Transitions of $B_c\rightarrow \psi(1S,2S)$ and the modified harmonic oscillator wave function in LFQM

TL;DR

This paper calculates decay form factors for B_c meson transitions using a modified harmonic oscillator wave function within LFQM, achieving predictions consistent with experimental data and demonstrating improved modeling accuracy.

Contribution

It introduces a modified harmonic oscillator wave function in LFQM to better model B_c decays, aligning theoretical predictions with experimental results.

Findings

Predicted decay ratios agree with experimental data within 1σ.

Modified harmonic oscillator wave function outperforms traditional models.

Form factors for B_c→J/ψ and B_c→ψ(2S) are numerically calculated.

Abstract

The LHC$_b$ collaboration has systematically measured the rates of $B_c\to J/\psi K$, $B_c\to J/\psi D_s$, $B_c\to J/\psi D_s^*$ and $B_c\to \psi(2S) \pi$. The new data enable us to study relevant theoretical models and further determine the model parameters. In this work, We calculate the form factors for the transitions $B_c\to J/\psi$ and $B_c\to \psi(2S)$ numerically, then determine the partial widths of the semi-leptonic and non-leptonic decays. The theoretical predictions on the ratios of $\Gamma(B_c\to J/\psi K)/\Gamma(B_c\to J/\psi \pi)$, $\Gamma(B_c\to J/\psi D_s)/\Gamma(B_c\to J/\psi \pi)$ and $\Gamma(B_c\to J/\psi D_s^*)/\Gamma(B_c\to J/\psi \pi)$ are consistent with data within only 1$\sigma$. Especially, for calculating $\Gamma(B_c\to \psi(2S)X)$ the modified harmonic oscillator wave function (HOWF) which we developed in early works is employed and the results indicate that the modified harmonic oscillator wave function works better than the traditional HOWF.