Probing the photon polarization in $B \to K^*\gamma$ with conversion

TL;DR

This paper proposes a novel method to measure photon polarization in B meson decays using photon conversion to lepton pairs, providing analytical expressions and kinematic strategies to enhance experimental sensitivity.

Contribution

It introduces a new angular analysis technique based on photon conversion, with compact amplitude expressions and optimized kinematic cuts for better measurement precision.

Findings

Interference allows probing photon polarization ratios and phases.

Kinematic cuts can enhance statistical sensitivity by an order of magnitude.

Numerical simulations verify the effectiveness of the proposed method.

Abstract

We re-examine the possibility to measure the photon polarization in $B \to K^*\gamma$ decays, via decays in which the photon subsequently undergoes nuclear conversion to a lepton pair. We obtain compact expressions for the full decay-plus-conversion amplitude. With these results we show that interference between the $B \to (K^*\to K\pi)\gamma$ decay and the $\gamma N \to \ell^+\ell^-N$ conversion permits both the ratio and relative weak phase between the left- and right-handed photon amplitudes to be probed by an angular observable, constructed from the final state dilepton, kaon and pion kinematic configuration. Exploiting this technique will be experimentally challenging. However, we present special kinematic cuts that enhance the statistical power of this technique by an $\mathcal{O}(1)$ factor. We verify this effect and extract pertinent angular kinematic distributions with dedicated numerical simulations.