Measurement of Branching Fractions and Resonance Contributions for B0 ->D0bar K+ pi- and Search for B0 ->D0 K+ pi- Decays

Using 226 million $\Upsilon(4S)\to B\bar{B}$ events collected with the BaBar detector at the PEP-II $e^+e^-$ storage ring at the Stanford Linear Accelerator Center, we measure the branching fraction for $B^0\to \bar{D}^0 K^+\pi^-$, excluding $B^0\to D^{*-} K^+$ to be $ {\cal B}(B^0\to \bar{D}^0 K^+\pi^-) = (88 \pm 15 \pm 9)\times 10^{-6} . $ We observe $B^0\to \bar{D}^0 K^*(892)^0$ and $B^0\to D_2^*(2460)^- K^+$ contributions. The ratio of branching fractions ${\cal B}(B^0\to D^{*-}K^+)/{\cal B}(B^0\to D^{*-}\pi^+) = (7.76\pm 0.34 \pm 0.29)%$ is measured separately. The branching fraction for the suppressed mode $B^0\to D^0 K^+\pi^-$ is $ {\cal B}(B^0\to D^0 K^+\pi^-)<19 \times 10^{-6} $ at the 90% confidence level.

PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er A theoretically clean method for measuring the angle γ = arg(−V ud V * ub /V cd V * cb ) in the unitarity triangle of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1] in the Standard Model of particle physics utilizes decay modes of the type B → DK. Several methods have been proposed [2][3][4] to extract γ from these decays using interference effects between b → ucs and b → cus processes. However, the b → ucs amplitude is suppressed by a color factor in addition to the CKM factor |V ub V * cs /V cb V * us | ≃ 0.4, and the extraction of γ with methods in Ref. [2,3] is subject to an eight-fold ambiguity due to unknown strong phases.
Three-body B → DKπ decays have been proposed [5,6] as an alternative method for measuring γ. In these modes, the CKM-suppressed b → ucs processes include color-allowed diagrams; thus larger decay rates and more significant CP violation effects are possible. In addition, a DKπ Dalitz plot analysis can resolve the strong phase and reduce the ambiguity to two-fold, similar to Ref. [4]. The sensitivity to γ in these decays is determined by the size of the overlapping b → cus and b → ucs amplitudes in the Dalitz plot.
In this Letter, we report the measurements of the branching fraction for the CKM-favored B 0 → D 0 K + π − [7] decay and dominant resonance contributions, and the search for the CKM-suppressed B 0 → D 0 K + π − decays. The flavor of the B meson is tagged by the charge of the prompt kaon. The favored mode has been previously observed through its dominant resonances D * − K + [8] and D 0 K * (892) 0 [9]. Since D * − K + occupies only a very small region of the allowed phase space, we treat it separately and measure the ratio r = B(B 0 → D * − K + )/B(B 0 → D * − π + ), which can be used to test factorization and flavor-SU(3) symmetry.
Signal events are selected from 226 million BB pairs collected with the BABAR detector [10] at the PEP-II asymmetric-energy storage ring. Charged tracks are detected by a five-layer silicon vertex tracker and a 40-layer drift chamber. Hadrons are identified based on the ion-ization energy loss in the tracking system and the opening angle of the Cherenkov radiation in a ring-image detector [11]. Photons are measured by an electromagnetic calorimeter. These systems are mounted inside a 1.5-T solenoidal super-conducting magnet.
The D 0 candidate is reconstructed through K − π + , K − π + π 0 , and K − π + π − π + channels, where the measured invariant mass is required to be within 20, 35, and 20 MeV/c 2 , respectively, of the nominal D 0 mass [12], corresponding to 3.0, 2.5 and 3.0 σ. A vertex fit is performed with the mass constrained to the nominal value. The π 0 candidate is formed from two photon candidates with invariant mass between 115 and 150 MeV/c 2 .
For the measurement of the ratio r, the D 0 is combined with a low momentum π to form a D * candidate, with its vertex constrained to the interaction point (beam spot). Candidates with mass difference m D 0 π − m D 0 between 144 and 147 MeV/c 2 are retained. A charged track, assumed to have the pion mass, is combined with the D * to form a B 0 candidate. The χ 2 probabilities for both the D * and B 0 vertex fits are required to be greater than 0.1%. To reject jet-like continuum background, the normalized Fox-Wolfram second moment R 2 [13], computed with charged tracks and neutral clusters, is required to be less than 0.5, and | cos θ T | less than 0.85 where θ T is the thrust angle between the B 0 candidate and the rest of the event in the e + e − center-of-mass (CM) frame.
For B 0 → D 0 K + π − and D 0 K + π − measurements, the B 0 candidate is formed by combining a D 0 candidate with oppositely charged pion and kaon candidates. We select candidates outside the D * − K + region (142.5 < m D 0 π − m D 0 < 148.5 MeV/c 2 , a 6σ window). The measured D 0 invariant mass must be within 12, 28, and 8.5 MeV/c 2 of the nominal D 0 mass for Kπ, Kππ 0 , and Kπππ modes, respectively. Candidates are rejected if the D 0 → Kππ 0 decay probability, computed with the Dalitz parameters measured in Ref. [14], is less than 6% of the maximum value. The χ 2 probability of the D 0 (B 0 ) vertex fit is required to be greater than 0.5% (2%).
All charged tracks are required to have at least 12 hits in the drift chamber and transverse momentum greater than 100 MeV/c. Both kaon candidates are required to be consistent with the kaon hypothesis. Prompt pion candidates consistent with the kaon hypothesis are rejected.
To further reduce the continuum background, | cos θ * B | must be less than 0.9, where θ * B is the polar angle of the B 0 candidate in the CM frame. A Fisher discriminant F is formed based on R 2 , cos θ T , θ * B , and two moments L 0 and L 2 , where L i = j p * j | cos θ * j | i , summed over the remaining particles j in the event, where θ * j and p * j are the angle with respect to the B 0 thrust and the momentum in the CM frame. Different cuts on F are applied for each mode to optimize the signal significance based on simulated event samples. Candidates used in the subsequent fits have beam-energy substituted mass where E * and p * are the energy and momentum of the B 0 candidate and √ s is the total energy in the CM frame.
We study five samples separately: is a pion or kaon. Samples (c) and (d) are subsets of (a), where the resonances are selected within 1.5 times their full widths [12].
For samples (a)-(d), a two-dimensional (m ES , ∆E) unbinned-maximum-likelihood fit is used to determine the signal yields. The signal component is the product of a Gaussian in m ES centered at the B 0 mass and a Crystal Ball lineshape [15] in ∆E centered near zero. The combinatorial background component is modeled with an Argus threshold function [16] in m ES and a second-order polynomial in ∆E. Two background components peak in m ES : peaking background A describes the B 0 → D * * − π + contribution, which also peaks in ∆E but the peak is shifted by about +50 MeV because the pion is misidentified as a kaon; peaking background B uses a second-order polynomial in ∆E to accommodate events such as D ( * ) K ( * ) π, and D ( * ) ρ, where one or more pions or photons are missed in the reconstruction and/or a pion is misidentified as a kaon. The probability density function (PDF) is the sum of the signal and three background components. A large B 0 → D * − π + data control sample is used to determine the signal shape in both ∆E and m ES , and the peaking background A in ∆E, where we assign the kaon mass to the pion candidate. We use the same parameters for signal and peaking backgrounds in m ES since they are consistent in simulation. The ∆E distributions and yields for the four components in the signal region are shown in Fig. 1 and Table I, respectively.
The signal yield for B 0 → D 0 K + π − is corrected for variations in signal efficiency across the DKπ Dalitz plot. Each event k with variables q k ≡ (m ES,k , ∆E k ) is as- for the three D 0 modes combined. Circles with error bars are data points. Four curves from top to bottom represent: the total PDF (solid), total background (dashed), combinatorial background plus peaking background B described in the text (dot-dashed) and combinatorial background only (dotted). In (a)-(c), the middle two curves overlap because the peaking background A is negligible.
signed a signal weight [17] , calculated from the four PDF components P j , their yields N j from the fit, and the covariance matrix elements V sig,j between N sig and N j . The efficiency-corrected signal yield is then k w sig ( q k )/ε k , where the efficiency ε k is estimated from the simulated events in the vicinity of each data point in the Dalitz plot. Figure 2 shows the signal weight distribution as a function of m K + π − and m D 0 π − . The peaks near m K * (892) 0 and m D * 2 (2460) − are clearly visible. We use the (m ES , ∆E) fit results and signal efficiencies estimated from simulated B 0 → D 0 K * (892) 0 and B 0 → D * 2 (2460) − K + samples to compute corresponding branching fractions. For the B 0 → D 0 K + π − mode, we assume a flat distribution on the Dalitz plot when determining the signal efficiency.
For modes in which we do not observe a significant signal, the 90% confidence level (C.L.) branching fraction upper limit is determined by integrating the product of the PDFs for the three D 0 modes as a function of branching fraction from 0 to B UL so that BUL 0 LdB = 0.9 ∞ 0 LdB, where L is the likelihood function. To measure r, we select events with m ES > 5.27 GeV/c 2 from sample (e). A two-dimensional PDF of ∆E and θ C (the reconstructed Cherenkov-light angle of the prompt track) is used to separate D * K from I: The yields of signal, combinatorial (comb.) and peaking (peak A, peak B) background PDFs of the samples (a)-(d) described in the text; values and errors are rescaled to represent the yields in the signal region (mES > 5.27 GeV/c 2 , |∆E| < 40 MeV). The bottom row shows the branching fractions with statistical errors. 229 ± 4 500 ± 5 528 ± 5 608 ± 5 918 ± 6 989 ± 6 17 ± 1 29 ± 1 30 ± 1 16 45 ± 9 76 ± 12 42 ± 10 50 ± 11 54 ± 14 45 ± 13 6 ± 3 10 ± 3 3 ± 3 2 ± 3 7 ± 3 0 ± 1 B (10 −6 ) 88 ± 15 −4 ± 12 38 ± 6 18.3 ± 4.0 D * π decays. Tracks with an estimated θ C uncertainty σ C > 4 mrad or n γ,s / √ n γ,s + n γ,b < 3 are removed, where n γ,s and n γ,b are the numbers of signal and background photons determined from a likelihood fit to the ring of Cherenkov photons associated with the track [11]. Finally events are rejected if θ C is smaller than the predicted Cherenkov angle for kaons by more than 4σ C , in order to remove particles heavier than kaon.
The ∆E signal peak PDF is a Crystal Ball lineshape and the background is a linear function plus a Gaussian peaked near −150 MeV to accommodate background events such as D * ρ and D * * π where a soft π is missed in the reconstruction.The distribution of (θ C − θ π C )/σ C is modeled by Gaussian functions. For the pion component, we use three Gaussian functions centered near zero. For the kaon component, a single Gaussian function centered near (θ K C − θ π C )/σ C is sufficient, where θ K C and θ π C are the expected Cherenkov angle for kaon and pion, respectively, based on the measured momentum. Most of the parameters are obtained from a fit to the pion or kaon tracks in a large cc → D * X → D 0 πX, D 0 → K − π + data control sample, except the total width of the distribution, which is free in the final fit to accommodate a small difference in width due to differences in momentum spectra between signal and control samples. Figure 3 shows the ∆E and (θ C − θ π C )/σ C distributions and PDF projections for B 0 → D * − h + (h = π Cherenkov angle (θC − θ π C )/σC distributions for D * − h + candidates and PDF projections. Circles with error bars are data points. Shaded distribution is combinatorial background, the dotted curve adds the D * π contribution, and the solid curve is the full PDF. The dashed curve represents the D * K contribution only. ∆E for D * π is centered near zero, while for D * K it is shifted to lower values because the prompt track is assumed to be a pion.
or K) candidates. We find 13400 signal events, of which f = (6.80±0.28)% are D * K events, and 4850 background events in the sample. The ratio r = f /(1 − f ) is corrected by the signal efficiency ratio r ε = ε D * K /ε D * π = (94.0 ± 2.3)% obtained from simulation. This ratio is smaller than unity because θ C for kaons is smaller (resulting in fewer Cherenkov photons) and more kaons than pions decay in flight within the tracking volume. The uncertainty on r ε includes simulation statistics and systematic uncertainties due to the two aforementioned effects.
For samples (a)-(d), the systematic uncertainties on the signal efficiency are studied with large τ lepton decay samples (for track reconstruction efficiency) and comparisons between signal simulation and B 0 → D * − π + data control sample. The fractional uncertainty, common to all four samples, on signal efficiency is 5% including the uncertainties on the number of BB events and the D 0 branching fractions. For the B 0 → D 0 K + π − mode, the uncertainty of efficiency variation on the Dalitz plot contributes an additional systematic error of 8%. In addition, we vary the control sample shapes in each fit by one standard error and sum the changes in signal yield in quadrature. The total signal yield variations are 8, 2.0, 3.4, and 2.6 events for D 0 K + π − , D 0 K + π − , D 0 K * (892) 0 , and D * 2 (2460) − K + , respectively. For the B 0 → D 0 K * (892) 0 and D * 2 (2460) − K + measurements, we consider possible contamination from each other and from the non-resonance contribution. Using the signal yields for B 0 → D 0 K * (892) 0 and D * 2 (2460) − K + , and the cross-feed efficiencies determined from simulation, we find that six events in each of these two B 0 modes could be attributed to the other mode and to non-resonance contributions. This contributes a 6% uncertainty for B 0 → D 0 K * (892) 0 and 11% for B 0 → D * 2 (2460) − K + . The uncertainty due to the full width of the D * 2 (2460) − and K * (892) 0 resonances is 8% for B 0 → D * 2 (2460) − K + and less than 1% for B 0 → D 0 K * (892) 0 .
The largest systematic uncertainties cancel in the branching ratio measurement (sample (e)). The remaining systematic errors are from PDF shapes, control sample distributions and contaminations (1.9%), residual uncertainties in the signal efficiency ratio (2.4%), and potential fit bias (2.1%). The last item has been evaluated with simulation samples including background.
In conclusion, we have measured the branching fraction for the B 0 → D 0 K + π − decay excluding D * − K + , as well as its two significant resonances, = (38 ± 6 ± 4) × 10 −6 , and The signal significances are 8.7, 8.3 and 5.0 standard deviations, respectively, determined from the change in the likelihood between the best fit and a fit with the signal yield fixed to zero (the first case) or the possible cross feed from other sources (six events for the latter two cases). From a fit excluding the observed resonances, assuming flat distriubtion on the Dalitz plot, we find B(B 0 → D 0 K + π − ) = (26 ± 8 ± 4) × 10 −6 , whose signal significance is 3.1σ and 90% confidence level upper limit is 37 × 10 −6 . We do not observe a significant signal for the CKM-suppressed B 0 → D 0 K + π − mode. The 90% confidence level upper limit is B(B 0 → D 0 K + π − ) < 19×10 −6 . The event yields in this channel are lower than anticipated [5] indicating that a significantly larger data sample is required to constrain γ through this method.
This ratio is consistent with (f K /f π ) 2 tan 2 θ Cab ≃ 0.072 [18], expected at tree level if factorization and flavor-SU(3) symmetry hold, where θ Cab is the Cabibbo angle and f K and f π are the decay constants of the kaon and pion, respectively.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE