Updated branching ratios and $CP$ asymmetries in $D \to PV$ decays

TL;DR

The paper develops an updated analysis of two-body charm decays $D \to PV$ within the factorization-assisted topological-amplitude (FAT) framework, incorporating flavor SU(3) breaking into topological amplitudes and expressing nonfactorizable effects via a compact set of universal parameters. It performs a global fit to 41 $D \to PV$ branching ratios, yielding precise values for 15 nonfactorizable parameters, notably including a non-negligible $\chi^T$ for the $T$ topology, and reports a good fit quality. With these updated parameters, the authors present refined predictions for branching fractions that align with current data and contemporary topological-diagram results, and compute direct CP asymmetries arising from tree–penguin interference, finding several modes with CP asymmetries around ${\cal O}(10^{-3})$. The results highlight substantial nonfactorizable effects in the $C$ amplitude and significant strong-phase shifts, underscoring the importance of accurate strong phases and SU(3) breaking in charm decays, and provide predictions for unobserved decays to guide future experiments at LHCb, Belle II, and BESIII.

Abstract

Motivated by extensive new high-precision experimental data, we present an updated analysis of the two-body charm decays $D \to PV$ (with $P =π,K, η^{(\prime)}$ and $V =ρ, K^*, ω, φ$) within the factorization-assisted topological-amplitude (FAT) approach. In the framework, flavor SU(3) symmetry breaking effect is incorporated into the topological amplitudes, allowing the nonfactorizable contributions from topological diagrams to be expressed as a minimal set of universal parameters determined through a global fit to experimental data. Thanks to the sufficient data with high precision, we are now able to quantify the nonfactorizable contribution of so-called ``factorization" $T$ diagram, which is essential for explaining the observed branching ratios. The parameters for the $C$, $E$, and $A$ diagrams are also updated with significant improved precision, and notably, the resulting strong phases differ substantially from those in the earlier FAT analysis. We find that the $C$ topological amplitude features substantial nonfactorizable effects in the charm sector. These refined parameters enable predictions of significantly improved accuracy, yielding branching ratios in good agreement with current data and the latest results in topological diagram approach, and the predicted direct $\mathit{CP}$ asymmetries differ distinctly form previous FAT results due to updated strong phases. In several modes, the $\mathit{CP}$ asymmetries are predicted to reach $\mathcal{O}(10^{-3})$, thereby making them promising observables for future high-precision experiments at LHCb, BESIII and Belle II. Predictions for unobserved decay modes, especially those with branching fractions of order $10^{-4}\sim10^{-3}$, are also provided for forthcoming experimental tests.

Figures (2)

• Figure 1: Topological tree diagrams for $D \to P \, V$ decay with a wavy line representing the $W$ boson: (i) color-favored tree diagram $T$, (ii) color-suppressed tree diagram $C$, (iii) $W$-exchange tree diagram $E$, and (iv) $W$-annihilation tree diagram $A$.
• Figure 2: Topological penguin diagrams for $D \to P \, V$ decay with a wavy line representing the $W$ boson and a curly line the gluon: (i) color-favored penguin diagram $PT$, (ii) color-suppressed penguin diagram $PC$, (iii) $W$-exchange penguin diagram $PE$, and (iv) $W$-annihilation penguin diagram $PA$.