# Double-heavy axial-vector tetraquark $T_{bc;\bar{u}\bar{d}}^{0}$

## TL;DR

This paper calculates the mass, decay widths, and lifetimes of the double-heavy axial-vector tetraquark $T_{bc}^{0}$ using QCD sum rules, providing predictions for its stability and decay modes relevant for experimental detection.

## Contribution

It presents the first detailed QCD sum rule analysis of the $T_{bc}^{0}$ tetraquark, including vacuum condensate effects up to dimension 10, and predicts its mass, decay widths, and lifetimes under different scenarios.

## Key findings

- Mass of $T_{bc}^{0}$ around 7105 MeV, below decay thresholds.
- Predicted lifetime of approximately 1.65 ps for the tetraquark.
- Full decay width varies from about $4 imes 10^{-10}$ MeV to 63.5 MeV depending on the decay mode.

## Abstract

The mass and coupling of the axial-vector tetraquark $T_{bc;\bar{u}\bar{d} }^{0}$ (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 $m=(7105 \pm 155)~\mathrm{ MeV}$ lies below the thresholds for the strong and electromagnetic decays of $T_{bc}^{0}$ state, and hence it transforms to conventional mesons only through the weak decays. In the case of $m=7260~\mathrm{MeV}$ 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 dominant semileptonic decays $T_{bc}^{0}\to T_{cc;\bar{ u}\bar{d}}^{+}l\overline{\nu }_{l}$ ($l=e,\ \mu, \tau$), where the final-state tetraquark is a scalar state. We compute also partial widths of the nonleptonic weak decays $T_{bc}^{0}\to T_{cc;\bar{u}\bar{d} }^{+}\pi^{-}(K^{-}, D^{-}, D_{s}^{-})$, 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 $T_{bc}^{0}\to B^{\ast -}D^{+}$ and $T_{bc}^{0}\to \overline{B}^{\ast 0}D^{0}$, and using these channels evaluate the full width of $T_{bc}^{0}$. Predictions for $\Gamma_{ \mathrm{full}} =(3.98\pm 0.51)\times 10^{-10}~\mathrm{MeV}$ and mean lifetime $\tau=1.65_{-0.18}^{+0.25}~\mathrm{ps}$ of $T_{bc}^{0}$ obtained in the context of the first option, as well as the full width $\Gamma_{\mathrm{ full}}=(63.5\pm 8.9)~\mathrm{MeV}$ extracted in the second scenario may be useful for experimental and theoretical exploration of double-heavy exotic mesons.