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 $b\to s{\gamma }^{(\ast )}$ decays. We focus on three methods and explore the following three decay modes: $B\to K^{\ast }(\to K_S{\pi }^0)\gamma$, $B\to K_1(\to K\pi \pi )\gamma$, and $B\to K^{\ast }(\to K\pi ){\ell }^{+}{\ell }^{-}$. 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 $C_{7\gamma }^{\prime }$.

Comments: 34 pages, 10 figures