Measurement of the ratio of branching fractions $\mathcal{B}(B_c^{+}\to B_s^0{\pi }^{+})\mathrm{/}\mathcal{B}(B_c^{+}\to J\mathrm{/}\psi {\pi }^{+})$

The ratio of branching fractions of $B_c^{+}\to B_s^0{\pi }^{+}$ and $B_c^{+}\to J\mathrm{/}\psi {\pi }^{+}$ decays is measured with proton-proton collision data of a centre-of-mass energy of $13\text{TeV}$. The data were collected with the LHCb experiment during 2016–2018, corresponding to an integrated luminosity of $5.4{\text{fb}}^{-1}$. The $B_s^0$ mesons are reconstructed via the decays $B_s^0\to J\mathrm{/}\psi \phi$ and $B_s^0\to D_s^{-}{\pi }^{+}$. The ratio of branching fractions is measured to be $\mathcal{B}(B_c^{+}\to B_s^0{\pi }^{+})\mathrm{/}\mathcal{B}(B_c^{+}\to J\mathrm{/}\psi {\pi }^{+})=91\pm 10\pm 8\pm 3$ where the first uncertainty is statistical, the second is systematic and the third is due to the knowledge of the branching fractions of the intermediate state decays.