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

The time-dependent $C P$ 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 $b \to s γ$ . 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 $C P$ properties. In this paper, we derive the $C P$ 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 $B^{0} \to π^{+} π^{-} K_{S}^{0} γ$ 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.

The time-dependent $C P$ asymmetry in $B^{0} \to K_{r e s} γ \to π^{+} π^{-} K_{S}^{0} γ$ decays

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The time-dependent $C P$ asymmetry in $B^{0} \to K_{r e s} γ \to π^{+} π^{-} K_{S}^{0} γ$ decays

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The time-dependent CPCP asymmetry in B0→Kresγ→π+π−KS0γB0→Kres​γ→π+π−KS0​γ decays

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The time-dependent CPCP asymmetry in B0→Kresγ→π+π−KS0γB0→Kres​γ→π+π−KS0​γ decays

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The time-dependent $C P$ asymmetry in $B^{0} \to K_{r e s} γ \to π^{+} π^{-} K_{S}^{0} γ$ decays

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The time-dependent $C P$ asymmetry in $B^{0} \to K_{r e s} γ \to π^{+} π^{-} K_{S}^{0} γ$ decays

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