On the S-wave pollution of B-> K* l+l- observables

Abstract

It has been argued recently that transverse asymmetries that are expected to be shielded from the presence of the S-wave (Kpi) pairs originating from the decay of a scalar K0* meson, are indeed affected by this pollution due to the impossibility to extract cleanly the normalization for these observables. In this short note we show how using folded distributions, which is nowadays the preferred method to obtain the information from the 4-body decay mode B-> K*(-> Kpi) l+l-, one can easily bypass this problem and extract the clean observables P_{1,2,3} and also P'_{4,5,6} in a way completely free from this pollution including all lepton mass corrections. We also show that in case one insists in using uniangular distributions to extract these observables it is possible to reduce this pollution to just lepton mass suppressed terms. On the contrary, the S_i observables, that are by definition normalized by the full differential decay distribution, will indeed suffer from this pollution via their normalization. Finally, we also present a procedure to minimize the error associated to neglecting lepton mass corrections in the distribution defining a massless-improved limit.