Possible solution of the puzzle for the branching ratio and $CP$ violation in $B\to \pi \pi$ decays with a modified perturbative QCD approach

Abstract

We study $B\to \pi \pi$ decay with a modified perturbative QCD approach. The branching ratios and $CP$ violation are calculated with the transverse momenta of partons considered. Sudakov factor associated with each meson is included to suppress soft contribution in QCD. With the wave function of $B$ meson obtained in QCD-inspired relativistic potential model being used, the suppression of Sudakov factor to the soft contribution is not effective enough. Soft scale cutoff and soft form factors of $B\pi$ transition and $\pi \pi$ production have to be introduced. The main next-to-leading-order contributions of vertex correction, the quark-loop and magnetic penguin are included. To solve the long-standing puzzle in $B\to \pi \pi$ decay, that is the theoretical prediction of the branching ratio of $B^0\to {\pi }^0{\pi }^0$ being seriously smaller than experimental data, color-octet matrix element which is of long-distance dynamics is introduced. With parameters taken with reasonable values, all the branching ratios and $CP$ violation are well consistent with experimental data.

arXiv comment13 pages, 1 figure, version to appear in Phys. Rev. D

References in corpus (30)

• Weak Decays Beyond Leading Logarithms
• 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
• Theoretical Update of Pseudoscalar Meson Distribution Amplitudes of Higher Twist: The Nonsinglet Case
• Resolution to the B -> pi K puzzle
• 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
• Study of Exclusive B->X_u l nu Decays and Extraction of |V_{ub}| using Full Reconstruction Tagging at the Belle Experiment
• Applicability of Perturbative QCD to $B\to D$ Decays
• The systematic study of $B\to \pi$ form factors in pQCD approach and its reliability
• Possible Large Direct CP Violations in Charmless B-Decays
• Wave functions and decay constants of $B$ and $D$ mesons in the relativistic potential model
• Possible resolution of the B -> pi pi, pi K puzzles
• 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
• Hochschild homology, trace map and $\zeta$-cycles
• Charmless two-body $B$ meson decays in perturbative QCD factorization approach
• $B\to \pi \pi$ decays and effects of the next-to-leading order contributions
• Glauber gluons in spectator amplitudes for $B\to \pi M$ decays
• 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
• Renormalization-Group Evolution of the None-local Matrix Element of $B$-meson In QCD and $B\to \pi$ transition form factor

Cited by in corpus (6)

• Revisiting $B\to K^{\ast }\pi$ and $B\to K\rho$ decays using the modified perturbative QCD approach
• Branching ratio and $CP$ violation of $B\to K\pi$ decays in a 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
• Phenomenological analysis of charmless $B\to PV$ 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