Abstract
In this paper, we investigate the factorization hypothesis step by step for the exclusive process $B \to \rho$ at next-to-leading order (NLO) with the collinear factorization approach, and then we extend our results to the $k_T$ factorization frame. We show that the soft divergence from the specific NLO diagrams will cancel each other at the quark level, while the remaining collinear divergence can be absorbed into the NLO wave functions. The full NLO amplitudes can be factorized into two parts: the NLO $B$ and $\rho$ meson wave functions containing the collinear divergence and the leading order (LO) finite hard kernels. We give the general form of the nonlocal hadron matrix for the NLO $B$ and $\rho$ meson wave functions and all results of factorization for different twists' combinations.
Highlights
As the foundation of the perturbative QCD formalism, the factorization theorem [1,2,3] claims that the hard part of the QCD interactions is finite and can be calculated perturbatively, the nonperturbative part can be factorized into the universal wave functions defined in an infinite momentum frame
We investigate the B → ρ transition process and give the proof of the factorization at the next-to-leading order (NLO) level in the kT factorization frame
The calculations of all these six channels will be very complex, which suggests that we are better to make estimation first for proportion of every channel in leading order (LO) level before the numerical calculations done at the NLO level
Summary
As the foundation of the perturbative QCD formalism, the factorization theorem [1,2,3] claims that the hard part of the QCD interactions is finite and can be calculated perturbatively, the nonperturbative part can be factorized into the universal wave functions defined in an infinite momentum frame. Process, show explicitly the structure of the infrared divergences at the NLO level for the combinations of the leading twist parts of the wave functions. By summing up the contributions from all subdiagrams, we can prove that the soft divergence will be canceled each other between the quark diagrams, and the remaining collinear divergence can be absorbed into the NLO meson wave functions. We will write down the hadronic matrix elements for B and ρ meson wave functions with its collinear parts in the kT factorization. IV, a brief summary and some discussions are given
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
