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We propose a theoretical framework for analyzing two-body nonleptonic $D$meson decays, based on the factorization of short-distance (long-distance)dynamics into Wilson coefficients (hadronic matrix elements of four-fermionoperators). The parametrization of hadronic matrix elements in terms of severalnonperturbative quantities is demonstrated for the $D\to PP$ decays, $P$denoting a pseudoscalar meson. We consider the evolution of Wilson coefficientswith energy release in individual decay modes, and the Glauber strong phaseassociated with the pion in nonfactorizable annihilation amplitudes, that isattributed to the unique role of the pion as a Nambu-Goldstone boson and aquark-anti-quark bound state simultaneously. The above inputs improve theglobal fit to the branching ratios involving the $\eta'$ meson, and resolvesthe long-standing puzzle from the $D^0\to\pi^+\pi^-$ and $D^0\to K^+K^-$branching ratios, respectively. Combining short-distance dynamics associatedwith penguin operators and the hadronic parameters determined from the globalfit to branching ratios, we predict direct CP asymmetries, to which the quarkloops and the scalar penguin annihilation give dominant contributions. Inparticular, we predict $\Delta A_{\rm CP}\equiv A_{\rm CP}(K^+K^-)-A_{\rmCP}(\pi^+\pi^-)=-1.00\times 10^{-3}$, lower than the LHCb and CDF data.

Branching ratios and direct CP asymmetries in $D\to PP$ decays