The time-dependent $CP$ asymmetry in $B^0 \to K_{\rm res} γ\to π^+ π^- K^0_{\scriptscriptstyle S} γ$ decays
英文摘要：
The time-dependent $CP$ asymmetry in $B^0 \to K_{\rm res} γ\to π^+ π^- K^0_{\scriptscriptstyle S} γ$ is sensitive to the photon polarisation in the quark level process $b \to s γ$. 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 $B^0 \to K_{\rm res} γ\to π^+ π^- K^0_{\scriptscriptstyle S} γ$ including the most dominant intermediate states. We propose a new observable that could be measured in a time-dependent amplitude analysis of $B^0 \to π^+ π^- K^0_{\scriptscriptstyle S} γ$ 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.
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