A new relation between the zero of $A_{FB}$ in $B^0 \to K^* \mu^+\mu^-$ and the anomaly in $P_5^\prime$

Understand

We present two exact relations, valid for any dilepton invariant mass region (large and low-recoil) and independent of any effective Hamiltonian computation, between the observables $P_i$ and $P_i^{CP}$ of the angular distribution of the 4-body decay $B \to K^*(\to K\pi) l^+l^-$.

• These relations emerge out of the symmetries of the angular distribution.
• We discuss the implications of these relations under the (testable) hypotheses of no scalar or tensor contributions and no New Physics weak phases in the Wilson coefficients.
• Under these hypotheses there is a direct relation among the observables $P_{1}$,$P_2$ and $P_{4,5}^\prime$.