B_(c)→J/ψhelicity form factors and the B_(c)^(+)→J/ψ+(P,V,ℓ^(+)ν_(ℓ))decays

In this paper,we calculate the B_(c)→J/ψhelicity 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)^(+)→J/ψ+(P,V,ℓ^(+)ν_(ℓ)),where P/V stand for light pseudoscalar and vector mesons,respectively.The branching fractions can be derived using the CKM matrix element and the B_(c)lifetime from the Particle Data Group,and we obtain B(B^(+)_(c)→J/ψπ^(+))=(0.136+0.002−0.002)%,B(B^(+)_(c)→J/ψK^(+))=(0.010+0.000−0.000)%,B(B^(+)_(c)→J/ψρ+)=(0.768+0.029−0.033)%,B(B^(+)_(c)→J/ψK^(∗+))=(0.043+0.001−0.001)%,B(B^(+)_(c)→J/ψ_(μ)+ν_(μ))=(2.802+0.526−0.675)%and B(B^(+)_(c)→J/ψτ^(+)ν_(τ))=(0.559+0.131−0.170)%.We then obtain R_(π^(+)/μ+ν_(μ))=0.048+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)=0.199+0.060−0.077,which like other theoretical predictions,is consistent with the LHCb measured value within 2σ-error.These 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→J/ψ+(P,V,ℓ^(+)ν_(ℓ)),and the HFFs obtained using LCSR in a new way implies that there may be new physics in the B_(c)→J/ψℓ^(+)ν_(ℓ)semi-leptonic decays.