Study of $B_{c} \rightarrow \psi(2S) K$, $\eta_{c}(2S)K$, $\psi(3770)K$ decays with perturbative QCD approach

TL;DR

This paper calculates the branching ratios of specific $B_c$ meson decays involving excited charmonium states using perturbative QCD, providing predictions that can be tested at LHC-b.

Contribution

It introduces a novel calculation of $B_c$ decay branching ratios with new orbitally excited charmonium distribution amplitudes and studies the impact of S-D mixing angles.

Findings

Branching ratios for $B_c o ext{excited charmonium} + K$ are around $10^{-5}$.

The $B_c o ext{psi(3770)} + K$ decay rate is sensitive to S-D mixing angles.

Predictions are testable at LHC-b experiments.

Abstract

We study the $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays with perturbative QCD approach (pQCD) based on $k_T$ factorization. The new orbitally excited charmonium distribution amplitudes $\psi(1^{3}D_{1})$ based on the Schr\"{o}dinger wave function of the $n=1$, $l=2$ state for the harmonic-oscillator potential are employed. By using the corresponding distribution amplitudes, we calculate the branching ratio of $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays and the form factors $A_{0,1,2}$ and $V$ for the transition $B_{c}$$\rightarrow$$\psi(1^{3}D_{1})$. We obtain the branching ratio of both $B_{c}$$\rightarrow$$\psi(2S)$K and $B_{c}$$\rightarrow$$\eta_{c}(2S)$K are at the order of $10^{-5}$. The effects of two sets of the S-D mixing angle $\theta=-12^{\circ}$ and $\theta=27^{\circ}$ for the decay $B_{c}$$\rightarrow$$\psi(3770)$K are studied firstly in this paper. Our calculations show that the branching ratio of the decay $B_{c}$$\rightarrow$$\psi(3770)$K can be raised from the order of $10^{-6}$ to the order of $10^{-5}$ at the mixing angle $\theta=-12^{\circ}$, which can be tested by the running LHC-b experiments.