Measurements of the branching fractions of ₂^+ ^+Kₒ^0, ₂^+ ^0 ^+, and ₂^+ ^0K+ at Belle and Belle II

A bstract Using 983. 0 fb − 1 and 427. 9 fb − 1 data samples collected with the Belle and Belle II detectors at the KEKB and SuperKEKB asymmetric energy e + e − colliders, respectively, we present studies of the Cabibbo-favored ₂^+ decays ₂^+ ^+Kₒ^0 and ₂^+ ^0 ^+, and the singly Cabibbo-suppressed decay ₂^+ ^0K^+. The ratios of branching fractions of ₂^+ ^+Kₒ^0 and ₂^+ ^0K^+ relative to that of ₂^+ ^- ^+ ^+ are measured for the first time, while the ratio B (₂^+ ^0 ^+) /B (₂^+ ^- ^+ ^+) is also determined and improved by an order of magnitude in precision. The measured branching fraction ratios are arraycB ({ ₂^+ ^+Kₒ^0) }B ({ ₂^+ ^- ^+ ^+) }=0. 067 0. 007 0. 003, \\ B ({ ₂^+ ^0 ^+) }B ({ ₂^+ ^- ^+ ^+) }=0. 251 0. 005 0. 010, \\ B ({ ₂^+ ^0K^+) }B ({ ₂^+ ^- ^+ ^+) }=0. 017 0. 003 0. 001. array Additionally, the ratio B (₂^+ ^0K^+) /B (₂^+ ^0 ^+) is measured to be 0. 068 ± 0. 010 ± 0. 004. Here, the first and second uncertainties are statistical and systematic, respectively. Multiplying the ratios by the branching fraction of the normalization mode, B (₂^+ ^- ^+ ^+) = (2. 9 1. 3) \%, we obtain the following absolute branching fractions arraycB (₂^+ ^+Kₒ^0) = (0. 194 0. 021 0. 009 0. 087) \%, \\ B (₂^+ ^0 ^+) = (0. 728 0. 014 0. 027 0. 326) \%, \\ B (₂^+ ^0K^+) = (0. 049 0. 007 0. 003 0. 022) \%, array where the third uncertainties are from B (₂^+ ^- ^+ ^+).