Novel Method to Reliably Determine the Photon Helicity in $B\to K_1\gamma$

A sizable right-handed photon polarization in $b\to s\gamma$ is a clear signal for new physics. In this Letter, 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 for extracting the photon polarization in the presence of different kaon resonances.

Figure 1

Kinematics for $D\to K_{\mathrm{res}}(\to K\pi \pi )e^{+}\nu$. The relative angle between the normal direction of the $K_{\mathrm{res}}$ decay plane and the opposite of $D$ flight direction in the $K_{\mathrm{res}}$ rest frame is denoted as ${\theta }_K$, while ${\theta }_l$ is introduced as the relative angle between the flight directions of $e^{+}$ in the $e^{+}\nu$ rest frame and the $e^{+}\nu$ in the $D$ rest frame.