Search for $CP$ violation in $D_{(s)}^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$ decays using triple and quadruple products

Abstract

We perform the first search for $CP$ violation in $D_{(s)}^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$ 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 ${\rm Y}(4S)$ 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 $D^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$ decays, and better than 0.3% for $D_s^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$ 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.

arXiv comment21 pages, 10 figures

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