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

TL;DR

This paper develops a theoretical framework for analyzing $D o PP$ decays, incorporating short- and long-distance effects, to improve predictions of branching ratios and CP asymmetries, addressing longstanding puzzles in charm physics.

Contribution

It introduces a novel factorization approach including Glauber phases and energy-dependent Wilson coefficients, enhancing the understanding of nonleptonic $D$ decays and CP violation predictions.

Findings

Improved fit to $D o PP$ branching ratios, especially with $ ext{eta'}$ meson.

Resolved the puzzle of $D^0 o\pi^+\pi^-$ and $D^0 o K^+K^-$ branching ratios.

Predicted direct CP asymmetry difference $ ext{Delta}A_{CP} = -1.00 imes 10^{-3}$.

Abstract

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-fermion operators). The parametrization of hadronic matrix elements in terms of several nonperturbative quantities is demonstrated for the $D\to PP$ decays, $P$ denoting a pseudoscalar meson. We consider the evolution of Wilson coefficients with energy release in individual decay modes, and the Glauber strong phase associated with the pion in nonfactorizable annihilation amplitudes, that is attributed to the unique role of the pion as a Nambu-Goldstone boson and a quark-anti-quark bound state simultaneously. The above inputs improve the global fit to the branching ratios involving the $\eta'$ meson, and resolves the long-standing puzzle from the $D^0\to\pi^+\pi^-$ and $D^0\to K^+K^-$ branching ratios, respectively. Combining short-distance dynamics associated with penguin operators and the hadronic parameters determined from the global fit to branching ratios, we predict direct CP asymmetries, to which the quark loops and the scalar penguin annihilation give dominant contributions. In particular, we predict $\Delta A_{\rm CP}\equiv A_{\rm CP}(K^+K^-)-A_{\rm CP}(\pi^+\pi^-)=-1.00\times 10^{-3}$, lower than the LHCb and CDF data.