The high b \bar b cross section produced by the LHC offers an excellent opportunity for the study of flavour changing neutral current B decays, where the effects of new physics can be probed. This thesis presents an analysis of the rare decay B0 → K∗ 0 e+e−, which can be used to measure the polarisation of the photon in the b → sγ transition. When the dilepton mass is low, the e+e− pair comes predominantly from a virtual photon, and the polarisation can be accessed via an angular analysis. It is predicted to be predominantly left handed in the Standard Model, and therefore an enhanced right handed amplitude would be a sign of new physics. A first step is to measure the branching fraction in the dilepton mass range, 30 MeV/c2 to 1 GeV. This decay has not yet been observed in this region, due to its small branching ratio. The analysis involves electrons with low transverse momentum, and is thus experimentally complex in the hadronic environment at the LHC. The branching ratio is measured relative to that of B0 → J/ψ (e + e−)K∗0 , which eliminates both certain experimental effects, and the need to determine absolute efficiencies. The result is obtained with an integrated luminosity of 1 fb−1 of pp collisions, collected by LHCb during 2011 and is found to be: B(B 0 → K∗ 0 e+e−)30−1000 MeV/c 2 = (3.19+0.75 −0.68 (stat) ± 0.21(syst) ± 0.15(PDG)) × 10− 7 when using the PDG value for the B0 → J/ψ (e + e−)K∗0 branching ratio. The last part of the thesis presents Monte Carlo studies, showing that with the inclusion of the 2012 data sample, the expected sensitivity on the fraction of right handed polarisation is approximately 0.1, which is comparable with the world average obtained with different methods.
