[Paper Review] Theory overview on amplitude analyses with charm decays

B. Loiseau|arXiv (Cornell University)|Nov 16, 2016

Particle physics theoretical and experimental studies14 references3 citations

TL;DR

This paper proposes advanced theoretical frameworks to improve amplitude analyses in multihadronic charm decays by incorporating final-state interactions and unitary effective field theories. It presents a Chiral Unitary approach combined with weak decay amplitudes to describe $f_0(980)$ production in $D_s^+ \to \pi^+\pi^+\pi^-$ and $D_s^+ \to \pi^+K^+K^-$, and advocates for unitary $\pi\pi$, $\pi K$, and $K\bar{K}$ form factors as alternatives to the standard isobar model, successfully applied to $D^0 \to K_S^0\pi^+\pi^-$ via quasi-two-body QCD factorization.

ABSTRACT

This contribution about amplitude analyses in multibody hadronic charm decays deals with some attempts to introduce theoretical constraints. Different effective hadronic formalism approaches are mentioned. A recent work, based on a basic weak interaction process and a Chiral unitary model to account for the final state interaction, is described in details for the $f_0(980)$ production in $D_s^+ o π^+ π^+ π^-$ and $D_s^+ o π^+ K^+ K^- $ decays. Within the framework of the diagrammatic approach and flavor symmetry, a global analysis of two-body $D$ decays into a vector meson and a pseudoscalar meson is presented. A quasi-two-body QCD factorization model for $D$ decays into three mesons and its recent application to $D^0 o K_S^0 π^+ π^-$ is outlined. For processes with final-state pions and kaons and as an alternative to the sum of Breit-Wigner amplitudes, often used in experimental Dalitz-plot analyses, amplitude parametrizations, in term of unitary $ππ$, $πK$ and $K \bar K$ form factors, are proposed. These parametrizations are derived from quasi-two-body factorization models.

Motivation & Objective

• To improve theoretical constraints in amplitude analyses of multibody charm decays beyond the standard isobar model.
• To address the limitations of sum-of-Breit-Wigner parametrizations in Dalitz plot analyses by introducing unitary, dynamically motivated form factors.
• To provide a phenomenologically consistent framework for modeling final-state interactions in $D$ decays using effective field theory and QCD factorization.
• To enable more accurate extraction of resonance properties and CP-violating effects from high-precision experimental data.

Proposed method

• Adopts a Chiral Unitary approach to model final-state interactions (FSI) in $D_s^+ \to \pi^+\pi^+\pi^-$ and $D_s^+ \to \pi^+K^+K^-$, incorporating coupled-channel dynamics.
• Uses a basic weak decay amplitude (e.g., $c \to s\bar{d}u$) combined with a $q\bar{q}$ matrix formalism to generate meson-meson components.
• Applies loop functions $G_l(s)$ and transition amplitudes $t_{ij \to kl}$ to compute $T$-matrix elements for $K^+K^-$ and $\pi^+\pi^-$ production.
• Employs a quasi-two-body QCD factorization model for three-body $D$ decays, with form factors derived from unitary $S$- and $P$-wave $\pi\pi$, $\pi K$, and $K\bar{K}$ interactions.
• Derives phenomenological amplitude parametrizations based on unitary form factors, replacing sum-of-Breit-Wigner terms in experimental Dalitz-plot analyses.
• Utilizes flavor SU(3) symmetry and diagrammatic amplitudes to perform a global analysis of $D \to VP$ decays, identifying dominant topologies.

Experimental results

Research questions

• RQ1 Can final-state interactions be systematically modeled in multibody charm decays using effective field theory?
• RQ2 How can the isobar model's limitations in describing resonant and non-resonant contributions be overcome in Dalitz plot analyses?
• RQ3 To what extent can unitary $\pi\pi$, $\pi K$, and $K\bar{K}$ form factors accurately describe three-body $D$ decays like $D^0 \to K_S^0\pi^+\pi^-$?
• RQ4 What is the role of $f_0(980)$ and other scalar resonances in $D_s^+$ decays when FSI is properly accounted for?
• RQ5 Can quasi-two-body factorization models with unitary form factors be extended to four-body charm decays such as $D^0 \to K^+K^-\pi^+\pi^-$?

Key findings

• The Chiral Unitary model successfully describes $f_0(980)$ production in $D_s^+ \to \pi^+\pi^+\pi^-$ and $D_s^+ \to \pi^+K^+K^-$, with $K^+K^-$ and $\pi^+\pi^-$ pairs generated via rescattering.
• The model predicts a branching fraction of 16.9% for the $\mathcal{M}_2$ component involving $f_0(500)$, $f_0(980)$, and $f_0(1400)$, consistent with Belle data.
• The quasi-two-body QCD factorization model describes $D^0 \to K_S^0\pi^+\pi^-$ data with good agreement, supporting the dominance of $K^{*0}(892)$ and $K^{*0}(1430)$ contributions.
• Unitary form factors for $\pi\pi$, $\pi K$, and $K\bar{K}$ systems provide a more dynamical and theoretically consistent alternative to the sum of Breit-Wigner amplitudes.
• The model predicts significant annihilation (W-exchange) contributions, especially in $D^+ \to \pi^+\pi^+\pi^-$, which may explain large SU(3) symmetry breaking.
• The framework is extendable to four-body decays such as $D^0 \to K^+K^-\pi^+\pi^-$, suggesting broader applicability in future analyses.