector and pseudoscalar diquarks, respectively. The masses $m=(18540\pm 50)\mathrm{MeV}$ and $\tilde{m}=(18858\pm 50)\mathrm{MeV}$ of these compounds calculated in our previous articles fix possible decay channels of these particles. In the present work, we consider their decays to $B_q{\overline{B}}_q$ and $B_q^{*}{\overline{B}}_q^{*}$ ($q=u$, $d$, $s$, $c$) mesons. In the case of $X_{4\mathrm{b}}$, the mass of which is below the $2{\eta }_b$ threshold, these channels determine essential part of its full width ${\mathrm{\Gamma }}_{4\mathrm{b}}$. The tetraquark $T_{4\mathrm{b}}$ can decay to the pair ${\eta }_b{\eta }_b$; therefore, partial widths of processes with $B(B^{*})$ mesons in the final state permit us to refine our estimate for the full width of this particle. The predictions ${\mathrm{\Gamma }}_{4\mathrm{b}}=(9.6\pm 1.1)\mathrm{MeV}$ and ${\tilde{\mathrm{\Gamma }}}_{4\mathrm{b}}^{\text{Full}}=(144\pm 29)\mathrm{MeV}$ obtained in this article can be used in future experimental investigations of four $b$-quark mesons.

Figure 1

QCD predictions and $\mathcal{F}(Q^2)$ functions for the form factors $g_1(Q^2)$ (solid line) and $g_5(Q^2)$ (dashed line). The couplings $g_1$ and $g_5$ are extracted at the points $Q^2=-m_B^2$ and $Q^2=-m_{B^{*}}^2$ labeled on the plot by the red diamond and star, respectively.

Figure 2

The strong coupling $g=g_1(2{\mathrm{GeV}}^2)$ as a function of the parameters $M_1^2$ and $M_2^2$ at $s_0=377.5{\mathrm{GeV}}^2$ and $s_0^{\prime }=34{\mathrm{GeV}}^2$.

Figure 3

The sum rule results and extrapolating functions for the form factors $G_1(Q^2)$ (solid line) and $G_5(Q^2)$ (dashed line). The strong couplings $G_1$ and $G_5$ are found at the points $Q^2=-m_B^2$ and $Q^2=-m_{B^{*}}^2$ and denoted by the red diamond and star, respectively.