Measurement of the $B^0_s \to J/\psi K^0_s$ branching fraction

The foreseen experimental precision on LHCb's key measurements makes the control of doubly Cabibbo-suppressed Standard Model corrections mandatory. Especially in the light of the search for new physics in $B^0$--$\overline{B}^0$ mixing, based on the measurement of $\sin2\beta$ from the well-known $B^0\to J/\psi K_S^0$ mode, such effects need to be controlled. With the help of the $U$-spin flavour symmetry of QCD, this can be accomplished using the $B_s^0\to J/\psi K_S^0$ channel, which is related to the former mode through the interchange of all $d$ and $s$ quarks. This analysis note reports the observation of the $B_s^0\to J/\psi K_S^0$ decay at LHCb, based on the $\int\mathcal{L}{\rm d}t$ = 380 pb$^{-1}$ data sample collected by end of June 2011. The signal selection uses a neural network classifier trained on the $B^0\to J/\psi K_S^0$ counterpart. The measured ratio of branching fractions ${\cal B}(B_s^0\to J/\psi K_S^0)/{\cal B}(B^0\to J/\psi K_S^0)$ is $0.0378\pm 0.0058 \: \text{(stat)} \pm 0.0020 \: \text{(syst)} \pm 0.0030 \: {(f_s/f_d)}$, from which the $B_s^0\to J/\psi K^0$ branching fraction can be extracted as $(3.29\pm0.51 \: \text{(stat)} \pm0.17 \: \text{(syst)} \pm0.26 \: {(f_s/f_d)} \pm0.12 \: \text{(PDG)} )\cdot10^{-5}$.