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

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$\mathrm{\_}$aMC@NLO and Pythia6, the phase space configuration in which the~$b b$ pair is likely to fragment as a diquark. In a jet-cone, defined by an invariant mass interval $m_{bb} < M_{T^{{bb}}{[\bar q \bar q’]}} + \Delta M$,thesought-aftertetraquarks$T^{{bb}}{[\bar q \bar q^\prime]}$ as well as the double-bottom baryons,~${\mathrm{\Xi }}_{bb}^{0,-}$, and ${\mathrm{\Omega }}_{bb}^{-}$, can be produced. Using the heavy quark–diquark symmetry, we estimate $$\mathcal{B}$ (Z \to T^{{bb}}{[\bar u \bar d]} + ; \bar b \bar b) = (1.4^{+1.1}{-0.5}) \times 10^{-6}$,andaboutahalfofthisforthe$T^{{bb}}{[\bar{u}\bar{s}]}$and$T^{{bb}}{[\bar d \bar s]}$. We also present an estimate of their lifetimes using the heavy quark expansion, yielding $\tau (T_{[\bar{q}{\bar{q}}^{\mathrm{\prime }}]}^{\{bb\}})\simeq 800$~fs. Measuring the tetraquark masses would require decays, such as $T^{{bb} -}{[\bar u \bar d]} \to B^- D^- \pi^+$,$T^{{bb} -}{[\bar u \bar d]} \to J/\psi \overline K^0 B^-$,$T^{{bb} -}{[\bar u \bar d]} \to J/\psi K^- \overline B^0$,$T^{{bb} -}{[\bar u \bar s]} \to \Xi_{bc}^0 \Sigma^-$,and$T^{{bb} 0}{[\bar d \bar s]} \to \Xi{bc}^0 \bar\Sigma^0$, 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 $T_{[\bar{q}{\bar{q}}^{\mathrm{\prime }}]}^{\{bb\}}$ at a Tera-$Z$ factory.