Abstract
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 $\phi_3(\gamma)=(75.1\pm2.9)^\circ$ consistent with the value in Particle Data Group are also obtained. It is straightforward to extend our analysis to higher orders and higher powers in the PQCD approach, and to the global determination of LCDAs for other hadrons.
Highlights
The study of heavy quark physics is firmly in the precision era nowadays
Fitting the perturbative QCD (PQCD) factorization formulas for B → PP; VP decays at leading order in the strong coupling αs to measured branching ratios and direct CP asymmetries, we determine the Gegenbauer moments in light meson light cone distribution amplitudes (LCDAs)
We determine the Gegenbauer moments and the weak phase φ3ðγÞ by fitting the branching ratios and direct CP asymmetries formulated from the decay amplitudes in Eq (13) to experimental data using the nonlinear leastχ2 method [53]
Summary
The study of heavy quark physics is firmly in the precision era nowadays. On the experimental side, the B factories, i.e., the BABAR, Belle, and LHCb, have collected abundant data of exclusive B meson decays, which can be employed to explore involved rich QCD dynamics and to probe the origin of CP violation and potential new physics signals [1]. Between experimental observations and the Standard Model [1], which may be vaguely attributed to new physics beyond the Standard Model This undoubtedly motivates the attempt to gain deeper understanding of QCD dynamics in exclusive B meson decays and better control of hadronic uncertainties. We will perform a global fit of the Gegenbauer moments in light meson LCDAs to measured branching ratios and direct CP asymmetries in hadronic two-body B meson decays in the PQCD approach. It is known that enormous efforts have been devoted for several decades to global determinations of parton distribution functions from experimental data, which serve as the nonperturbative inputs to the factorization of inclusive QCD processes. The explicit factorization formulas and their ingredients are collected in the Appendix
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