Study of $\bar{B^{0}} \to D^{(*)0} \pi^+ \pi^-$ Decays

We report on a study of $\bar{B^{0}} \to D^{(*) 0} \pi^+ \pi^-$ decays using 29.1 fb$^{-1}$ of $e^{+}e^{-}$ annihilation data recorded at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB storage ring. Making no assumptions about the intermediate mechanism, the branching fractions for $\bar{B}^0 \to D^0 \pi^+ \pi^-$ and $\bar{B}^0 \to D^{* 0} \pi^+ \pi^-$ are determined to be $(8.0 \pm 0.6 \pm 1.5) \times 10^{-4} $ and $ (6.2 \pm 1.2 \pm 1.8) \times 10^{-4}$ respectively. An analysis of $\bar{B^{0}} \to D^{0} \pi^+ \pi^-$ candidates yields to the first observation of the color-suppressed hadronic decay $\bar{B}^0 \to D^0 \rho^0$ with the branching fraction $(2.9 \pm 1.0 \pm 0.4) \times 10^{-4}$. We measure the ratio of branching fractions ${\mathcal B}(\bar{B^0} \to D^0 \rho^0) / {\mathcal B}(\bar{B^0} \to D^0 \omega)$ = 1.6 $\pm$ 0.8.


Introduction
Exclusive hadronic decay rates provide important tests of models for B meson decay [1]. B decays to final states that include a D 0 or a D * 0 accompanied by two charged pions are interesting, because such decays provide a precision testing ground for factorization [2], and because one can search for resonant substructure in the final state. At present, only an upper limit B(B 0 → D 0 π + π − ) < 1.6 × 10 −3 [3], has been measured. The D ( * )0 π + π − final state includes theB 0 → D ( * )0 ρ 0 decay which has not yet been observed [4]. As shown in Fig. 1(a) this decay proceeds via an internal spectator diagram, and is "color-suppressed" since the color of the quarks produced by the weak current must correspond to the color of the c quark and the spectator quark. Recent measurements [5] of the branching fractions for the color-suppressed decaysB 0 → D 0 X 0 , where X 0 = π 0 , η or ω, are all higher than theoretical predictions [6] providing evidence for failure of the naïve factorization model and suggesting sizable final state interactions (FSI). In the heavy quark limit, the QCD factorization model works effectively for color-allowed decays, while color-suppressed decays require substantial correction [7]. Assuming SU(3) symmetry for the FSI rescattering phase, the observed discrepancy can be accommodated and branching fractions, such as B(B 0 → D 0 ρ 0 ), can be predicted [8]. It is important to test whetherB 0 → D 0 ρ 0 , once observed, supports the current pattern of QCD effects in color-suppressed B decays.
The dominant diagrams for such neutral B meson decays preserve the spectator d-quark and therefore require that the final state neutral light meson be produced via its d −d component ( Fig. 1(a)). These diagrams predict equal branching fractions for D 0 ρ 0 and D 0 ω and for D * 0 ρ 0 and D * 0 ω. Other diagrams, such as W-exchange ( Fig. 1(b)) or final state interactions can produce the u −ū state and therefore give different branching fractions. This equality is therefore a very sensitive test for small amplitudes in which the spectator d-quark does not appear in the final state and the ρ or ω are produced via their u −ū components [8,9].
In this paper, we will report on the study ofB 0 decays that have one D 0 or D * 0 and two oppositely charged pions in the final state. Inclusion of charge conjugate modes is implied throughout this paper.

Data Sample and Selection Criteria
The data sample used in this paper was collected with the Belle detector at KEKB [10]. It is based on an integrated luminosity of 29.1 fb −1 at the Υ(4S) resonance, corresponding to 31.3 million BB events.
The Belle detector [11] is a large-solid-angle magnetic spectrometer that consists of a three-layer silicon vertex detector, a 50-layer central drift chamber (CDC), an array of aerogel thresholdČerenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a super-conducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil is instrumented to detect K 0 L mesons and to identify muons (KLM).
Hadronic event selection is described elsewhere [12]. π 0 candidates are formed by combining two photons detected in the ECL, whose invariant mass is within a ±16 MeV/c 2 mass window around the π 0 peak. The π 0 daughter photons are required to have energies greater than 20 MeV. We require the point of closest approach to the origin of each track to be within ±5 mm from the beam axis and ±3 cm along the beam axis from the interaction point to remove background. Tracks identified as electrons (from the responses of the CDC and ECL) or muons (from the response of the KLM) are removed. Kaon and pion candidates are distinguished by combining the dE/dx information from the CDC, time of flight information from the TOF and hit information from the ACC.
D 0 candidates are reconstructed in the decay modes K − π + , K − π + π 0 , and K − π + π − π + . For D 0 → K − π + π 0 , the π 0 daughter photons are required to have energies greater than 50 MeV and we select regions of the Dalitz plot with large decay amplitudes to further suppress the combinatorial background [13]. The invariant masses of D 0 candidates are required to be within 2.5σ of the nominal mass. The selected π 0 s and D 0 s are then kinematically fit with their masses constrained to their nominal values [14]. D * 0 candidates are formed by combining D 0 and π 0 candidates and selecting those with mass difference δm = M D * 0 − M D 0 in the range 0.1400 GeV/c 2 < δm < 0.1445 GeV/c 2 .

B Meson Reconstruction
After selecting D 0 and D * 0 candidates, we combine them with two oppositely charged pions to form B candidates. The two oppositely charged candidate pions from the B decay are required to come from a single vertex. To remove K 0 S candidates from the sample, the distance of the π + π − vertex from the beam interaction point in the r − φ plane is required to be less than 0.8 cm. Two kinematic variables are used to identify signal candidates, the beam constrained mass, are the center of mass (CM) energy and momentum of theB 0 candidate, and E CM beam = √ s/2 = 5.29 GeV. We select events with |∆E| < 0.2 GeV and 5.272 GeV/c 2 < M bc < 5.288 GeV/c 2 (5.271 GeV/c 2 < M bc < 5.289 GeV/c 2 ) for D 0 π + π − (D * 0 π + π − ) final states. Further, if there are multiple B candidates in an event, we choose the candidate with the smallest χ 2 combination, where, χ 2 D 0 and χ 2 π + π − are obtained from D 0 and π + π − vertex fitting respectively. For decay modes containing D * 0 , χ 2 δm -defined as the square of the difference of δm from its nominal value, in units of its resolution, (∆(δm)/σ(δm)) 2 -is additionally included in the best candidate selection requirement.

Background Suppression
Since the continuum background (arising from e + e − → qq(q = u, d, c, s) transitions) has a different event topology, shape variables are very effective at improving the signal to noise ratio. Events are required to satisfy R 2 < 0.5, where R 2 is the ratio of the second Fox-Wolfram moment to the zeroth moment determined using charged tracks and unmatched neutral showers [15]. The angle between the B candidate direction and the thrust axis [16] of the rest of the event (θ T ) is required to satisfy | cos(θ T )| < 0.7.
For theB 0 → D ( * )0 π + π − branching fraction measurements, we make no assumptions about the intermediate mechanism, except that we reject the large contribution from the well-established decayB 0 → D * + π − to the D 0 π + π − final state. These events are rejected by requiring M 2 D 0 π + > 4.62 GeV 2 /c 4 (Fig.  2), which removes 1% of the phase space forB 0 → D 0 π + π − . As the decaȳ B 0 → D * 2 (2460) + π − is not well established [14], no attempt is made to reject it and this mode is thus included in our branching fraction measurement.
Color-favored decays can also cause a background when a final state pion is replaced by a pion from the decay of the other B (for example B − → D ( * )0 ρ − may be reconstructed asB 0 → D ( * )0 π + π − ). To reduce this background we veto events which can also be reconstructed in a color-favored mode. This requirement removes 1% of the signal candidates. Using a sample of 44 million generic b → c decays generated via Monte Carlo (MC) simulation, the small remaining background is studied and found not to peak in M bc or ∆E.
5 Branching Fractions for D 0 π + π − and D * 0 π + π − final states The distribution in ∆E for the surviving candidates forB 0 → D 0 π + π − is shown in Fig. 3(a). Since intermediate resonances dominate the decay rate we obtain a non-uniform distribution of events on the Dalitz plot. In addition, the efficiency varies across the Dalitz plot due to momentum dependences of the reconstruction and particle identification efficiencies. We divide the Dalitz plot into six different regions expected to be dominated by different intermediate processes as shown in Fig. 2 and determine the efficiency [17] and signal yield (from ∆E fit) for each. Table 1 summarizes our results. For each Dalitz plot region we model the signal in ∆E with a Gaussian function where both the mean and width are fixed from MC studies. The background shape in this fit is modeled by two components: (1) a linear shape for continuum background obtained from the sideband data (5.20 GeV/c 2 < M bc < 5.26 GeV/c 2 ); (2) a smooth histogram shape forB 0 → D * 0 π + π − feeddown obtained from MC. The normalizations of the signal and background  components are free parameters in the fit. We obtain the branching fraction forB 0 → D 0 π + π − by taking the sum of the branching fractions in the six regions of the Dalitz plot and making a correction of 1% for the unobserved region where M 2 D 0 π + < 4.62 GeV 2 /c 4 . In all branching fraction calculations we assume equal production of B 0B0 and B + B − pairs from the Υ(4S).
To estimate the branching fraction forB 0 → D * 0 π + π − decays, we make no restriction on M 2 D * 0 π + . Due to limited statistics, we do not estimate the branching fraction region by region. Instead, we use the yield from the ∆E fit ( Fig. 3(b)) and include a model dependent systematic error (19%) that arises from the difference between the detection efficiency when the signal MC events areB 0 → D * 0 π + π − andB 0 → D * 0 ρ 0 . The two detection efficiencies are 0.26% and 0.32%, respectively where theB 0 → D * 0 ρ 0 decay is generated with equal rates to each helicity state.
The background near the lower side of the ∆E distribution is modeled by B + → D * 0 a + 1 feed-down measured using MC. The yield from the fit is 62 ± 12 events. We measure the branching fraction forB 0 → D * 0 π + π − using the phase space MC efficiency. The results are summarized in Table 2.
6 Search for Color-SuppressedB 0 → D ( * )0 ρ 0 Decays Multi-body decays of B mesons can occur through various strong resonances that can interfere with each other. We search for color-suppressedB 0 → D ( * )0 ρ 0 decays in the D ( * )0 π + π − final state. We study the π + π − invariant mass of the events in the signal region (|∆E| < 0.030 GeV for D 0 π + π − and |∆E| < 0.035 GeV for D * 0 π + π − ) and fit the ρ 0 yield with a relativistic Breit-Wigner function whose mean and width are fixed to the PDG values [14] to estimate the branching fraction.
To study the color-suppressed decay modeB 0 → D 0 ρ 0 , we require M 2 D 0 π + > 14.0 GeV 2 /c 4 to remove backgrounds from D * + π − , D * + 2 π − decays and other D resonances. After this requirement, we clearly see an excess at the ρ 0 mass in the π + π − invariant mass distribution ( Fig. 4(a)). The excess around 1.45 GeV/c 2 can be modeled by either a ρ(1450) or an f 0 (1370) resonance; we cannot discriminate between these states, or alternative models of the excess, based on the fit. Events near 0.5 GeV/c 2 may come from the σ [18] resonance. We extract the ρ 0 yield using a one dimensional likelihood fit. We use a model which includes one low mass and one high mass wide resonance. The masses and widths are fixed, and the amplitudes and phases are free parameters in the fit. The error from the fit therefore incorporates the error from the relative phases of the interfering terms: this tends to increase the error on the yield. The background under the signal events is described reasonably well by data from the ∆E sideband (0.06 GeV < ∆E < 0.20 GeV) shown as the hatched histogram in Fig. 4(a). We model this shape with a combination of phase space, a polynomial and a Breit-Wigner function, where the third term takes into account the possible contribution of true ρ 0 in the background. From the fit, we obtain 86 ± 30 signal events corresponding to a branching fraction of B(B 0 → D 0 ρ 0 ) = (2.9 ± 1.0 ± 0.4)×10 −4 . The statistical significance of the signal, calculated as −2 ln(L 0 /L max ) where L max is the likelihood with the nominal yield and L 0 is the likelihood with the signal constrained to be zero, is 6.1σ. We find a strong correlation between the amplitude of the ρ 0 component and its relative phase with respect to the higher mass resonance; if the amplitudes and phases of the high and low mass resonances are fixed at their obtained values, and the fit is repeated, a ρ 0 yield of 86±24 events is obtained. We have repeated the fit with a number of different models including vector and scalar resonances at different masses and with different widths; the variation in the central value of the ρ 0 yield is negligible compared to the error from our default fit. As a further cross-check, we examine the the helicity angle (Θ ρ ), defined as the angle in the ρ 0 rest frame between the direction of the π + and the ρ 0 direction in the B rest frame, and find it to be consistent with the expected shape [19].

Summary
In summary, we report the first observation of the color-suppressedB 0 → D 0 ρ 0 decays and measure the branching fraction forB 0 → D ( * )0 π + π − . Our measurement of B(B 0 → D 0 ρ 0 ) is higher than the factorization prediction of 0.7 × 10 −4 [6], thus continuing the trend mentioned in the introduction. When we compare the branching fraction ofB 0 → D 0 ρ 0 to our previous measurement of the branching fraction ofB 0 → D 0 ω [5], we obtain the ratio B(B 0 → D 0 ρ 0 )/B(B 0 → D 0 ω) = 1.6 ± 0.8. The error includes both statistical and systematic errors where the correlation of the systematic errors has been taken into account. Future measurements with more statistics will allow precise tests of the mechanisms involved in color-suppressed B decays.