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

Abstract

In this paper, we calculate the Bc → J/ψ helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules 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 → J/ψ + (P, V, ℓ + ν ℓ ), where P and V stand for a light pseudo-scalar meson and a vector meson, respectively. The branching fractions can be derived by using the CKM matrix element and the Bc lifetime from the Particle Data Group, and we obtain B(B + c → J/ψπ + ) = (0.132 +0.002 −0.002 )%, B(B + c → J/ψK + ) = (0.010 +0.000 −0.000 )%, B(B + c → J/ψρ + ) = (0.755 +0.030 −0.034 )%, B(B + c → J/ψK * + ) = (0.043 +0.001 −0.001 )%, B(B + c → J/ψµ + νµ) = (2.808 +0.547 −0.704 )% and B(B + c → J/ψτ + ντ ) = (0.563 +0.137 −0.178 )%. We then obtain R π + /µ + νµ = 0.047 +0.009 −0.012 and R K + /π + = 0.075 +0.005 −0.005 , which agree with the LHCb measured value within 1σ-error. We also obtain R J/ψ = 0.200 +0.062 −0.081 , which like other theoretical predictions, are consistent with the LHCb measured value within 2σ-error.