The time-dependent $CP$ asymmetry in $B^0 \to K_{\rm res} \gamma \to \pi^+ \pi^- K^0_{\scriptscriptstyle S} \gamma$ decays

TL;DR

This paper develops a formalism for measuring time-dependent $CP$ asymmetry in specific $B^0$ decays to probe photon polarization, which could reveal new physics beyond the Standard Model.

Contribution

It derives $CP$ violation formulas for $B^0$ decays including dominant intermediate states and proposes a new observable for experimental measurement.

Findings

Formulated $CP$ violation expressions for $B^0$ decays.

Proposed a new observable for photon polarization measurement.

Discussed prospects for constraints from Belle II and LHCb.

Abstract

The time-dependent $CP$ asymmetry in $B^0 \to K_{\rm res} \gamma \to \pi^+ \pi^- K^0_{\scriptscriptstyle S} \gamma$ is sensitive to the photon polarisation in the quark level process $b \to s \gamma$. While this polarisation is predominantly left-handed in the standard model, it could be modified by the existence of new physics contributions that may possess different $CP$ properties. In this paper, we derive the $CP$ violation formulae for $B^0 \to K_{\rm res} \gamma \to \pi^+ \pi^- K^0_{\scriptscriptstyle S} \gamma$ including the most dominant intermediate states. We propose a new observable that could be measured in a time-dependent amplitude analysis of $B^0 \to \pi^+ \pi^- K^0_{\scriptscriptstyle S} \gamma$ decays, providing a stringent contraint on the photon polarisation. We discuss the future prospects for obtaining such constraints from measurements at Belle II and LHCb.