(A)symmetries of weak decays at and near the kinematic endpoint

Abstract

At the kinematic endpoint of zero recoil physical momenta are parallel which leads to symmetries in the decay distributions. We implement this observation for decays of the type $A \to (B_1 B_2) C$ by extending the helicity formalism to include an unphysical timelike polarisation. The symmetries of the helicity amplitudes are worked out for a generic dimension six Hamiltonian for a $B \to V \ell \ell$ decay type. We obtain \emph{exact} predictions for angular observables, e.g.,for the fraction of longitudinally polarized vector mesons, $F_L = 1/3$, which may be used to guide experimental analyses. We investigate the vicinity of the endpoint through an expansion in the three momentum of the vector meson. New physics can be searched for in the slope of the observables near the endpoint. Current experimental data on $B \to K^* \ell \ell$ decays are found to be in agreement with our predictions within uncertainties. Application to other semileptonic $B$ and $D$ decays, including $B \to V \ell^+ \ell^-$, $V=K^*,ϕ, ρ$ and $B \to V \ell ν$, $V=ρ,D^*$ is straightforward. For hadronic modes of the types $B \to V p \bar p, V Λ\bar Λ, ..$ and $B \to V ππ, V πK, .. $ endpoint relations apply as long as they are not overwhelmed by sizeable final state interactions between the $V$ and the hadron pair.