Use of $B_{s}^{0} \to D_{s}^{-}\mu^{+}\nu_{\mu}$ channel to control the flavour tagging in LHCb

The measurement of the Phi_s angle is one of the first goal of the LHCb experiment. This observable will be extracted from time dependent CP asymmetries of B0s->J/Psi Phi decays. This measurement requires the estimation of the initial state flavour of the b-quark contained in the B0s meson. The fact that the final state of B0s->J/Psi Phi is a mixture of CP eigenstates makes the measurement of its mistag rate in real data very difficult. The B0s->Ds Pi channel is usually considered to control the mistag B0s rate. This mistag can be extracted, either from a fit of the B0s oscillation amplitude, which requires an excellent proper time resolution; or from the double tagging method. In this last one, we exploit events where same side and opposite side flavour tags are available. In this report, we study for the first time the B0s->Ds mu nu channel to control the mistag, because of its high branching ratio. The generation and the selection of this channel is presented. After correcting for the missing the neutrino, a B0s momentum resolution of 15% is achieved. The main source of background are B->D D X events, and a muon coming from b->c->mu cascade decays. The outcome of our selection is a background over signal ratio of 0.5, and we select approximately 1 million B0s->Ds mu nu events per year, after trigger, including HLT. This is about 10 times more than B0s->Ds Pi. The proper time resolution is approximately 175 fs, i.e. 3 times worse than B0s->Ds Pi. This means that the B0s->Ds mu nu channel, with our current selection, is not competitive with Bs->Ds Pi for the mistag extraction using amplitude fit. However, the Bs->Ds mu nu events should be very useful to extract the same side mistag using the double tagging method. Indeed, the uncertainty on the same side mistag rate is improved from 1.4 % to 0.7 % using B0s->Ds mu nu with respect to using B0s->Ds Pi alone. We also carefully check the tagging performance differences between the CP channel B0s->J/Psi Phi and the two control channels Bs->Ds Pi and Bs->Ds mu nu. The expected differences due to trigger biases and to kinematic correlations between the two b-hadrons have been studied. We conclude that the tagging performances of B0s->Ds mu nu are "in between" B0s->J/Psi Phi and B0s->Ds Pi.