Measurement of the $CP$ asymmetry in $D^0 oπ^+π^-π^0$ decays at Belle II

We measure the time- and phase-space-integrated $CP$ asymmetry $A_{CP}$ in $D^0\toπ^+π^-π^0$ decays reconstructed in $e^+e^-\to c\bar c$ events collected by the Belle II experiment from 2019 to 2022. This sample corresponds to an integrated luminosity of 428 fb$^{-1}$. We require $D^0$ mesons to be produced in $D^{*+}\to D^0π^+$ decays to determine their flavor at production. Control samples of $D^0\to K^-π^+$ decays are used to correct for reconstruction-induced asymmetries. The result, $A_{CP}(D^0\toπ^+π^-π^0)=(0.29\pm0.27\pm0.13)%$, where the first uncertainty is statistical and the second systematic, is the most precise result to date and is consistent with $CP$ conservation.

💡 Research Summary

The Belle II Collaboration presents a measurement of the time‑ and phase‑space‑integrated CP asymmetry (A_CP) in the singly Cabibbo‑suppressed decay D⁰ → π⁺π⁻π⁰ using data collected from 2019 to 2022. The dataset corresponds to an integrated luminosity of 428 fb⁻¹ of e⁺e⁻ → c c̄ events recorded at the SuperKEKB asymmetric‑energy collider. The analysis exploits D*⁺ → D⁰π⁺ tagging to determine the flavor of the neutral D meson at production; the charge of the low‑momentum “tag pion” identifies whether the reconstructed D⁰ originated as a D⁰ or an anti‑D⁰.

To isolate the genuine CP asymmetry from detector‑induced effects, the study uses a control channel, D⁰ → K⁻π⁺, which is Cabibbo‑favored and thus expected to have negligible intrinsic CP violation. Two samples of this control decay are built: a “tagged” sample that includes the D*⁺ → D⁰π⁺ decay and an “untagged” sample that does not. The raw asymmetries of these samples provide a direct measurement of the tag‑pion reconstruction asymmetry (A_tag ε) via the difference A_tag ε = A_tagged_raw – A_untagged_raw. The D⁰ reconstruction asymmetry (A_πππ⁰ ε) is shown by simulation to be negligible, and a small systematic uncertainty is assigned.

A production asymmetry (A_prod) arises from γ–Z⁰ interference and higher‑order QED effects in e⁺e⁻ → c c̄, manifesting as an odd function of the D⁰ polar angle in the center‑of‑mass frame (cos θ_CM). To cancel this contribution, the data are divided into eight symmetric bins of cos θ_D⁰_CM (four positive, four negative). In each bin the raw signal asymmetry is corrected for the tag‑pion asymmetry, and the CP asymmetry for a pair of opposite‑sign bins is obtained as A_i^CP = (A_{+i} + A_{‑i})/2. The final A_CP is the average of the four A_i^CP values, which removes the odd component of A_prod.

Signal candidates are reconstructed by combining two oppositely charged pion tracks with a π⁰ → γγ candidate. Photon clusters are required to satisfy stringent timing, energy, and shower‑shape criteria, and a boosted‑decision‑tree classifier based on Zernike moments further suppresses hadronic background. The π⁰ mass window (116–150 MeV/c²) and momentum requirement (> 0.5 GeV/c) give a mass resolution of about 6.5 MeV/c². Charged pions are identified with a neural‑network particle‑identification algorithm (NNPID) with a loose selection (NNPID > 0.2) to reduce kaon mis‑identification. The D⁰ candidates are combined with a low‑momentum tag pion to form D*⁺ candidates.

A two‑dimensional unbinned maximum‑likelihood fit to the D⁰ invariant mass and the mass difference ΔM = M(D*⁺) – M(D⁰) extracts the signal yield and raw asymmetry in each angular bin. Background components include combinatorial sources, mis‑identified D⁰ → K⁻π⁺π⁰ decays, and feed‑down from other charm processes. Monte Carlo simulations, scaled to match data distributions, are used to model these backgrounds and to validate the fitting procedure.

The analysis yields approximately 1.2 × 10⁵ signal candidates. The measured CP asymmetry is

A_CP(D⁰ → π⁺π⁻π⁰) = (0.29 ± 0.27 (stat) ± 0.13 (syst)) %,

which is the most precise determination to date. The statistical uncertainty dominates, while systematic uncertainties arise mainly from the tag‑pion asymmetry correction, the angular‑binning scheme, background modeling, and the MC re‑weighting procedure. This result is consistent with CP conservation and with the Standard Model expectation of asymmetries at the 10⁻⁴–10⁻³ level. It also improves upon the previous BABAR measurement (0.31 ± 0.41 ± 0.17 %) by roughly a factor of two in precision.

The paper emphasizes that, although no evidence for new physics is observed in this channel, the methodology—particularly the use of angular binning to cancel production asymmetries and the data‑driven tag‑pion correction—sets a robust framework for future Belle II analyses. With the anticipated accumulation of several ab⁻¹ of data, statistical uncertainties will shrink substantially, enabling sensitivity to CP asymmetries at the 10⁻⁴ level. Moreover, extending the analysis to a full Dalitz‑plot amplitude fit or incorporating time‑dependent measurements could provide complementary probes of direct and indirect CP violation, further constraining possible contributions from physics beyond the Standard Model.