Non-perturbative Methods In QCD: Light-cone Sum Rule And AdS/QCD

In this thesis I will present some results in studying strong interaction with some non-perturbative methods, namely light-cone sum rule and AdS/QCD.First, we will focus on the application of light-cone sum rule in studying the weak decays of heavy mesons. To eliminate the contributions of the poorly known higher-twist distribution amplitudes, people introduce chiral current correlators to calculate the form factors of some semileptonic processes. We generalize this approach to more complicated case where the final state involves a vector meson. Moreover, we find simple relations between the form factors of all the semileptonic decays, which are almost identical to the ones found over ten years ago by Stech. Then we try to use these sum rules to study the decay process when the final state meson contains a heavy quark, such as B→Dlv, and all the semileptonic decays of the B_c meson. The meson containing a heavy quark can be well described by some models, for example, by employing the BHL model to describe the J/ψ(η_c) meson we can get the resultσ(e~+e~-→J/ψ+η_c) consistent with experiments of Belle and BaBar.Recently the AdS/QCD approach, which is based on the famous AdS/CFT correspondence , has made remarkable achievements in studying hadron spectrum and strong dynamics. Here we just make some discussions on a phenomenological model, the socalled soft wall model. Due to the lack of an explicit infrared cutoff, theρcouplings with any hadron H in this model is not universal as in general AdS/QCD models, but expresses a linear increasing behavior with the exciting number of H. Based on quasi-classical approximation , we can give a simple explanation of this behavior. At the same time, we don't have an infrared boundary condition to constrain the non-normalized mode. However , we can use the correlation relation obtained from dispersion relation to determine the solution. In other words, we are actually determining the non-normalized mode for the corresponding normalized modes. Due to the explicit Regge trajectory in this model, the expansion of the correlation function necessarily contains a dimension-two term.