The Weak Decays And CP Violation Of B Mesons Under PQCD Approach

B physics has been one hot topic of particle physics for many years. How to deal with the QCD dynamics in B meson decays is a very important topic. There are many successful models and approaches, PQCD, who can deal with the exclusive decays very well, is one of them. In a very brief way we review several popular topics in B physics such as neutral B meson mixing, CP violation, the effective Hamiltonian for B meson electro-weak decays, and the frame of PQCD approach.With the PQCD approach we study the form factors of B meson to the two kinds of axial vector mesons,3P1 and 1P1 states, respectively. The form factors are calculated directly in the large recoiling region and extrapolated to the whole kinematics region within dipole parametrization. As a byproduct, we calculate all the charged current semi-leptonic decays of B meson to axial vector mesons. Most of the branching ratios of B→Alvl are of the order of 10-4, which still need experimental tests in the ongoing and forthcoming experiments. The strange axial vector mesons K1A and K1B via SU(3) breaking effect. In order to reduce the ambiguities in the mixing angle between them, we propose a model-independent way that utilize B decay data.We study the B→K1(1270)l+l- and B→K1(1400)l+l- decays with the form factors we get. Using the technique of helicity amplitudes, we express the de-cay amplitudes in terms of several independent and Lorentz invariant pieces. We study the dilepton invariant mass distributions, branching ratios, polarizations, and forward-backward asymmetries of B→K1l+l- decays. The ambiguity of the sign of the mixing angle will induce very large differences to branching ratios of the semi-leptonic B decays:branching ratios without resonant contributions either have the order of 10-6 or 10-8. But the polariztions and the forward-backward asymmetries are not sensitive to the mixing angles. We find that the resonant contributions will dramatically change the dilepton invariant mass dis-tributions in the resonant region. We also provide the angular distributions of B→K1l+l-→(Kππ)l+l- decays.We also apply the PQCD approach to the charmful decays of B mesons. In this type of decays large ambiguity exists in the wave function of D mesons. Using experimental data of B→DP (P denotes a light pseudoscalar meson) decay channels, we determine the D meson wave function by x2 fit.With the D meson wave function obtained, we study the 154 decay channels of B→D(*)(D(*))M (M denotes a light meson) and 40 channels of B meson to two charmed mesons to the leading order of mD/mB and AQCD/mD expansion. We calculate all the branching ratios, polarization fractions, CP asymmetries, and other quantities that are useful for theory or experiments. Most of our results agree with the current experimental data amazing well.Our calculation gives the right relative strong phase of a2/a1 that agrees with the experiments. In the B→D(*)M decays, the nonfactorizable emis-sion and annihilation diagrams are not negligible in many channels, which are very different from the situation of B meson decays to light mesons. The ratiowhich are very important for the extraction of CKM angleγexperimentally, is obtained as r=0.092-0.003-0.003+0.012+0.003. This value is too small for experiments to extractγwith a high accuracy.In the study of B meson to two charmed mesons, we find that the factorizable emission diagrams are dominant. The agreement between our results and the experimental data indicates that the factorization theorem is reliable in predicting branching ratios of these decays. In the decays of a B meson to two vector charmed mesons, the transverse polarization states contribute 40% - 50% both in the processes with an external W emission and in the pure annihilation decays. This is in agreement with the present experimental data. The CP asymmetries obtained is very small. Thus observation of any large direct CP asymmetry will be a signal for new physics. The mixing induced CP asymmetry in the neutral modes is large. This is also in agreement with the current experimental measurements. They can give a cross check of the sin 2βmeasurement from other channels.Our calculations for the Bs meson decays will be confronted with the future experiments.