Future prospects for the determination of the Wilson coefficient $C_{7{\hat{I}}^3}^{\prime }$

Abstract

We discuss the possibilities of assessing a non-zero $C_{7{\hat{I}}^3}^{\prime }$ from the direct and the indirect measurements of the photon polarization in the exclusive $b \to sγ^{(*)}$ decays. We focus on three methods and explore the following three decay modes: $B\to K^{\ast }(\to K_S\ddot{I}{€}^0){\hat{I}}^3$, $B\to K_1(\to K\ddot{I}€\ddot{I}€){\hat{I}}^3$, and $B\to K^{\ast }(\to K\ddot{I}€){\ell }^{+}{\ell }^{-}$. 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 $C_{7{\hat{I}}^3}$ and $C_{7{\hat{I}}^3}^{\prime }$.

34 pages, 10 figures