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

TL;DR

This paper estimates the branching fractions for specific B meson decays involving $ ext{psi}(2S)$ and compares them with experimental data, finding good agreement when including NLO QCD effects.

Contribution

It provides theoretical estimates of B meson decay branching ratios using generalized factorization with NLO QCD corrections, aligning well with experimental results.

Findings

Estimated branching ratios match experimental data.

NLO QCD contributions significantly enhance decay rate predictions.

The approach confirms the validity of the generalized factorization method.

Abstract

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.