$B_c \\to J/\\psi$ helicity form factors and the $B_c^+ \\to J/\\psi+(P, V, \\ell^+ \\nu_\\ell)$ decays

Abstract In this paper, we calculate the $B_c\\to J/\\psi$ helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules (LCSR) approach. After extrapolating those HFFs to the physically allowable $q^2$ region, we investigate the $B^+_c$-meson two-body decays and semi-leptonic decays $B_c^+ \\to J/\\psi+(P, V, \\ell^+ \\nu_\\ell)$ with $P/V$ stands for light pseudoscalar/vector meson, respectively. The branching fractions can be derived by using the CKM matrix element and the $B_c$ lifetime from the Particle Data Group, and we obtain ${\\cal B}(B_c^+ \\to J/\\psi \\pi^+)=(0.136^{+0.002}_{-0.002})\\%$, ${\\cal B}(B_c^+ \\to J/\\psi K^+)=(0.010^{+0.000}_{-0.000})\\%$, ${\\cal B}(B_c^+ \\to J/\\psi \\rho^+) =(0.768^{+0.029}_{-0.033})\\%$, ${\\cal B}(B_c^+ \\to J/\\psi K^{\\ast +})=(0.043^{+0.001}_{-0.001})\\%$, ${\\cal B}(B_c^+ \\to J/\\psi \\mu^+\\nu_\\mu)=(2.802^{+0.526}_{-0.675})\\%$ and ${\\cal B}(B_c^+ \\to J/\\psi \\tau^+\\nu_\\tau)=(0.559^{+0.131}_{-0.170})\\%$. We then obtain ${\\cal R}_{\\pi^+/\\mu^+\\nu_\\mu} = 0.048^{+ 0.009}_{-0.012}$ and ${\\cal R}_{K^+ / \\pi^+} = 0.075^{+0.005}_{-0.005}$, which agree with the LHCb measured value within $1\\sigma$-error. We also obtain ${\\cal R}_{J/\\psi}=0.199^{+ 0.060}_{-0.077}$, which like other theoretical predictions, is consistent with the LHCb measured value within $2\\sigma$-error. Those imply that the HFFs under the LCSR approach are also applicable to the $B^+_c$ meson two-body decays and semi-leptonic decays $B_c^+ \\to J/\\psi+(P, V, \\ell^+ \\nu_\\ell)$, and the HFFs obtained by using LCSR from a new way implies that there may be a new physic in the $B_c\\to J/\\psi \\ell^+ \\nu_\\ell$ semi-leptonic decays. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.