Measurement of time-dependent CP asymmetries in $${B}^{0}\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}\gamma $$ decays at Belle and Belle II

A bstract We present a measurement of the time-dependent CP asymmetry in $${B}^{0}\to {K}_{\text{S}}^{0}{\pi }^{+}{\pi }^{-}\gamma $$ decays using a data set of 365 fb − 1 recorded by the Belle II experiment and the final data set of 711 fb − 1 recorded by the Belle experiment at the Υ(4S) resonance. The direct and mixing-induced time-dependent CP violation parameters C and S are determined along with two additional quantities, S + and S − , defined in the two halves of the $${m}^{2}\left({K}_{\text{S}}^{0}{\pi }^{+}\right)-{m}^{2}\left({K}_{\text{S}}^{0}{\pi }^{-}\right)$$ plane. The measured values are C = − 0 . 17 ± 0 . 09 ± 0 . 04, S = − 0 . 29 ± 0 . 11 ± 0 . 05, S + = −0 . 57 ± 0 . 23 ± 0 . 10 and S − = 0 . 31 ± 0 . 24 ± 0 . 05, where the first uncertainty is statistical and the second systematic.