This article presents a detailed analysis of $B^0 \to K_S^0 \pi^\pm \pi^\mp \gamma$ channel based on a full Monte-Carlo simulation of the Belle II experiment.
This channel belongs to $b \to s \gamma$ penguin processes, which serve as sensitive probes of New Physics. Within the Standard Model the time-dependent $CP$ violation is expected to be small in \btsg\ processes due to the chiral structure of the Standard Model. Therefore, any significant $CP$ asymmetry in the \process\ decay suggests a contribution of physics beyond the Standard Model.
The precision achieved by previous $B$-Factories, BaBar and Belle, on the $CP$ violating parameters in the $B^0 \to K_S^0 \pi^\pm \pi^\mp \gamma$ channel was statistically limited. This motivates a new measurement using the high integrated luminosity delivered by SuperKEKB and Belle II detector.
The statistical precision reached with the full Belle II dataset is expected to be $\delta S \approx 0.046$ and it will be comparable to the systematic uncertainty.