Novel method to reliably determine the photon helicity in $b\to s\gamma$

A sizable right-handed photon polarization in $b\to s\gamma$ is a clear signal for new physics. In this work we point out that the photon helicity in $b\to s\gamma$ can be unambiguously extracted by combining the measurements in $B\to K_1\gamma$ and the Cabibbo-favored $D\to K_1 e^+\nu$ decay. We propose a ratio of up-down asymmetries in $D\to K_1 e^+\nu$ to quantify the hadronic effects. { A method for measuring in experiment the involved partial decay widths in the ratio is discussed, and experimental facilities like BESIII, Belle-II and LHCb are likely to measure this ratio. We also give the angular distribution that is useful to extract the photon polarization in the presence of different kaon resonances. }