The effect of S-wave interference on the B⁰ → K*⁰ ℓ⁺ ℓ- Angular observables

The rare decay B⁰ → K*⁰ ℓ⁺ ℓ^- 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*⁰ P-wave that decays into the K⁺ π^- final state. In this paper the addition of an S-wave within the K ⁺π^- system of B⁰ → K*⁰ ℓ⁺ ℓ^- 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 → K*⁰ ℓ⁺ ℓ^- 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 → J/ψK*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⁺ π^- ℓ⁺ ℓ^- final state will have to take the S-wave contribution into account.