Measurement of the ratio

We report a high-statistics measurement of the relative branching fraction B ( D 0 → π + π − π 0 )/ B ( D 0 → K − π + π 0 ). A 357 fb − 1 data sample collected with the Belle detector at the KEKB asymmetric-energy e + e − collider was used for the analysis. The relative branching fraction B ( D 0 → π + π − π 0 )/ B ( D 0 → K − π + π 0 ) is determined with an accuracy comparable to the latest world average value.


INTRODUCTION
This measurement is the first step towards a high-statistics Dalitz-plot analysis of the D 0 → π + π − π 0 decay. The latter could give insight into the controversy on the S-wave π + π − contribution in these decays [1,2], as well as a sensitive study of the CP violation in the neutral D meson system. Knowledge of B(D 0 → ρπ)/B(D 0 → K * K) (also based on the D 0 → π + π − π 0 Dalitz analysis) could improve our understanding of the apparent discrepancy of the measured two-body branching fractions (D 0 → KK, ππ) with the theoretical expectations [3]. The accuracy of the value of B(D 0 → π + π − π 0 ) as reported in PDG04 [4] is poor. Using a large data sample of D 0 decays accumulated with the Belle detector, we provide a significantly improved measurement using the D 0 → K − π + π 0 decay mode for normalization. Since both decay modes involve a neutral pion and the same number of charged tracks in the final state, several sources of the systematic uncertainties are avoided in a determination of the relative branching fraction. The obtained result can then be compared to recent measurements by the CLEO [5] and BABAR [6] collaborations. A detailed study of the D 0 → π + π − π 0 decay as well as of other D 0 CP -symmetric final states, can be used to further improve statistics for the measurement of the angle φ 3 (γ) of the CKM-matrix . EXPERIMENT The Belle detector is a large-solid-angle magnetic spectrometer located at the KEKB e + e − storage rings, which collide 8.0 GeV electrons with 3.5 GeV positrons and produce Υ(4S) at the energy of 10.58 GeV. Closest to the interaction point is a silicon vertex detector (SVD), surrounded by a 50-layer central drift chamber (CDC), an array of aerogel Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight (TOF) scintillation counters, and an electromagnetic calorimeter (ECL) comprised of CsI (Tl) crystals. These subdetectors are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return yoke located outside the coil is instrumented to detect K 0 L mesons and identify muons. The detector is described in detail elsewhere [7,8].

DATA SELECTION
For this analysis, we used a data sample of 357 fb −1 accumulated with the Belle detector. D 0 candidates are selected from D * → D 0 π slow decays where the charge of the π slow tags the D 0 flavour: D * ± → D 0 /D 0 π ± slow . D * 's originate mainly from continuum. Although we do not apply any topological cuts, the yield of D * 's from B-meson decays is negligible; such events are rejected by other kinematical cuts such as the strong p cms (D * ) requirement. D 0 mesons are reconstructed from combinations of two oppositely charged pions (or a charged pion and kaon in the case of K − π + π 0 ) and one neutral pion. The latter is reconstructed from two γ candidates satisfying the π 0 mass requirement given below.
The following kinematic criteria are applied to the charged track candidates: the distance from the nominal interaction point to the point of closest approach of the track is required to be within 0.15 cm in the radial direction (dr) and 0.3 cm along the beam direction (dz).
We also require the transverse momentum of the track p ⊥ > 0.050 GeV/c to suppress beam background. Kaons and pions are separated by combining the responses of the ACC and the TOF with the dE/dx measurement from the CDC to form a likelihood L(h) where h is a pion or a kaon. Charged particles are identified as pions or kaons using the likelihood ratio R PID = L(K)/(L(K) + L(π)). For charged pion identification, we require R PID < 0.4. This requirement selects pions with an efficiency of 93% and misidentified kaons with an efficiency of 9%. For the identification of charged kaons, the requirement is R PID > 0.6; in this case, the efficiency for kaon identification is 86% and the probability to misidentify a pion is 4%.

EFFICIENCY CALCULATION
To obtain detection efficiencies, about 1.2×10 6 phase-space distributed MC events have been generated for each of the two modes, processed using the GEANT-based detector simulation [9] and reconstructed with the same selection criteria as the data.
The obtained yield is normalized to the same MC data but before detector simulation and before application of selection criteria. Since for the relative branching fraction measurement only the ratio of π + π − π 0 and K − π + π 0 efficiencies is needed, we only generate events in the p cms (D * ) range from 3.5 to 4.3 GeV/c where MC is in good agreement with the data (see Fig. 1, left). The obtained efficiencies are: ε(π + π − π 0 ) = (13.433 ± 0.077)%, ε(K − π + π 0 ) = (13.065 ± 0.074)%.

BACKGROUND DESCRIPTION
To describe the background shape in the M(π + π − π 0 ) signal region, a sample of generic MC, equivalent to ∼250 fb −1 , has been processed with the same selection criteria as data. The contributions of uū, dd, ss, cc and BB backgrounds have been summed up. For the cc sample signal events were excluded. Figure 3 shows the individual contributions to the M(π + π − π 0 ) distribution where also a partial data sample, corresponding to the luminosity of MC, is shown. The M(π + π − π 0 ) background distribution is fitted with a 2 nd order polynomial multiplied by an error function (kaon misidentification region) plus a 1 st order polynomial (combinatoric background) and a small Gaussian peak in the signal region (see Fig. 3, right). The Gaussian contribution is mainly due to combinations of a correctly reconstructed D 0 and a random π slow candidate.
Most of the background is from e + e − → cc; the BB background is negligible and uū, dd, ss backgrounds are linearly distributed in the M(π + π − π 0 ) signal region. Among the cc background sources D * → D 0 (Kππ 0 )π is dominant: charged kaons are misidentified as pions and M(π fake ππ 0 ) is typically shifted downwards by ∼ 0.1 GeV/c 2 thus being well separated from the signal.
The background shape in the M(K − π + π 0 ) distribution is obtained using a generic MC sample. The level of background in this mode is low but still has a nontrivial structure (see Fig. 4, right). The distribution has three distinctive peaks: the rightmost one is due to misidentified pions from D 0 → π + π − π 0 , the central one has the same origin as the one in the D 0 → π + π − π 0 case (random π slow ), the leftmost feature originates mainly from D 0 → Knπ where n ≥ 3. The distribution is fitted by the sum of a 2 nd order polynomial and a 2 nd order polynomial multiplied by an error function (left peak) and two Gaussians.

SIGNAL FIT
The shape of the signal peak in the experimental π + π − π 0 invariant mass distribution (see Fig. 5, left) is partially fixed to the MC one [13]: the latter was fitted with a bifurcated hyperbolic Gaussian [14,15] and a regular Gaussian (see Fig. 1, right). The obtained shape with floating normalization and σ's, together with the background shape with its floating normalization (i.e. 5 free parameters) is then used as the fit function for the measured M(π + π − π 0 ) distribution.
To fit the experimental Kππ 0 invariant mass distribution we use a Kππ 0 background shape with floating normalization and the sum of two bifurcated and a regular Gaussian for the signal peak (see Fig. 4, right). Here, the parameters of the signal peak are free in the fit since the level of background is low and statistics are large enough.
The yields of signal events in each channel, as obtained from the fit, are given in Table I: 22803 ± 203 13.433 ± 0.077 K − π + π 0 237520 ± 500 13.065 ± 0.074 signal M (π + π − π 0 ) distribution, fitted to the signal MC shape (Fig. 1, right) for the signal peak and with the generic MC shape (background). Right: misidentification shape, generic MC, used for an alternative background fit to estimate the corresponding systematic error.

SYSTEMATIC UNCERTAINTIES
Uncertainty on the tracking efficiency for the two charged tracks -π + π − or K − π +cancels in the ratio of D 0 → π + π − π 0 and D 0 → K − π + π 0 branching fractions. The same holds for π 0 and slow pion (from D * ) reconstruction efficiencies. A possible difference in the efficiency of particle identification selection criteria between MC and data is taken into account as a correction to the branching ratio (r K /r π = 0.962 ± 0.015) and the uncertainty of this correction contributes to the systematic uncertainty of the result. The polar angle and momentum dependent data/MC corrections are measured independently using a large sample of D 0 → K − π + decays. The uncertainty in the correction yields a systematic error of 1.6%.
As mentioned above, we use the generic MC shape in the M(π + π − π 0 ) signal region as the default background description (when calculating the central value of B(D 0 → π + π − π 0 )). To estimate the systematic error related to the description of background, we use an alternative function for the background fit. To do so, we extract true Kππ 0 events from generic MC reconstructed as π + π − π 0 . The shape obtained (see Fig. 5, right) is fitted with a 2 nd order polynomial multiplied by an error function and a 1 st order polynomial. We use this parameterization for the misidentification background, while another 1 st order polynomial is added to fit the other charm-(other than misidentification), light-and b-quark linear contributions. The difference between this and the default fit (0.4%) is added in quadrature to the systematic error.
To determine the signal fit uncertainty, a different D 0 → π + π − π 0 signal parameterization, composed of two bifurcated Gaussians and one regular Gaussian is used. For the D 0 → Kππ 0 decay channel we use a bifurcated hyperbolic Gaussian and a regular Gaussian. The relative differences to the default fit are found to be 0.3% and 0.5% for the π + π − π 0 and K − π + π 0 mode, respectively, and are added to the total systematic uncertainty.
Finally, we varied the selection criteria and estimate the systematic error corresponding to the possible inadequate background description. The particle identification selection was changed to R PID (π) < 0.2, R PID (K) > 0.8, and the resulting systematic uncertainty is found to be negligible. Change of the p cms (D * ) requirement (3.0 GeV/c) results in a 0.4% error. A significant uncertainty is due to the Ks veto; after excluding the region 0.195 GeV 2 /c 4 < M 2 (π + π − ) < 0.305 GeV 2 /c 4 , the resulting π + π − π 0 yield changes by 1.6%.
The individual sources of the systematic error are listed in Table II. The total uncertainty is obtained by adding all contributions in quadrature.
Finally, we can compare our measurement of the ratio with the ratio obtained from the latest world average values of B(D 0 →π + π − π 0 ) B(D 0 →K − π + ) and B(D 0 → π − π + π 0 ) [11]. Our result (9.71 ± 0.31)% is consistent with the world average one (9.29 ± 0.54)% and has better accuracy. By choosing the normalization mode D 0 → K − π + π 0 we avoid many sources of systematic uncertainty including the π 0 detection efficiency and uncertainty in the tracking efficiency. The PID efficiency partially cancels out.