Form Factors Of Light Meson In The Perturbation QCD Factorization Approach

B meson physics is a hot topic for both the theoretical and experimental studies of high energy particle physics. In the theory side, the study of B meson weak decays plays an important role in the precision test of the standard model (SM) and the search for the signals of the new physics beyond the SM. The B meson weak decays do involve many energy scales, and have been studied systematically by employing the low energy effective Hamiltonian method. The perturbation QCD (PQCD) factorization approach, based on the kT theorem, is currently one of the most popular method being used to study the B meson decays. In the framework of the PQCD factorization approach, the transverse momentum kT is retained in order to suppress the endpoint singularity; The Sudakov form factor could be obtained through the resummation of those large double logarithmic terms, which in turn can provide further suppression to the end-point divergence and can therefore ensure the convergency of the perturbative calculations. In the experiment side, the BaBar and Belle collaboration in the two B factory experiments found the CP violation in B meson system and collected large amount of data about the production and decays of B meson. The ATLAS and CMS collaboration, working in the Large Hadron Collider (LHC) experiment in CERN, reported their discovery of the SM Higgs boson in July of 2012. The LHCb collaboration has also done a very good job to measure the production and decays of various b mesons: including the Bu,d, Bs and Bc mesons,as well as some kinds of b-baryons. The Super-B factory in Japan will begin physics running in the late 2017. The high accuracy of experimental measurements does require the precise theoretical predictions. So it's very important for us to make calculations at the next-to-leading order (NLO) for those physical observables of the B meson decay processes.In the framework of the SM, many studies about the major decay modes of B mesons have been accomplished recently. But it is still very difficult to explain those anomalies or puzzles being found in the B factory and the LHC experiments. So there is an urgent requirement to improve the calculation precision and its credibility by taking into account the higher-order contributions or something new from the new physics beyond the SM.These works can help us to improve the PQCD factorization approach as well as the QCD itself, and can play an important role in ones effort to analyze the massive data successively.In the first chapter of this thesis, I gave a brief introduction for current status of the particle physics. In chapter two, I presented a short review about the framework of the weak interactions and quantum chromodynamics (QCD) of the SM. A systematic overview for those main factorization approaches, specifically the perturbative QCD factorization approach based on the so-called kT factorization theorem, is given in detail in chapter three. My own works are presented in the chapter four and five, the main part of this thesis. By employing the PQCD factorization approach, we studied the exclusive processes??* ?? and ??*?? and found the following results:(1) Through our studies for both ??* ?? and ??* ?? transitions, we calculated at the leading order the ?? transition form factor Q4??(Q2) and the ? meson elec-tromagnetic form factor ,FLL,TT(Q2) and F1,2,3(Q2) For the ??* ?? transi-tion process, the major contribution to transition form factor Q4F??(Q2) comes from the terms proportional to ??T(x1)??P(x2). The PQCD predictions for the Q2-dependence of the form factor Q4F??(Q2) are consistent with those from the Ad-S/QCD model and the light-cone QCD sum rules. For the ??* ?? transition process,we found an approximate relation about the p meson electromagnetic form factor FLL,LT,TT(Q2): FLT(Q2) > FLL:(Q2) >> FTT(Q2)? Although there is an en-hancement factor of Q/M? for FLL(Q2) against FLT(Q2) but there is an additional suppression from x2, this general expectation agree well with our result. In the region of Q2 > 2GeV2, the PQCD predictions for the electromagnetic form factor F1,2(Q2) agree well with those from the LCSR. But the PQCD prediction for the value of F3(Q2) is however much larger than the one from LCSR.(2) Than we first demonstrate that the fact.orization hypothesis is valid at the next-to-leading order (NLO) for the exclusive process ??* ?? by employing the collinear factorization approach, and then extend this proof to the case of the kT factoriza-tion by taking into account the transversal momentum of the light external quark(antiquark) lines in the p meson. We also write down the polarized NLO p meson wave functions in the form of nonlocal hadron matrix elements with the gauge factor integral path deviating from the light cone. We find that the soft divergences cancel and collinear divergences are grouped into a p wave function. Then a full amplitude is expressed as the convolution of a hard amplitude with hadron wave function.