Testing New Physics Effects in $B \to K^*\ell^+\ell^-$

It is generally believed that the decay mode $B\to K^*\ell^+\ell^-$ is one of the best modes to search for physics beyond the standard model. The angular distribution enables the independent measurement of several observables as a function of the dilepton invariant mass. The plethora of observables so obtained enable unique tests of the standard model contributions. We start by writing the most general parametric form of the standard model amplitude for $B\to K^*\ell^+\ell^-$ taking into account comprehensively all contributions within SM. These include all short-distance and long-distance effects, factorizable and non-factorizable contributions, complete electromagnetic corrections to hadronic operators up to all orders, resonance contributions and the finite lepton and quark masses. The parametric form of the amplitude in the standard model results a new relation involving all the $CP$ conserving observables. The derivation of this relation only needs the parametric form of the amplitude and not a detailed calculation of it. Hence, we make no approximations, however, innocuous. The violation of this relation will provide a smoking gun signal of new physics. We use the $1 \text{fb}^{-1}$ LHC$b$ data to explicitly show how our relation can be used to test standard model and search for new physics that might contribute to this decay.