Future prospects for the determination of the Wilson coefficient $C_{7\gamma}^\prime$

Abstract

We discuss the possibilities of assessing a non-zero $C_{7\gamma}^\prime$ from the direct and the indirect measurements of the photon polarization in the exclusive $b \to s\gamma^{(*)}$ decays. We focus on three methods and explore the following three decay modes: $B \to K^*(\to K_S\pi^0)\gamma$, $B \to K_1(\to K\pi\pi)\gamma$, and $B \to K^*(\to K\pi)\ell^+\ell^-$. By studying different New Physics scenarios we show that the future measurement of conveniently defined observables in these decays could provide us with the full determination of $C_{7\gamma}$ and $C_{7\gamma}^\prime$.