| In this paper,we were calculated D→ρ,D→ P(π,K)and Bc→(ηc,J/Ψ)semileptonic decay by applying the QCD light-cone sum rule(LCSR)approach.Heavy flavor physics is the frontier and hot-spot of particle physics re-search at present.Firstiy,the measured branching ratio of the D-meson semilep-tonic decay D→ρe+ve,which is based on the 0.82 fb-1 CLEO data taken at the peak of Ψ(3770)resonance,disagrees with the traditional Shifman-Vainshtein-Zakharov(SVZ)sum rules analysis by about three times.In the paper,we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules(LCSR)approach to calculate the D→p transition form factors and the branching ratios.we obtain(?)and(?),which agree with the CLEO measurements within errors.We also calculate the branching ratios of the two D meson radiative processes and obtain(?)and(?),which also agree with the Belle measure-ments within errors.Secondly,the calculation of the D→ P(π,K)decay process.The resultant HFFs at(?)We obtain the decay widths and the branching fractions for semileptonic decay processes of D→ Plve,our predictions also agree with BES-Ⅲ collaboration within errors,especially for D→πlvl decay process.Finally,we present the forward-backward asymmetry AFBl(q2)and lepton convexity parameter CFl(q2),and further calculate the mean value of these two observations<AFBl>and<CFl>,which may provide a way to test those HFFs in future experiments.Finally,new physics in the Bc semileptonic decay processes might be neces-sary to address anomalies between experimental and theoretical predictions.In this paper,we discussed Bc→ηc and Bc→J/Ψ semileptonic decays within the Standard Model and beyond.We calculate the semileptonic branching fractions and find for the ratios,(?)Both predic-tions are in agreement with other existing calculations and support the current tension in RJ/Ψ at 2a level with the experiment.So it is very important to cal-culate the Bc semileptonic decay processes of new physics(NP).Meanwhile this paper calculated the forward-backward asymmetry AFB,the convexity parameter CFτ and the longitudinal polarization PL and transverse polarizationPT. |