The semi-leptonic transition to tensor meson of negative parity in the QCD sum rules approach

The semi-leptonic transition of ${\overline{B}}_{s}\to {D}_{s2}\ell \overline{\nu }$ to tensor meson of negative parity ${J}^{P}={2}^{-}$ is examined in the content of the QCD sum rules approach. The three-point correlation function is used to calculate the transition form-factors of the hadronic matrix element involved in these channels. With these transition form-factors, the predicted branching ratios are estimated as: $BR\left[{\overline{B}}_{s}\to {D}_{s2}e{\overline{\nu }}_{e}\right]={4.32}_{-2.0}^{+2.0}×{10}^{-3}$, $BR\left[{\overline{B}}_{s}\to {D}_{s2}\mu {\overline{\nu }}_{\mu }\right]={4.29}_{-2.0}^{+2.0}×{10}^{-3}$, and $BR\left[{\overline{B}}_{s}\to {D}_{s2}\tau {\overline{\nu }}_{\tau }\right]={3.1}_{-1.4}^{+1.4}×{10}^{-4}$. We also calculated the leptonic angular spectra and leptonic forward-backward asymmetries. The effect of the leptonic decay constant ${f}_{{D}_{s2}}$ on these observables is also considered. The obtained orders of the branching ratios in this work are indicating that these channels can be investigated at LHCb in the near future.