Double-heavy axial-vector tetraquark

The mass and coupling of the axial-vector tetraquark ${T}_{bc;\overline{u}\overline{d}}^{0}$ (in a short form ${T}_{bc}^{0}$) are calculated by means of the QCD two-point sum rule method. In computations we take into account contributions arising from various quark, gluon and mixed vacuum condensates up to dimension 10. The central value of the mass $m=\left(7105±155\right)\phantom{\rule{0.25em}{0ex}}\text{MeV}$ lies below the thresholds for the strong and electromagnetic decays of the ${T}_{bc}^{0}$ state, and hence it transforms to conventional mesons only through the weak decays. In the case of $m=7260\phantom{\rule{0.25em}{0ex}}\text{MeV}$ the tetraquark ${T}_{bc}^{0}$ becomes the strong- and electromagnetic-interaction unstable particle. In the first case, we find the full width and mean lifetime of ${T}_{bc}^{0}$ using its semileptonic decays ${T}_{bc}^{0}\to {T}_{cc;\overline{u}\overline{d}}^{+}l{\stackrel{‾}{\nu }}_{l}$ ($l=e,\phantom{\rule{0.25em}{0ex}}\mu ,\tau $), where the final-state tetraquark is a scalar state. We compute also partial widths of the nonleptonic weak decays ${T}_{bc}^{0}\to {T}_{cc;\overline{u}\overline{d}}^{+}{\pi }^{-}\left({K}^{-},{D}^{-},{D}_{s}^{-}\right)$, and take into account their effects on the full width of ${T}_{bc}^{0}$. In the context of the second scenario we calculate partial widths of S-wave strong decays ${T}_{bc}^{0}\to {B}^{⁎-}{D}^{+}$ and ${T}_{bc}^{0}\to {\stackrel{‾}{B}}^{⁎0}{D}^{0}$, and using these channels evaluate the full width of ${T}_{bc}^{0}$. Predictions for ${\Gamma }_{\mathrm{full}}=\left(3.98±0.51\right)×{10}^{-10}\phantom{\rule{0.25em}{0ex}}\text{MeV}$ and mean lifetime $\tau ={1.65}_{-0.18}^{+0.25}\phantom{\rule{0.25em}{0ex}}\mathrm{ps}$ of ${T}_{bc}^{0}$ obtained in the context of the first option, as well as the full width ${\Gamma }_{\mathrm{full}}=\left(63.5±8.9\right)\phantom{\rule{0.25em}{0ex}}\text{MeV}$ extracted in the second scenario may be useful for experimental and theoretical exploration of double-heavy exotic mesons.