Observation of B${}^0$ → ψ(2S)K${}_S^0$π${}^{+}$π${}^{-}$ and B${}_s^0$ → ψ(2S)K${}_S^0$ decays

Using a data sample of $\sqrt{s}$ = 13 TeV proton-proton collisions collected by the CMS experiment at the LHC in 2017 and 2018 with an integrated luminosity of 103 fb${}^{-1}$, the B${}_s^0$ → ψ(2S)K${}_S^0$ and B${}^0$ → ψ(2S)K${}_S^0$π${}^{+}$π${}^{-}$ decays are observed with significances exceeding 5 standard deviations. The resulting branching fraction ratios, measured for the first time, correspond to B(B${}_s^0$ → ψ(2S)K${}_S^0$/B(B${}^0$ → ψ(2S)K${}_S^0$) = (3.33 ± 0.69(stat) ± 0.11(syst) ± 0.34 ($f_s$/$f_d$)) × 10${}^{-2}$ and B(B${}^0$ → ψ(2S)K${}_S^0$π${}^{+}$π${}^{-}$/B(B${}^0$ → ψ(2S)K${}_S^0$) = 0.480 ± 0.013(stat) ± 0.032(syst), where the last uncertainty in the first ratio is related to the uncertainty in the ratio of production cross sections of B${}_s^0$ and B${}^0$ mesons, $f_s$/$f_d$.