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

We discuss the possibilities of assessing a non-zero $C_{7γ}^\prime$ 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: $B \to K^*(\to K_Sπ^0)γ$, $B \to K_1(\to Kππ)γ$, and $B \to K^*(\to Kπ)\ell^+\ell^-$. 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 $C_{7γ}$ and $C_{7γ}^\prime$.

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