A non-parametric method to estimate the Forward-Backward Asymmetry from the $B_{d} \rigtharrow K^{*} \mu^{+} \mu^{-}$

This note discusses the use of a non-parametric unbinned method to evaluate the dimuon mass squared distribution and the Forward Backward asymmetry (FBA) from the $B_d\rightarrow K^* \mu^{+}\mu^{-}$ decay.This method gives access to the complete shape of the FBA distribution: the FBA zero point is obtained directly, no straight line fit or other assumptions on the shape of the distribution are required.The implementation of this approach and the results obtained using simulated events generated within the LHCb software framework are presented. The sensitivity obtained for the FBA zero point was $\sigma_{Zero Point} = 0.40~\rm \pm 0.04~GeV^{2}/c^{4}$ for an integrated luminosity of $\rm 2~fb^{-1}$.