Renormalization-Group Evolution of the None-local Matrix Element of $B$-meson In QCD and $B\to \pi$ transition form factor

Abstract

We consider the renormalization-group evolution of the matrix element of $⟨0|\bar{q}(z{)}_{\beta }[z,0]b(0{)}_{\alpha }|\bar{B}⟩$, which can be used to define the distribution amplitudes for $B$ meson and widely applied in studies of $B$ meson decays. The contribution to the renormalization constant of the non-local operator $\bar{q}(z{)}_{\beta }[z,0]b(0{)}_{\alpha }$ is considered up to one-loop order in QCD. Since the quark fields in this operator are not directly coupled fields, momentum can not flow freely through this non-local operator. Momentum involved in this operator can be treated stringently in coordinate space. We find that the ultraviolet divergences regulated by dimensional parameter $\epsilon$ cancel with each other, and the evolution effect vanishes. The matrix element $⟨0|\bar{q}(z{)}_{\beta }[z,0]b(0{)}_{\alpha }|\bar{B}⟩$ escapes from the renormalization-group evolution. We then apply the matrix element in calculating $B\to \pi$ transition form factor, where the matrix element is obtained by using the $B$ meson wave function calculated in QCD-inspired potential model. By comparing with experimental data for the semileptonic decay of $B\to \pi \ell \nu$ and light-cone sum rule calculation, we analyse the perturbative and non-perturbative contributions to $B\to \pi$ transition form factor in the frame work of perturbative QCD approach. We find that the effectiveness of the suppression of Sudakov factor to soft contribution depends on the end-point behavior of $B$ meson wave function, and with the $B$-meson wave function used in this work, soft contribution can not be well suppressed. The hard contribution to the $B\to \pi$ transition form factor is about 59\%, and soft contribution can be as large as 41\% in the naive calculation. To make the perturbative calculation reliable, a soft momentum cutoff in the calculation and soft form factor have to be introduced.

arXiv comment11 pages, 2 figure, version to appear in Nucl. Phys. B

References in corpus (31)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• QCD factorization for B->PP and B->PV decays
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD
• Fat penguins and imaginary penguins in perturbative QCD
• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach
• Asymptotics of Heavy-Meson Form Factors
• Higher-Twist Distribution Amplitudes of the K Meson in QCD
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Extraction of $V_{ub}$ from the Decay $B\to \pi l\nu$
• B to light meson transition form factors calculated in perturbative QCD approach
• Perturbative QCD Analysis of $B$ Meson Decays
• Threshold resummation for exclusive B meson decays
• $B\to \pi \rho$, $\pi \omega$ Decays in Perturbative QCD Approach
• Renormalization-Group Evolution of the B-Meson Light-Cone Distribution Amplitude
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• Study of Exclusive B->X_u l nu Decays and Extraction of |V_{ub}| using Full Reconstruction Tagging at the Belle Experiment
• Measurement of the decay $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and determination of $|V_{ub}|$
• Next-to-leading-order corrections to $B\to \pi$ form factors in $k_T$ factorization
• Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
• Applicability of Perturbative QCD to $B\to D$ Decays
• The systematic study of $B\to \pi$ form factors in pQCD approach and its reliability
• Two-loop Corrections to the B to pi Form Factor from QCD Sum Rules on the Light-Cone and |V(ub)|
• Wave functions and decay constants of $B$ and $D$ mesons in the relativistic potential model
• Spectrum of the charmed and b-flavored mesons in the relativistic potential model
• Spectrum of Higher excitations of $B$ and $D$ mesons in the relativistic potential model
• Decay Constants and Distribution Amplitudes of B Meson in the Relativistic Potential Model
• PQCD analysis of inclusive semileptonic decays of B mesons
• Wave Functions and Leptonic Decays of Bottom Mesons In the Relativistic Potential Model

Cited by in corpus (5)

• Possible solution of the puzzle for the branching ratio and $CP$ violation in $B\to \pi \pi$ decays with a modified perturbative QCD approach
• Revisiting $B\to K^{\ast }\pi$ and $B\to K\rho$ decays using the modified perturbative QCD approach
• Study of $B\to PP$ decays in the modified perturbative QCD approach
• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• Branching fraction, $CP$ asymmetry, and polarization in $B\to \rho \rho$ decays with the modified perturbative QCD approach