Abstract
We study decay with a modified perturbative QCD approach. The branching ratios and 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 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 transition and 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 decay, that is the theoretical prediction of the branching ratio of 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 violation are well consistent with experimental data.
- Received 29 November 2022
- Accepted 28 December 2022
DOI:https://doi.org/10.1103/PhysRevD.107.013004
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society