$B_c\to J/\psi$ 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 $\mathcal{B}(B_c^{+}\to J/\psi {\pi }^{+})=(0.136_{-0.002}^{+0.002})\%$, $\mathcal{B}(B_c^{+}\to J/\psi K^{+})=(0.010_{-0.000}^{+0.000})\%$, $\mathcal{B}(B_c^{+}\to J/\psi {\rho }^{+})=(0.768_{-0.033}^{+0.029})\%$, $\mathcal{B}(B_c^{+}\to J/\psi K^{\ast +})=(0.043_{-0.001}^{+0.001})\%$, $\mathcal{B}(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })=(2.802_{-0.675}^{+0.526})\%$ and $\mathcal{B}(B_c^{+}\to J/\psi {\tau }^{+}{\nu }_{\tau })=(0.559_{-0.170}^{+0.131})\%$. We then obtain ${\mathcal{R}}_{{\pi }^{+}/{\mu }^{+}{\nu }_{\mu }}=0.048_{-0.012}^{+0.009}$ and ${\mathcal{R}}_{K^{+}/{\pi }^{+}}=0.075_{-0.005}^{+0.005}$, which agree with the LHCb measured value within $1\sigma$-error. We also obtain ${\mathcal{R}}_{J/\psi }=0.199_{-0.077}^{+0.060}$, 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 in a new way implies that there may be new physics in the $B_c\to J/\psi {\ell }^{+}{\nu }_{\ell }$ semi-leptonic decays.

Comments: 10 pages, 4 figures, published version