Non-leptonic decays of Charmed mesons into two Pseudoscalars

TL;DR

This paper investigates the decay processes of charmed mesons into two pseudoscalar particles, emphasizing the importance of final state interactions, weak annihilation, and exchange contributions, and achieves good agreement with experimental data.

Contribution

It introduces a comprehensive model incorporating resonant FSI, non-factorizable corrections, and unitarized amplitudes to accurately describe D meson decay modes.

Findings

Successful explanation of challenging $D^0 ightarrow K^+K^-, \pi^+\pi^-$ decays.

Correct branching ratio for $D ightarrow K^0ar{K^0}$ requires both FSI and weak exchange effects.

Strong phase difference aligns with recent experimental measurements.

Abstract

We examine the role of resonant coupled channel final state interactions (FSI), as well as weak annihilation and exchange contributions in explaining all the two body hadronic $D\rightarrow PP$ decay modes data. In the un-unitarized amplitudes we include modified Wilson coefficients with non-factorizable corrections as parameters. For the hadronic form factors, the z-series expansion method is used to get the $q^2$ dependence. The FSI effects are incorporated via a phenomenological approach with widths of resonances to various channels taken from observations where available, and others as additional parameters to be determined from fits of all the theoretical rates to the measured ones. Our results for the rather hard to explain $D^0\rightarrow K^+K^-, \pi^+\pi^- $ are in agreement with measured values. We demonstrate that both weak exchange as well as FSI effects are required to get the correct branching ratio for the $D^ \rightarrow K^0\bar{K^0}$ mode. Using our unitarized amplitudes we evaluate the strong phase difference between the amplitudes for $D^0\rightarrow K^-\pi^+$ and $D^0\rightarrow K^+\pi^-$ and find it to be in complete agreement with the recent BES III result.