$B\rightarrow K^{*}l^+ l^-$: Zeroes of angular observables as test of standard model

Abstract

We calculate the zeroes of angular observables $P_4^{'}$ and $P_5^{'}$ of 4 - body angular distribution of $B\rightarrow K^{*} (\rightarrow K π) l^+ l^-$ where LHCb, in its analysis of form factor independent angular observables, has found deviations from standard model predictions in one of the $q^2$ bins. In the large recoil region, we obtain relations between the zeroes of $P_4^{'}$, $P_5^{'}$ and the zero of forward-backward asymmetry of lepton pair. These relations, in the considered region, are independent of hadronic uncertainties and depend only on Wilson coefficients. We also construct a new observable, $\mathcal{O}_T^{L,R}$, whose zero in the standard model coincides with the zero of forward-backward asymmetry but in presence of new physics contributions will show different behavior. Moreover, the profile of the new observable, even within the standard model, is very different from the forward backward asymmetry. We point out that precise measurements of these zeroes in near future would provide crucial test of the standard model and would be useful in distinguishing between different possible new physics contributions to Wilson coefficients.