Estimating the branching fraction for $B^0\rightarrow \psi(2S)\pi^0$ decay

I present estimates of the branching fractions in the non-leptonic charmonium two-body decay rates for $B^0\rightarrow \psi(2S)\pi^0$ decay and the same decays of $B^+\rightarrow \psi(2S)\pi^+$, $B^0\rightarrow \psi(2S)K^0$ and $B^+\rightarrow \psi(2S)K^+$. These estimates are based on a generalized factorization approach making use of leading order (LO) and next-to-leading order (NLO) contributions. I find that when the large enhancements from the known NLO contributions by using the QCD factorization approach are taken into account, the branching ratios are the following: $Br(B^0\rightarrow \psi(2S)\pi^0)=(1.067\pm0.059)\times10^{-5}$, $Br(B^+\rightarrow \psi(2S)\pi^+)=(2.134\pm0.0.118)\times10^{-5}$, $Br(B^0\rightarrow \psi(2S)K^0)=(6.344\pm0.376)\times10^{-4}$ and $Br(B^+\rightarrow \psi(2S)K^+)=(6.344\pm0.376)\times10^{-4}$, while the experimental results are $(1.17\pm 0.17)\times 10^{-5}$, $(2.44\pm 0.30)\times 10^{-5}$, $(6.20\pm 0.50)\times 10^{-4}$ and $(6.39\pm 0.33)\times 10^{-4}$ respectively. All estimates are in good agreement with the experimental results.