Next-to-leading-order Corrections To B Meson Weak Decays In κ_T Factorization Theorem

As the hot cross discipline of effective Hamilton theory of weak interaction and the QCD factorization theory, B meson physics provides a good place to test the standard model (SM), to investigate the dynamics of the CP violation and to find the evidence or signal of new physics beyond the SM. The two B factory experiments, BaBar in US and Belle in Japan, have made a great success. The LHC experiment in CERN, whose first running has found the Higgs particle hunted for about fifty years by the physicists around the world, will begin its second run in early 2015 with the collision energy being up to 13TeV. The Super-B factory in Japan will also start its running in 2017. All these high energy experiments will provide the strong push for B meson physics research. These experiments would provide more accurate measurements of B meson weak decays, which require much more precise theoretical works for the phenomenological analysis of massive experimental data, and will enable us to resolve those long standing "puzzles" in B meson physics.In this thesis, based on kT factorization theory, we calculated the next-to-leading or-der(NLO) corrections to several form factors involved in two-body charmless B decays, and found some interesting results. We try to improve the reliability and completeness of the perturbative QCD(pQCD) factorization approach by the inclusion of the NLO contributions, to increase the accuracy of the calculation based on the pQCD approach, and provide rea-sonable interpretation for the "ππ" or other puzzles. In the review part (chapter 2 and 3),the author firstly gave a brief review for the basic structure of the SM theory, and then presented an detailed introduction for the B meson mixing and various decays, as well as the main theoretical approaches being used in our studies. In chapter 3, the author made a complete description for the kT factorization theorem and the pQCD factorization approach, discussed the ultraviolet and/or infrared divergences appeared in the theoretical calculations and the possible ways to delete them.In the fourth chapter, by employing the collinear and kj factorization frameworks, we made an detailed investigation for the factorization of the infrared divergence for some exclusive transition processes, such as Ï€r*â†'r(Ï€) and B â†'(Ï€)lv. We made the proofs for the factorization at the NLO level. We found that all the infrared information from the gluon radiated from the external quarks can be absorbed into the nonlocal hadronic matrix elements of the initial and final meson wave functions, whose gauge-invariance were also guaranteed by the Wilson lines.The Chapter 5 and 6 are the main working part of this thesis. In these two chapters, we extracted the NLO correction factor to the hard function H for those considered exclusive transition processes by making the analytic calculations for the NLO transition amplitudes for the full quark level Feynman diagrams as well as for the corresponding effective diagrams of wave function. The Chapter 5 is mainly about the NLO correction to the Ï€ transition electromagnetic form factors, while the Chapter 6 is the NLO calculation for the B â†'Ï€ transition form factors and the studies for the B â†'ππt decays.From the analytical calculations, the numerical results and the phenomenological anal-ysis, the author found the following points:(1) The NLO corrections to the Ï€ transition form factors could bring only ～5% contri-bution to the LO results. For Ï€r*â†'Ï€ it transition, the NLO corrections to the pion electromagnetic form factors come from both the twist-2 and twist-3 part of the pion wave-function. The twist-2 part can provide a ～30% enhancement to the LO result, but it is largely canceled by the negative contributions from the twist-3 part, and finally leaves a net ～5% enhancement to the LO ones.(2) For B â†'Ï€ transition form factor FBx(0), the previous studies showed that the NLO twist-2 contribution can provide a ～25% enhancement to its LO result. We firstly made the calculation for the NLO twist-3 contribution to the form factor FBÏ€(0) and found that the NLO twist-3 part is ～17% in size but has an opposite sign with the NLO twist-2 part:consequently, leaves a net ～8% enhancement to its LO counterpart. This is consistent with the general expectations from the power counting role of the pQCD calculations.(3) The annihilation diagrams in B â†'ππ decays play an important role in understanding the large CP violation in such decays and the large branching ratio of Br(B â†'Ï€0Ï€0). The author made the first calculation for the NLO contributions to the factorizable annihilation diagrams for such decays. For the time-like scalar Ï€ form factors, we found that the NLO correction is very small in size, and the correction to the relative phase is also tiny.(4) With the inclusion of all currently known NLO contributions, we recalculated the branching ratios of the B â†'ππ decays and found that:(a) the color-allowed de-cays B0â†'Ï€+Ï€-, B+ â†' Ï€+Ï€0 were effected moderately by the NLO corrections, and the NLO pQCD predictions become well consistent with the measured values; (b) for the color-suppressed B0 â†'Ï€0Ï€0 decay, the NLO contribution from the time-like scalar pion form factor is the small part of the total NLO contribution and thus play a minor role; and (c) for B0â†'Ï€0Ï€0 decay, although the total NLO contribution can result in a～100% enhancement to thw LO prediction for its branching ratio, but such enhancement is still not large enough to interpret the data.