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The first observation of the $B^0_s\!\to D^{*+}D^{*-}$ decay and themeasurement of its branching ratio relative to the $B^0\!\to D^{*+}D^{*-}$decay are presented. The data sample used corresponds to an integratedluminosity of $9\,\text{fb}^{-1}$ of proton-proton collisions recorded by theLHCb experiment at centre-of-mass energies of 7, 8 and $13\,\text{TeV}$ between2011 and 2018. The decay is observed with more than $10$ standard deviationsand the time-integrated ratio of branching fractions is determined to be\begin{align*}  \frac{\mathcal{B}(B^0_s\!\to D^{*+}D^{*-})}{\mathcal{B}(B^0\!\toD^{*+}D^{*-})} = 0.269 \pm 0.032 \pm 0.011 \pm 0.008\, , \end{align*} where thefirst uncertainty is statistical, the second systematic and the third due tothe uncertainty of the fragmentation fraction ratio $f_s/f_d$. The $B^0_s\!\toD^{*+}D^{*-}$ branching fraction is calculated to be \begin{align*}  \mathcal{B}(B^0_s\!\to D^{*+}D^{*-}) = (2.15 \pm 0.26 \pm 0.09 \pm 0.06 \pm0.16)\times 10^{-4} \,, \end{align*} where the fourth uncertainty is due to the$B^0\!\to D^{*+}D^{*-}$branching fraction. These results are calculated usingthe average $B^0_s$ meson lifetime in simulation. Correction factors arereported for scenarios where either a purely heavy or a purely light $B^0_s$eigenstate is considered.

Observation of the $B^0_s\!\to D^{*+}D^{*-}$ decay

Observation of the $B^0_s\!\to D^{+}D^{-}$ decay