Study of $B_c\to \psi (2S)K$, ${\eta }_c(2S)K$, $\psi (3770)K$ decays with perturbative QCD approach

Abstract

We study the $B_c$$\to$$\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 Schrödinger 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$$\to$$\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$$\to$$\psi (1^3{D}_1)$. We obtain the branching ratio of both $B_c$$\to$$\psi (2S)$K and $B_c$$\to$${\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$$\to$$\psi (3770)$K are studied firstly in this paper. Our calculations show that the branching ratio of the decay $B_c$$\to$$\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.

arXiv comment12pages, 2 figures

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Cited by in corpus (3)

• Study the contributions of S, P, and D-wave resonances to the quasi-two-body decays $B_s^0\to \psi (3686,3770)K\pi$ in perturbative QCD approach
• Study of the quasi-two-body decays B^{0}_{s} \rightarrow ψ(3770)(ψ(3686))π^+π^- with perturbative QCD approach
• Systematic analysis of the transition form factors of $B_c$ to $D$-wave charmonia and corresponding semileptonic decays