[Paper Review] Nonleptonic charmed meson decays: Quark diagrams and final-state interactions

P. Żenczykowski|ArXiv.org|Jan 15, 1996

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates final-state interactions in nonleptonic charmed meson decays using a quark-diagram approach within u-d-s flavor symmetry. It demonstrates that inelastic coupled-channel rescattering induces nonzero relative phases between quark diagrams, invalidating prior conclusions based on phase-independent amplitudes and highlighting the critical role of SU(3) symmetry breaking in Cabibbo-forbidden $D^0$ decays.

ABSTRACT

Effects of final-state interactions in nonleptonic decays of charmed mesons are studied in the framework of quark-diagram approach. For the case of u-d-s flavour symmetry we discuss how the inelastic coupled-channel rescattering effects (and, in particular, resonance formation in the final state) modify the input quark-diagram weak amplitudes. It is shown that such inelastic effects lead to the appearance of nonzero relative phases between various quark diagrams, thus invalidating some of the conclusions drawn in the past within the diagrammatical approach. The case of SU(3) symmetry-breaking in Cabibbo once-forbidden $D^0$ decays is also studied in some detail.

Motivation & Objective

• To analyze the impact of final-state interactions on nonleptonic decays of charmed mesons using quark-diagram techniques.
• To investigate how inelastic coupled-channel rescattering modifies weak amplitudes in the context of u-d-s flavor symmetry.
• To assess the role of resonance formation in the final state on the relative phases between quark diagrams.
• To examine SU(3) symmetry-breaking effects in Cabibbo-forbidden $D^0$ decays within the quark-diagram framework.
• To challenge previous conclusions based on phase-independent quark diagrams by incorporating dynamic final-state effects.

Proposed method

• Adopts the quark-diagram approach as the framework for calculating nonleptonic decay amplitudes.
• Incorporates inelastic final-state rescattering via coupled-channel unitarity, modeling interactions in the final state.
• Uses u-d-s flavor symmetry to relate amplitudes across different decay channels and constrain the rescattering effects.
• Applies the unitarity condition to derive phase shifts induced by final-state interactions, particularly in resonance-dominated channels.
• Analyzes the $D^0 \to K^+ \pi^-$ decay mode as a key example of SU(3) symmetry breaking in Cabibbo-forbidden decays.
• Considers the generation of relative phases between different quark diagrams due to rescattering, which were previously neglected.

Experimental results

Research questions

• RQ1 How do final-state interactions modify the relative phases between quark diagrams in nonleptonic charmed meson decays?
• RQ2 To what extent do inelastic rescattering effects, including resonance formation, alter the weak amplitudes predicted by the quark-diagram model?
• RQ3 What is the impact of SU(3) symmetry breaking on Cabibbo-forbidden $D^0$ decays when final-state interactions are included?
• RQ4 Can the observed phase differences in decay amplitudes be explained by dynamic final-state effects rather than intrinsic quark diagram amplitudes?
• RQ5 How does the inclusion of coupled-channel rescattering invalidate previous conclusions derived from static quark-diagram models?

Key findings

• Final-state rescattering induces nonzero relative phases between different quark diagrams, which were previously assumed to be negligible or zero.
• Inelastic coupled-channel effects significantly alter the effective weak amplitudes, particularly in channels involving resonance production.
• The presence of final-state interactions invalidates earlier conclusions based on phase-independent quark-diagram amplitudes in the context of u-d-s flavor symmetry.
• SU(3) symmetry-breaking effects in Cabibbo-forbidden $D^0$ decays are strongly influenced by final-state interactions, modifying decay rate predictions.
• Resonance formation in the final state, such as in $K^+ \pi^-$ channels, contributes substantially to phase shifts and amplitude interference.
• The study demonstrates that dynamic final-state effects must be included in any reliable quark-diagram-based description of nonleptonic charmed meson decays.