Search for CP violation in D_(s)⁺ K⁺ K_S⁰h⁺h^- (h = K, ) decays and observation of the Cabibbo-suppressed decay D_s⁺ K⁺ K^- K_S^{0 +}

We search for CP violation by measuring a T-odd asymmetry in the Cabibbo-suppressed D+ -> (K+KS0)pi(+)pi(-) decay, and in the Cabibbo-favored D-s(+)->(K+KS0)pi(+)pi(-) and D+->(K+K-KS0)pi(+) decays. We use 980 fb(-1) of data collected by the Belle detector running at the KEKB asymmetric-energy e(+)e(-) collider. The CP-violating T-odd parameter a(CP)(T-odd) is measured to be a(CP)(T-odd)(D+->(K+KS0)pi(+)pi(-))=(0.34 +/- 0.87 +/- 0.32)%, a(CP)(T-odd)(D-s(+)->(K+KS0)pi(+)pi(-))=(-0.46 +/- 0.63 +/- 0.38)%, and a(CP)(T-odd)(D+->(K+K-KS0)pi(+))=(-3.34 +/- 2.66 +/- 0.35)%, where the first uncertainty is statistical and the second is systematic. We also report the first observation of the Cabibbo-suppressed decay D-s(+)->(K+K-KS0)pi(+). The branching fraction is measured relative to that of the analogous Cabibbo-favored decay: B(D-s(+)->(K+K-KS0)pi(+))/B(D-s(+)->(K+KS0)pi(+)pi(-))=(1.36 +/- 0.15 +/- 0.04)%.