B Meson Transition Form Factors Within The PQCD Approach

It is an important task of physicists to test the Standard Model (SM) and to determine the parameters in the SM since the SM was established. A study of the B→light meson exclusive processes'transition form factors plays an importantly complementary role in determining the fundamental parameters in the SM and in developing the quantum chromodynamics (QCD) theory. There are various approaches to calculate the B→light meson transition form factors, such as the lattice QCD, the QCD light-cone sum rule (QCD LCSR) and the perturbative QCD (pQCD) approach and so on. The lattice QCD calculations are available only for the soft regions, i.e. q² > 15GeV². The QCD LCSR can treat both hard and soft contributions with q²â‰¤18GeV². The pQCD calculation is reliable only in the large recoil regions, i.e. in the small q² regions. The results from the pQCD approach, the lattice QCD approach, and the QCD LCSR are complementary to each other and by combining the results of those three approaches, one may obtain an understanding of the B→light meson transition form factors in the whole physical regions.In this paper, we have dicussed the properties of B→π,K transition form factors within the pQCD and the main factors influencing the form factors. We get some resonable regions of parameters by comparing the results wihtin the pQCD and the QCD LCSR. To over come the trouble of multiple free-degree, we apply the kT factorization approach to separate the contributions of long-distance and short-distance. The transverse momentum dependence for the wavefunction, Sudakov effects and threshold effects are included to regulate the endpoint singularity and to derive a more reasonalbe result.In this paper, we apply the pQCD approach to deal with the B→π,K transition form factors and in the large recoil regions. We find the results of and are consistent with the QCD LCSR results in the large recoil regions. We also find the form factors and will decrease with the increment ofΛ, and will increase with the increment ofδ, whereΛstands for the effective mass of B meson andδis a typical parameter that determines the broadness of the B meson transverse distribution. It can be found that the form factor shall be slightly increased with the increment of the first Gegenbauer moment a₁^K (1GeV) = 0.05±0.02 in twist-2 wave functionΨ_K. And we get . We also discuss the contributions of the form factors and from different parts of the pion, the kaon and the B meson wave functions. We find the most contributions of form factors come fromΨπ,K andΨB, but the contributions ofΨσfrom the pion and the kaon meson, the contribution ofΔfrom B meson are very small, and can be neglected in most of the calculations. The contributions ofΨp from the pion and the kaon meson, the contribution ofΨB from B meson are not very small, and can not be safely neglected for giving more resonable results of form factors.The B meson wavefunction is a major source of uncertainty in the study of B meson decays. The B→πand B→K transition form factors provide a good platform to determine the possible regions for the two typical phenomenological parametersΛandδ. So the properties of the B meson light-cone wavefunction up to next-leading order Fock state expansion have been studied through a comparative study of the B→π,K transition form factors within the kT factorization approach and the QCD LCSR analysis in this paper. The transition form factors and are carefully re-calculated up to O (1 mb 2) within the kT factorization approach in the large recoil region, in which the main theoretical uncertainties are discussed. The QCD LCSR is applicable in the large and intermediate energy regions, and the QCD LCSR results in Ref. [1] are adopted for such a comparative study. It is found that when the two phenomenological parametersΛ∈[0.50,0.55] andδ∈[0.25,0.30], the results of and from these two approaches are consistent with each other in the large recoil energy region. Finally, to illustrate the SU f(3)-breaking effects in the B→K transition form factors within the kT factorization approach, we calculated the ratio: , which favors small SU_f(3)-breaking effects.