This thesis presents a first search for the fully leptonic decay B+ → μ+ μ− μ+ ν in any
experiment. This search is performed using proton-proton collision data at LHCb
corresponding to an integrated luminosity of 4.7 fb^{−1} . The search is carried out in the
region where the minimum of the two μ+ μ− mass combinations is below 980 MeV/c^{2}.
The measurement of the branching fraction of this decay is even more interesting given
that the recent theoretical prediction [1] of the branching fraction for B+ → μ+ μ− μ+ ν of
1.3 × 10^{−7} is high. Moreover, this decay is sensitive to the magnitude of the coupling
strength between b and u quarks, which is of great interest given that there are some
tensions in measurements of this magnitude.
The data are consistent with the background only hypothesis and a limit of 1.4×10^{−8}
at 95% confidence level is set on the branching fraction in the stated kinematic region.
This is therefore not consistent with the theoretical prediction made in Ref. [1].
This thesis also presents a study of the response of the detector if three muons pass
through it. This study shows that correlations induced by a trimuon system in the
detector are substantial and they need to be addressed properly.