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

TL;DR

This paper analyzes the zeroes of angular observables in B to K* l+ l- decays, proposing relations and a new observable to test the standard model and identify new physics effects.

Contribution

It derives hadronic-uncertainty-independent relations between zeroes of angular observables and introduces a new zero-crossing observable for probing new physics.

Findings

Relations between zeroes of P4' and P5' observables are independent of hadronic uncertainties.

A new observable, O_T^{L,R}, is constructed with a zero that coincides with the forward-backward asymmetry in the SM.

Precise measurement of these zeroes can distinguish between different new physics contributions.

Abstract

We calculate the zeroes of angular observables $P_4^{'}$ and $P_5^{'}$ of 4 - body angular distribution of $B\rightarrow K^{*} (\rightarrow K \pi) l^+ l^-$ 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.