Based on the flavor structure of four-quark effective operators, we develop an automatic computation program to calculate hadronic two-body $B$ meson decay amplitudes, and apply it to their global analysis in the perturbative QCD (PQCD) approach. Fitting the PQCD factorization formulas for $B\to PP,VP$ decays at leading order in the strong coupling ${\alpha }_s$ to measured branching ratios and direct $CP$ asymmetries, we determine the Gegenbauer moments in light meson light cone distribution amplitudes (LCDAs). It is found that most of the fitted Gegenbauer moments of the twist-2 and twist-3 LCDAs for the pseudoscalar meson $P$ ($P=\pi$, $K$) and vector meson $V$ ($V=\rho$, $K^{*}$) agree with those derived in QCD sum rules. The shape parameter for the $B_s$ meson distribution amplitude and the weak phase ${\varphi }_3(\gamma )=(75.2\pm 2.9)°$ consistent with the value in Particle Data Group are also obtained. It is straightforward to extend our analysis to higher orders and higher powers, when the corresponding subleading contributions are available in the PQCD approach, and to the global determination of LCDAs for other hadrons.

• Received 7 January 2021
• Accepted 8 July 2021

DOI:https://doi.org/10.1103/PhysRevD.104.016025

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Published by the American Physical Society