Novel method to reliably determine the photon helicity in $b\to s{\hat{I}}^3$

Abstract

A sizable right-handed photon polarization in $b\to s{\hat{I}}^3$ is a clear signal for new physics. In this work we point out that the photon helicity in $b\to s{\hat{I}}^3$ can be unambiguously extracted by combining the measurements in $B\to K_1{\hat{I}}^3$ and the Cabibbo-favored $D\to K_1{e}^{+}\hat{I}½$ decay. We propose a ratio of up-down asymmetries in $D\to K_1{e}^{+}\hat{I}½$ 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. }

5 pages, 1 figure; v2: title changed, a method for experimental measurements of the involved partial decay widths is given, accepted for publication in Physical Review Letters