Amplitude Analysis and Branching Fraction Measurement of $D^+ o π^+π^0π^0$

We present the first amplitude analysis of the hadronic decay $D^+\toπ^+π^0π^0$, using $e^{+}e^{-}$ collision data collected with the BESIII detector at a center-of-mass energy of 3.773GeV, corresponding to an integrated luminosity of 20.3fb$^{-1}$. The fit fractions of the intermediate processes are measured, in which the $D^+ \to ρ(770)^+π^0$ component is found to be dominant with a branching fraction of $(3.08\kern0.15em\pm\kern0.15em0.10_{\rm stat.}\pm0.05_{\rm syst.})\times10^{-3}$. Based on the amplitude analysis, the branching fraction of $D^+ \to π^+π^0π^0$ is measured to be $(4.84\kern0.1em\pm\kern0.1em0.05_{\rm stat.}\kern0.1em\pm\kern0.1em0.05_{\rm syst.})\times10^{-3}$. In addition, the CP asymmetries, both for specific amplitudes and integrated over the entire phase space, are measured.

💡 Research Summary

This paper presents a comprehensive experimental study of the hadronic decay D+ → π+π0π0 conducted by the BESIII collaboration, marking the first amplitude analysis of this decay channel. The analysis is based on a substantial data sample of 20.3 fb⁻¹ collected at a center-of-mass energy of 3.773 GeV, corresponding to the ψ(3770) resonance, which predominantly decays into D+D- pairs.

The core of the work is a detailed amplitude analysis using the isobar model to describe the complex dynamics within the three-body decay. The total amplitude is constructed from a coherent sum of intermediate resonant contributions, including ρ(770)+, ρ(1450)+, ρ(1700)+, f0(500), f0(980), f0(1370), and f2(1270). An unbinned maximum likelihood fit to the Dalitz plot distribution reveals that the decay is dominated by the quasi-two-body process D+ → ρ(770)+ π0, which accounts for (63.6 ± 2.0 ± 0.6)% of the total decay rate. Other resonances make smaller but significant contributions.

Leveraging the results of the amplitude analysis, the paper reports a precise measurement of the absolute branching fraction (BF) for D+ → π+π0π0 using the double-tag technique. The BF is determined to be (4.84 ± 0.05_stat ± 0.05_syst) × 10⁻³. Furthermore, the BF for the dominant sub-process D+ → ρ(770)+ π0 is measured to be (3.08 ± 0.10_stat ± 0.05_syst) × 10⁻³. These results provide stringent tests for theoretical models like the pole model, topological diagram approach, and factorization-assisted topological-amplitude method, whose predictions range from 2.5 to 4.44 × 10⁻³ for the ρ(770)+ π0 channel.

A significant part of the investigation is dedicated to the search for CP violation, which is predicted to be at the level of 10⁻⁴ to 10⁻³ in singly Cabibbo-suppressed charm decays. The researchers measure the integrated CP asymmetry (A_CP) between D+ and D- decays over the entire phase space, finding A_CP = (-1.3 ± 4.0_stat ± 0.8_syst) × 10⁻³, consistent with no asymmetry. They also measure the CP asymmetry in the fit fraction for the ρ(770)+ π0 component, Δf_CP, yielding (-4.4 ± 4.8_stat ± 1.2_syst) × 10⁻³. While neither result shows statistical significance, they establish crucial baseline measurements and methodologies for future investigations with larger datasets, where local CP asymmetries in specific regions of the Dalitz plot might be enhanced.

In summary, this pioneering work successfully unravels the resonant structure of the D+ → π+π0π0 decay with high precision, delivers the most accurate branching fractions to date, and lays the groundwork for sensitive probes of CP violation in charged charm meson decays. The findings offer valuable inputs for understanding non-perturbative QCD dynamics and testing the Standard Model in the charm sector.