Search for $C\!P$ violation in $D^+_{(s)}\to{}K_{S}^{0}K^{-}π^{+}π^{+}$ decays using triple and quadruple products

We perform the first search for CP violation in Ds+→KS0K−π+π+ decays. We use a combined data set from the Belle and Belle II experiments, which study e+e− collisions at center-of-mass energies at or near the Υ(4S) resonance. We use 980 fb−1 of data from Belle and 428 fb−1 of data from Belle II. We measure six CP-violating asymmetries that are based on triple products and quadruple products of the momenta of final-state particles, and also the particles’ helicity angles. We obtain a precision at the level of 0.5% for D+→KS0K−π+π+ decays, and better than 0.3% for Ds+→KS0K−π+π+ decays. No evidence of CP violation is found. Our results for the triple-product asymmetries are the most precise to date for singly-Cabibbo-suppressed D+ decays. Our results for the other asymmetries are the first such measurements performed for charm decays.