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

Published 18 Jul 2021 in hep-ph | (2107.08405v2)

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 in a new way implies that there may be new physics in the $B_c\to J/\psi \ell⁺ \nu_\ell$ semi-leptonic decays.