First observations of the $B^0_s rightarrow psi(2S) eta$, $B^0 rightarrow psi(2S) pi^+ pi^-$ and $B^0_s rightarrow psi(2S) pi^+ pi^-$ decays are made using a dataset corresponding to an integrated luminosity of 1.0~$fb^{-1}$ collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of $sqrt{s}=7$ TeV. The ratios of the branching fractions of each of the $psi(2S)$ modes with respect to the corresponding $J/psi$ decays are [ frac{mathcal{B}(B^0_s rightarrow psi(2S) eta) }{mathcal{B}(B^0_s rightarrow J/psi eta)} =0.83pm0.14,(stat)pm0.12,(syst)pm0.02,(mathcalB}), ] [ frac{mathcal{B}(B^0 rightarrow psi(2S) pi^+ pi^-)}{mathcal{B}(B^0 rightarrow J/psi pi^+ pi^-)} =0.56pm0.07,(stat)pm0.05,(syst)pm0.01,(mathcal{B}), ] [ frac{mathcal{B}(B^0_s rightarrow psi(2S) pi^+ pi^-)}{mathcal{B}(B^0_s rightarrow J/psi pi^+ pi^-)} =0.34pm0.04,(stat)pm0.03,(syst)pm0.01,(mathcal{B}), ] where the third uncertainty corresponds to the uncertainties of the dilepton branching fractions of the $J/psi$ and $psi(2S)$ meson decays.
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