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

TL;DR

This paper develops a comprehensive parametric framework for the decay $B o K^* \, \ell^+ \ell^-$ within the Standard Model, deriving a new relation among observables that can signal new physics if violated.

Contribution

It introduces a complete, approximation-free parametric form of the decay amplitude, leading to a novel relation among CP-conserving observables for testing the Standard Model.

Findings

Derived a new relation among observables that signals new physics if violated.

Demonstrated the application of the relation using LHCb data.

Provided a comprehensive amplitude parametrization including all SM effects.

Abstract

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.