Prospects of discovering stable double-heavy tetraquarks at a Tera-$Z$ factory

Abstract

Motivated by a number of theoretical considerations, predicting the deeply bound double-heavy tetraquarks $T_{[\bar{u}\bar{d}]}^{\{bb\}}$, $T_{[\bar{u}\bar{s}]}^{\{bb\}}$ and $T_{[\bar{d}\bar{s}]}^{\{bb\}}$, we explore the potential of their discovery at Tera-$Z$ factories. Using the process $Z\to b\bar{b}b\bar{b}$, we calculate, employing the Monte Carlo generators MadGraph5$\_$aMC@NLO and Pythia6, the phase space configuration in which the~$bb$ pair is likely to fragment as a diquark. In a jet-cone, defined by an invariant mass interval $m_{bb}<M_{T_{[\bar{q}{\bar{q}}^{\prime }]}^{\{bb\}}}+\Delta M$, the sought-after tetraquarks $T_{[\bar{q}{\bar{q}}^{\prime }]}^{\{bb\}}$ as well as the double-bottom baryons,~${\Xi }_{bb}^{0,-}$, and ${\Omega }_{bb}^{-}$, can be produced. Using the heavy quark--diquark symmetry, we estimate $\mathcal{B}(Z\to T_{[\bar{u}\bar{d}]}^{\{bb\}}+\bar{b}\bar{b})=(1.4_{-0.5}^{+1.1})\times 10^{-6}$, and about a half of this for the $T_{[\bar{u}\bar{s}]}^{\{bb\}}$ and $T_{[\bar{d}\bar{s}]}^{\{bb\}}$. We also present an estimate of their lifetimes using the heavy quark expansion, yielding $\tau (T_{[\bar{q}{\bar{q}}^{\prime }]}^{\{bb\}})\simeq 800$~fs. Measuring the tetraquark masses would require decays, such as $T_{[\bar{u}\bar{d}]}^{\{bb\}-}\to B^{-}{D}^{-}{\pi }^{+}$, $T_{[\bar{u}\bar{d}]}^{\{bb\}-}\to J/\psi {\overline{K}}^0{B}^{-}$, $T_{[\bar{u}\bar{d}]}^{\{bb\}-}\to J/\psi K^{-}{\overline{B}}^0$, $T_{[\bar{u}\bar{s}]}^{\{bb\}-}\to {\Xi }_{bc}^0{\Sigma }^{-}$, and $T_{[\bar{d}\bar{s}]}^{\{bb\}0}\to {\Xi }_{bc}^0{\bar{\Sigma }}^0$, with subsequent decay chains in exclusive non-leptonic final states. We estimate a couple of the decay widths and find that the product branching ratios do not exceed~$10^{-5}$. Hence, a good fraction of these modes will be required for a discovery of $T_{[\bar{q}{\bar{q}}^{\prime }]}^{\{bb\}}$ at a Tera-$Z$ factory.

Comments: 11 pages, 11 figures; v2: version to appear in PLB