The effect of S-wave interference on the $B^0 \to K^{\ast 0}\ell^+\ell^-$ angular observables

TL;DR

This paper investigates how S-wave interference in the $K^+\pi^-$ system affects angular measurements in the rare decay $B^0 o K^{ ext{*}0}\, ext{l}^+ ext{l}^-$, highlighting the importance of accounting for S-wave contributions in future analyses.

Contribution

It introduces the impact of S-wave interference on angular observables in $B^0 o K^{ ext{*}0}\, ext{l}^+ ext{l}^-$ decays and quantifies the bias caused by neglecting S-wave effects.

Findings

S-wave causes measurable bias in angular observables.

Bias becomes significant for datasets with over 200 signal decays.

Future analyses must include S-wave contributions for accurate results.

Abstract

The rare decay $B^0 \to K^{\ast 0}\ell^+\ell^-$ is a flavour changing neutral current decay with a high sensitivity to physics beyond the Standard Model. Nearly all theoretical predictions and all experimental measurements so far have assumed a $K^{\ast 0}$ P-wave that decays into the $K^+\pi^-$ final state. In this paper the addition of an S-wave within the $K^+\pi^-$ system of $B^0 \to K^{\ast 0}\ell^+\ell^-$ and the subsequent impact of this on the angular distribution of the final state particles is explored. The inclusion of the S-wave causes a distinction between the values of the angular observables obtained from counting experiments and those obtained from fits to the angular distribution. The effect of a non-zero S-wave on an angular analysis of $B^0 \to K^{\ast 0}\ell^+\ell^-$ is assessed as a function of dataset size and the relative size of the S-wave amplitude. An S-wave contribution, equivalent to what is measured in $B^0 \to J/\psi K^{\ast 0}$ at BaBar, leads to a significant bias on the angular observables for datasets of above 200 signal decays. Any future experimental analysis of the $K^+\pi^-\ell^+\ell^-$ final state will have to take the S-wave contribution into account.