# Study of the $B_c^+ \rightarrow J/\psi D_s^+$ and $B_c^+ \rightarrow J/\psi D_s^{*+}$ decays with the ATLAS detector

The decays $B_c^+ \to J/\psi D_s^+$ and $B_c^+ \to J/\psi D_s^{*+}$ are studied with the ATLAS detector at the LHC using a dataset corresponding to integrated luminosities of 4.9 fb$^{-1}$ and 20.6 fb$^{-1}$ of $pp$ collisions collected at centre-of-mass energies $\sqrt{s} = 7$ TeV and 8 TeV, respectively. Signal candidates are identified through $J/\psi\to\mu^+\mu^-$ and $D_s^{(*)+}\to\phi\pi^+(\gamma/\pi^0)$ decays. With a two-dimensional likelihood fit involving the $B_c^+$ reconstructed invariant mass and an angle between the $\mu^+$ and $D_s^+$ candidate momenta in the muon pair rest frame, the yields of $B_c^+ \to J/\psi D_s^+$ and $B_c^+ \to J/\psi D_s^{*+}$, and the transverse polarisation fraction in $B_c^+ \to J/\psi D_s^{*+}$ decay are measured. The transverse polarisation fraction is determined to be $\Gamma_{\pm\pm}(B_c^+ \to J/\psi D_s^{*+})/\Gamma(B_c^+ \to J/\psi D_s^{*+}) = 0.38 \pm 0.23 \pm 0.07$, and the derived ratio of the branching fractions of the two modes is $\mathcal{B}_{B_c^+ \to J/\psi D_s^{*+}}/\mathcal{B}_{B_c^+ \to J/\psi D_s^+} = 2.8 \,^{+1.2}_{-0.8} \pm 0.3$, where the first error is statistical and the second is systematic. Finally, a sample of $B_c^+\to J/\psi\pi^+$ decays is used to derive the ratios of branching fractions $\mathcal{B}_{B_c^+ \to J/\psi D_s^+}/\mathcal{B}_{B_c^+ \to J/\psi \pi^+} = 3.8 \pm 1.1 \pm 0.4 \pm 0.2$ and $\mathcal{B}_{B_c^+ \to J/\psi D_s^{*+}}/\mathcal{B}_{B_c^+ \to J/\psi \pi^+} = 10.4 \pm 3.1 \pm 1.5 \pm 0.6$, where the third error corresponds to the uncertainty of the branching fraction of $D_s^+\to\phi(K^+K^-)\pi^+$ decay. The available theoretical predictions are generally consistent with the measurement.