A study of rare B-meson decay with muons in the final state with the LHCb detector

The Standard Model (SM) gives a successful description of known phenomena in particle physics, however there are many indications of the existence of New Physics (NP) at the TeV scale. Physicists are building a very large and expensive machine in this belief: the LHC (Large Hadron Collider), which is foreseen to start in the middle 2008. Three of the experiments of the LHC are mainly devoted to the search of NP. Among these, the LHCb experiment is dedicated to the physics of b-hadrons. It will look for indirect evidences of new particles or new degrees of freedom, measuring branching ratios, decay amplitudes and CP asymmetries, which can be sensitive to New Physics effects. Three analysis will be presented: the sensitivity to the $B_{s,d}^0 \rightarrow e^{\pm} \mu^{\mp}$ decays, the sensitivity to the $B_{s,d}^0 \rightarrow \mu^+ \mu^- \gamma$ decays and the correction of angular biases in the $B_d^0 \rightarrow K^{*0} \mu^+ \mu^-$ decay. The $B_{s,d}^0 \rightarrow e^{\pm} \mu^{\mp}$ decays are forbidden in the SM, being lepton flavor violating, but are allowed in some of its extensions. The $90\%$ CL upper bounds that the LHCb experiment can set in $1$ year, running at nominal luminosity, will be presented. These results will be discussed in the context of some Pati-Salam models. The branching ratio of the decays $B_{s,d}^0 \rightarrow \mu^+ \mu^- \gamma$ can be enhanced by NP contributions, such as SUSY contributions. Th e LHCb sensitivity to these decays will be presented. %NP can affect the angular distributions of the $B_d^0 \rightarrrow K^{*0} \mu^+ \mu^-$. The $A_T^2$ asymmetry in the $B_d^0 \rightarrow K^{*0} \mu^+ \mu^-$ decay is sensitive to NP involving right-handed currents. This asymmetry can be extracted by looking at the angular distributions of the decay products. However this measurement is not straightforward. Two methods for the angular distribution recovering, using the $B_d^{0} \rightarrow J/\psi K^{*0}$ as a control channel, will be presented.