The decays $B\to \Psi (2S)\pi (K),{\eta }_c(2S)\pi (K)$ in the pQCD approach beyond the leading-order

Abstract

Two body $B$ meson decays involving the radially excited meson $\psi (2S)/{\eta }_c(2S)$ in the final states are studied by using the perturbative QCD (pQCD) approach. We find that: (a) The branching ratios for the decays involving $K$ meson are predicted as $Br(B^{+}\to \psi (2S)K^{+})=(5.37_{-2.22}^{+1.85})\times 10^{-4},Br(B^0\to \psi (2S)K^0)=(4.98_{-2.06}^{+1.71})\times 10^{-4},Br(B^{+}\to {\eta }_c(2S)K^{+})=(3.54_{-3.09}^{+3.18})\times 10^{-4}$, which are consistent well with the present data when including the next-to-leading-order (NLO) effects. Here the NLO effects are from the vertex corrections and the NLO Wilson coefficients. The large errors in the decay $B^{+}\to {\eta }_c(2S)K^{+}$ are mainly induced by using the decay constant $f_{{\eta }_c(2S)}=0.243_{-0.111}^{+0.079}$ 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 $\pi$ meson, $Br(B^{+}\to \psi (2S){\pi }^{+})=(1.17_{-0.50}^{+0.42})\times 10^{-5},Br(B^0\to \psi (2S){\pi }^0)=0.54_{-0.23}^{+0.20}\times 10^{-5}$, which are smaller than the present data. The results for other decays can be tested at the running LHCb and forthcoming Super-B experiments. (c) There is no obvious evidence of the direct CP violation being seen in the decays $B\to \psi (2S)\pi (K),{\eta }_c(2S)\pi (K)$ in the present experiments, which is supported by our calculations. If a few percent value is confirmed in the future , it would indicate new physics definitely.

Comments: 11 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.00524