  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
$Br(B^+\to\psi(2S)K^+)=(5.37^{+1.85}_{-2.22})\times10^{-4},
Br(B^0\to\psi(2S)K^0)=(4.98^{+1.71}_{-2.06})\times10^{-4},
Br(B^+\to\eta_c(2S)K^+)=(3.54^{+3.18}_{-3.09})\times10^{-4}$, 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
$f_{\eta_c(2S)}=0.243^{+0.079}_{-0.111}$ 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, $Br(B^+\to\psi(2S)\pi^+)=(1.17^{+0.42}_{-0.50})\times10^{-5},
Br(B^0\to\psi(2S)\pi^0)=0.54^{+0.20}_{-0.23}\times10^{-5}$, 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.
