The decays B → Ψ(2S)π(K),ηc(2S)π(K) in the pQCD approach beyond the leading-order

Two body B meson decays involving the radially excited meson ψ(2S)/ηc(2S) in the final states are studied by using the perturbative QCD (pQCD) approach. We find that: (a) The branching ratios for the decays involving a K meson are predicted as Br(B+→ψ(2S)K+)=(5.37−2.22+1.85)×10−4, Br(B0→ψ(2S)K0)=(4.98−2.06+1.71)×10−4, Br(B+→ηc(2S)K+)=(3.54−3.09+3.18)×10−4, which are consistent with the present data when the next-to-leading-order (NLO) effects are included. Here the NLO effects are from the vertex corrections and the NLO Wilson coefficients. The large errors in the decay B+→ηc(2S)K+ are mainly induced by using the decay constant fηc(2S)=0.243−0.111+0.079 GeV with large uncertainties. (b) While there seems to be some room left for other higher order corrections or the non-perturbative long distance contributions in the decays involving a π meson, Br(B+→ψ(2S)π+)=(1.17−0.50+0.42)×10−5, Br(B0→ψ(2S)π0)=0.54−0.23+0.20×10−5, which are smaller than the present data. The results for other decays can be tested via running LHCb and forthcoming Super-B experiments. (c) There is no obvious evidence of the direct CP violation being seen in the decays B→ψ(2S)π(K),ηc(2S)π(K) in the present experiments, which is supported by our calculations. If a few percent value is confirmed in the future, this would definitely indicate the existence of new physics.