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

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.