First Evidence for cos 2 β > 0 and Resolution of the Cabibbo-Kobayashi-Maskawa Quark-Mixing Unitarity Triangle Ambiguity

I. Adachi, T. Adye, H. Ahmed, J. K. Ahn, H. Aihara, S. Akar, M. S. Alam, J. Albert, F. Anulli, N. Arnaud, D. M. Asner, D. Aston, H. Atmacan, T. Aushev, R. Ayad, V. Babu, I. Badhrees, A. M. Bakich, Sw. Banerjee, V. Bansal, R. J. Barlow, G. Batignani, A. Beaulieu, P. Behera, M. Bellis, E. Ben-Haim, D. Bernard, F. U. Bernlochner, S. Bettarini, D. Bettoni, A. J. Bevan, V. Bhardwaj, B. Bhuyan, F. Bianchi, M. Biasini, J. Biswal, V. E. Blinov, M. Bomben, A. Bondar, G. R. Bonneaud, A. Bozek, C. Bozzi, M. Bračko, T. E. Browder, D. N. Brown, D. N. Brown, C. Bünger, P. R. Burchat, A. R. Buzykaev, R. Calabrese, A. Calcaterra, G. Calderini, S. Di Carlo, M. Carpinelli, C. Cartaro, G. Casarosa, R. Cenci, D. S. Chao, J. Chauveau, R. Cheaib, A. Chen, C. Chen, C. H. Cheng, B. G. Cheon, K. Chilikin, K. Cho, Y. Choi, S. Choudhury, M. Chrzaszcz, G. Cibinetto, D. Cinabro, J. Cochran, J. P. Coleman, M. R. Convery, G. Cowan, R. Cowan, L. Cremaldi, S. Cunliffe, N. Dash, M. Davier, C. L. Davis, F. De Mori, G. De Nardo, A. G. Denig, R. de Sangro, B. Dey, F. Di Lodovico, S. Dittrich, Z. Doležal, J. Dorfan, Z. Drásal, V. P. Druzhinin, W. Dunwoodie, M. Ebert, B. Echenard, S. Eidelman, G. Eigen, A. M. Eisner, S. Emery, D. Epifanov, J. A. Ernst, R. Faccini, J. E. Fast, M. Feindt, T. Ferber, F. Ferrarotto, F. Ferroni, R. C. Field, A. Filippi, G. Finocchiaro, E. Fioravanti, K. T. Flood, F. Forti, M. Fritsch, B. G. Fulsom, E. Gabathuler, D. Gamba, R. Garg, A. Garmash, J. W. Gary, I. Garzia, V. Gaur, A. Gaz, M. Gelb, T. J. Gershon, L. Li Gioi, M. A. Giorgi, A. Giri, R. Godang, P. Goldenzweig, B. Golob, V. B. Golubev, R. Gorodeisky, W. Gradl, M. T. Graham, E. Grauges, K. Griessinger, A. V. Gritsan, O. Grünberg, Y. Guan, E. Guido, N. Guttman, J. Haba, A. Hafner, T. Hara, P. F. Harrison, C. Hast, K. Hayasaka, H. Hayashii, C. Hearty, M. Heck, M. T. Hedges, M. Heß, S. Hirose, D. G. Hitlin, K. Honscheid, W.-S. Hou, C.-L. Hsu, Z. Huard, C. Van Hulse, D. E. Hutchcroft, K. Inami, G. Inguglia, W. R. Innes, A. Ishikawa, R. Itoh, M. Iwasaki, Y. Iwasaki, J. M. Izen, W.W. Jacobs, A. Jawahery, C. P. Jessop, S. Jia, Y. Jin, K. K. Joo, T. Julius, A. B. Kaliyar, K. H. Kang, G. Karyan, R. Kass, H. Kichimi, D. Y. Kim, J. B. Kim, K. T. Kim, S. H. Kim, J. Kim, P. Kim, G. J. King, K. Kinoshita, H. Koch, P. Kodyš, Yu. G. Kolomensky, S. Korpar, D. Kotchetkov, R. Kowalewski, E. A. Kravchenko, P. Križan, R. Kroeger, P. Krokovny, T. Kuhr, R. Kulasiri, T. Kumita, A. Kuzmin, Y.-J. Kwon, H. M. Lacker, G. D. Lafferty, L. Lanceri, J. S. Lange, D. J. Lange, A. J. Lankford, T. E. Latham, T. Leddig, F. Le Diberder, I. S. Lee, S. C. Lee, J. P. Lees, D.W. G. S. Leith, L. K. Li, Y. B. Li, Y. Li, J. Libby, D. Liventsev, W. S. Lockman, O. Long, J. M. LoSecco, X. C. Lou, M. Lubej, T. Lueck, S. Luitz, T. Luo, E. Luppi, A. Lusiani, A. M. Lutz, D. B. MacFarlane, J. MacNaughton, U. Mallik, E. Manoni, G. Marchiori, M. Margoni, S. Martellotti, F. Martinez-Vidal, M. Masuda, T. Matsuda, T. S. Mattison, D. Matvienko, J. A. McKenna, B. T. Meadows, M. Merola, K. Miyabayashi, T. S. Miyashita, H. Miyata, R. Mizuk, G. B. Mohanty, H. K. Moon, T. Mori, D. R. Muller, T. Müller, R. Mussa, E. Nakano, M. Nakao, T. Nanut, K. J. Nath, M. Nayak, H. Neal, N. Neri, N. K. Nisar, S. Nishida, I. M. Nugent, B. Oberhof, J. Ocariz, S. Ogawa, P. Ongmongkolkul, H. Ono, A. P. Onuchin, Y. Onuki, A. Oyanguren, P. Pakhlov, G. Pakhlova, B. Pal, A. Palano, F. Palombo, W. Panduro Vazquez, E. Paoloni, S. Pardi, H. Park, S. Passaggio, C. Patrignani,A26,∥ P. Patteri, S. Paul, I. Pavelkin, D. J. Payne, T. K. Pedlar, D. R. Peimer, I. M. Peruzzi, R. Pestotnik, M. Piccolo, L. E. Piilonen, A. Pilloni, G. Piredda, V. Poireau, V. Popov, F. C. Porter, M. Posocco, S. Prell, R. Prepost, E. M. T. Puccio, M. V. Purohit, B. G. Pushpawela, M. Rama, A. Randle-Conde, B. N. Ratcliff, G. Raven, P. K. Resmi, J. L. Ritchie, M. Ritter, G. Rizzo, D. A. Roberts, S. H. Robertson, M. Röhrken, J. M. Roney, A. Roodman, A. Rossi, M. Rotondo, PHYSICAL REVIEW LETTERS 121, 261801 (2018)

We present first evidence that the cosine of the CP-violating weak phase 2β is positive, and hence exclude trigonometric multifold solutions of the Cabibbo-Kobayashi-Maskawa (CKM) Unitarity Triangle using a time-dependent Dalitz plot analysis of B 0 → D ðÃÞ h 0 with D → K 0 S π þ π − decays, where h 0 ∈ fπ 0 ; η; ωg denotes a light unflavored and neutral hadron.The measurement is performed combining the final data sets of the BABAR and Belle experiments collected at the ϒð4SÞ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively.The data samples contain ð471 AE 3Þ × 10 6 B B pairs recorded by the BABAR detector and ð772 AE 11Þ × 10 6 B B pairs recorded by the Belle detector.The results of the measurement are sin 2β ¼ 0.80 AE 0.14ðstatÞ AE 0.06ðsystÞ AE 0.03ðmodelÞ and cos 2β ¼ 0.91 AE 0.22ðstatÞ AE 0.09ðsystÞ AE 0.07ðmodelÞ.The result for the direct measurement of the angle β of the CKM Unitarity Triangle is β ¼ ½22.5 AE 4.4ðstatÞ AE 1.2ðsystÞ AE 0.6ðmodelÞ°.The measurement assumes no direct CP violation in B 0 → D ðÃÞ h 0 decays.The quoted model uncertainties are due to the composition of the D 0 → K 0 S π þ π − decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics e þ e − → cc data sample.CP violation is observed in B 0 → D ðÃÞ h 0 decays at the level of 5.1 standard deviations.The significance for cos 2β > 0 is 3.7 standard deviations.The trigonometric multifold solution π=2 − β ¼ ð68.1 AE 0.7Þ°is excluded at the level of 7.3 standard deviations.The measurement resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle.DOI: 10.1103/PhysRevLett.121.261801 In the standard model (SM) of electroweak interactions, the only source of CP violation is the irreducible complex phase in the three-family Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1].The BABAR and Belle experiments discovered CP violation in the B meson system [2][3][4][5].In particular, by time-dependent CP violation measurements of the "gold plated" decay mode B 0 → J=ψK 0 S and other decays mediated by b → ccs transitions [6,7], BABAR and Belle precisely determined the parameter sin 2β ≡ sin 2ϕ 1 (BABAR uses the notation β and Belle uses ϕ 1 ; hereinafter β is used), where the angle β of the CKM Unitarity Triangle is defined as arg ½−V cd V Ã cb =V td V Ã tb and V ij denotes a CKM matrix element.(In this Letter, the inclusion of charge-conjugated decay modes is implied unless otherwise stated.)Inferring the CP-violating weak phase 2β from these measurements of sin 2β leads to the trigonometric twofold ambiguity, 2β and π − 2β (a fourfold ambiguity in β), and therefore to an ambiguity on the CKM Unitarity Triangle.This ambiguity can be resolved by also measuring cos 2β, which is experimentally accessible in B meson decay modes involving multibody final states such as [16][17][18].However, no previous single measurement has been sufficiently sensitive to establish the sign of cos 2β, to resolve the ambiguity without further assumptions.
The decays B 0 → D ðÃÞ h 0 , with D → K 0 S π þ π − and h 0 ∈ fπ 0 ; η; ωg denoting a light neutral hadron, provide an elegant way to access cos 2β [19].The B 0 → D ðÃÞ h 0 decay is predominantly mediated by CKM-favored b → cu d tree amplitudes.Additional contributions from CKM-disfavored b → ūc d tree amplitudes that carry different weak phases are suppressed by jV ub V Ã cd =V cb V Ã ud j ≈ 0.02 relative to the leading amplitudes and can be neglected at the experimental sensitivity of the presented measurement.The D → K 0 S π þ π − decay exhibits complex interference structures that receive resonant and nonresonant contributions to the three-body final state from a rich variety of intermediate CP eigenstates and quasi-flavor-specific decays.Knowledge of the variations on the relative strong phase as a function of the three-body Dalitz plot phase space enables measurements of both sin 2β and cos 2β from the time evolution of the Assuming no CP violation in B 0 − B0 mixing and no direct CP violation, the rate of the where Δt denotes the proper-time interval between the decays of the two B mesons produced in the e þ e − → ϒð4SÞ → B 0 B0 event, and q ¼ þ1 (−1) represents the bflavor content when the accompanying B meson is tagged as a B 0 ( B0 ).The parameters τ B 0 and Δm d are the neutral B meson lifetime and the B 0 − B0 oscillation frequency, respectively.The symbols denote the D 0 and D0 decay amplitudes as functions of the Lorentz-invariant Dalitz plot variables M 2 , where the symbol p i represents the fourmomentum of a final state particle i.The factor η h 0 is the CP eigenvalue of h 0 .The quantity L is the orbital angular momentum of the Dh 0 or D Ã h 0 system.The last term in Eq. ( 1) can be rewritten as which allows sin 2β and cos 2β to be treated as independent parameters.Measurements of sin 2β and cos 2β in B 0 → D ðÃÞ h 0 with D → K 0 S π þ π − decays are experimentally challenging.The branching fractions of the B and D meson decays are low [Oð10 −4 Þ and Oð10 −2 Þ, respectively], and the neutral particles in the final state lead to large backgrounds and low reconstruction efficiencies.In addition, a detailed Dalitz plot amplitude model or other experimental knowledge of the relative strong phase in the three-body D meson decay is required.Previous measurements of these decays performed separately by BABAR and Belle were not sufficiently sensitive to establish CP violation [16][17][18], obtaining results far outside of the physical region of the parameter space [16], and using different Dalitz plot amplitude models [16,17], which complicates the combination of individual results.
In this Letter, we present measurements of sin 2β and cos 2β from a time-dependent Dalitz plot analysis of B 0 → D ðÃÞ h 0 with D → K 0 S π þ π − decays that combines the final data samples collected by the BABAR and Belle experiments, totaling 1.1 ab −1 collected at the ϒð4SÞ resonance.The combined approach enables unique experimental sensitivity to cos 2β by increasing the available data sample and by applying common assumptions and the same Dalitz plot amplitude model simultaneously to the data collected by both experiments.As part of the analysis, an improved This allows the propagation of the model uncertainties to the results on sin 2β and cos 2β obtained in B 0 → D ðÃÞ h 0 with D 0 → K 0 S π þ π − decays in a straightforward way.In the following, the extraction of the D 0 → K 0 S π þ π − Dalitz plot amplitude model parameters from Belle e þ e − → cc data is summarized.Thereafter, the time-dependent Dalitz plot analysis of the B meson decay combining BABAR and Belle data is described.A more detailed description of the analysis is provided in Ref. [20].
To measure the D 0 → K 0 S π þ π − decay amplitudes, we use a data sample of 924 fb −1 recorded at or near the ϒð4SÞ and ϒð5SÞ resonances with the Belle detector [21] at the asymmetric-energy e þ e − collider KEKB [22].This gives a large sample of D mesons enabling precise measurement of the decay amplitudes, so there is no benefit to be gained from including the equivalent BABAR data.The decays reconstructed, and the flavor of the neutral D meson is identified as D 0 ( D0 ) by the positive (negative) charge of the slow pion π þ s emitted from the D Ãþ decay.Charged pion candidates are formed from reconstructed tracks, and the selection requirements described in Refs.[23,24] are applied to K 0 S candidates.To reject background originating from B meson decays, a requirement of p Ã ðD Ãþ Þ > 2.5ð3.1ÞGeV=c for candidates reconstructed from ϒð4SÞ [ϒð5SÞ] data is applied, where p Ã denotes the momentum evaluated in the e þ e − center-of-mass (c.m.) frame.Events are selected by the D 0 candidate mass M D 0 and the D Ãþ − D 0 mass difference ΔM, and a yield of 1 217300 AE 2 000 signal decays is obtained by a two-dimensional unbinned maximumlikelihood fit to the M D 0 and ΔM distributions [20].
Similar to previous D 0 − D0 oscillation analyses and measurements of the Unitarity Triangle angle γ [25] by BABAR, Belle, and LHCb [26][27][28][29], the The symbols a r and ϕ r represent the magnitude and phase of the rth intermediate quasi-two-body amplitude A r contributing to the Pand D-waves.These amplitudes are parametrized using an isobar ansatz [30] by relativistic Breit-Wigner (BW) propagators with mass-dependent widths, Blatt-Weisskopf penetration factors [31], and Zemach tensors for the angular distributions [32].The following intermediate two-body resonances are included: the Cabibbo-favored and the CP eigenstates K 0 S ρð770Þ 0 , K 0 S ωð782Þ, K 0 S f 2 ð1270Þ, and K 0 S ρð1450Þ 0 .The symbol F 1 denotes the amplitude for the ππS-wave using the K-matrix formalism in the P-vector approximation with four physical poles [33,34].The symbol A Kπ L¼0 represents the amplitude for the KπS-wave using the LASS parametrization [35], which combines a BW for the K Ã 0 ð1430Þ AE with a coherent nonresonant contribution governed by an effective range and a phase shift.
The D 0 → K 0 S π þ π − decay amplitude model parameters are determined by an unbinned maximum-likelihood Dalitz fit performed for events in the signal region of the flavor-tagged D 0 sample.The probability density function (p.d.f.) for the signal is constructed from Eq. ( 3) with a correction to account for reconstruction efficiency variations over the Dalitz plot phase space due to experimental acceptance effects [36], and an additional term to account for wrong flavor identifications of D mesons.In addition, the likelihood function contains a p.d.f. for the background that is constructed from the distributions taken from the M D 0 and ΔM data sidebands.The a r and ϕ r parameters for each resonance are floated in the fit and measured relative to the K 0 S ρð770Þ 0 amplitude, which is fixed to a K 0 S ρð770Þ 0 ¼ 1 and ϕ K 0 S ρð770Þ 0 ¼ 0°.The masses and widths of the resonances are fixed to the world averages [37] except for those of the K Ã ð892Þ and K Ã 0 ð1430Þ, which are floated to improve the fit quality.The LASS parameters and several parameters in the K-matrix are floated in the fit.
The results of the Dalitz fit are summarized in Table III of Ref. [20].The data distributions and projections of the fit are shown in Fig. 1.By a two-dimensional χ 2 test, a reduced χ 2 of 1.05 is obtained for 31 272 degrees of freedom based on statistical uncertainties only, indicating a relatively good quality of the fit [26][27][28]38,39].
The B 0 → D ðÃÞ h 0 yields are determined by threedimensional unbinned maximum-likelihood fits to the distributions of the observables M 0 bc , ΔE, and C 0 NN out .The beam-energy-constrained mass M 0 bc defined in Ref. [43] is computed from the beam energy E Ã beam in the c.m. frame, the D ðÃÞ candidate momenta, and the h 0 candidate direction of flight.The quantity M 0 bc provides an observable that is insensitive to possible correlations with the energy difference ΔE ¼ E Ã B − E Ã beam that can be induced by energy mismeasurements for particles detected in the electromagnetic calorimeters, e.g., caused by shower leakage effects.The variable C 0 NN out defined in Ref. [44] is constructed from the output of a neural network multivariate classifier trained on event shape information based on a combination of 16 modified Fox-Wolfram moments [45,46] to identify background originating from e þ e − → q q ðq ∈ fu; d; s; cgÞ continuum events.The fit model accounts for contributions from B 0 → D ðÃÞ h 0 signal decays, cross-feed from partially reconstructed B 0 → D Ã h 0 decays, background from partially reconstructed B þ → DðÃÞ0 ρ þ decays, combinatorial background from B B decays, and background from continuum events.In total, a B 0 → D ðÃÞ h 0 signal yield of 1129 AE 48 events in the BABAR data sample and 1567 AE 56 events in the Belle data sample is obtained.The signal yields are summarized in Table IV of Ref. [20].The M 0 bc , ΔE, and C 0 NN out data distributions and fit projections are shown in Fig. 2.
The time-dependent Dalitz plot analysis follows the technique established in the previous combined BABAR +Belle time-dependent CP violation measurement of B0 → D ðÃÞ CP h 0 decays [24].The measurement is performed by maximizing the log-likelihood function constructed from the events reconstructed from BABAR and Belle data [20].The measurement includes all events used in the previous M 0 bc , ΔE, and C 0 NN out fits.In the log-likelihood function, the p.d.f.'s are functions of the experimental flavor-tagged proper-time interval and Dalitz plot distributions for the signal and background components.The signal p.d.f.s are constructed from Eqs. ( 1) and ( 2) convolved with experiment-specific resolution functions to account for the finite vertex resolution [6,47] and including the effect of incorrect flavor assignments [6,48].The p.d.f.'s for the proper-time interval distributions of the combinatorial background from B B decays and background from continuum events account for background from nonprompt and prompt particles convolved with effective resolution functions.The partially reconstructed B 0 → D Ã h 0 decays are modeled by the signal p.d.f. with a different set of parameters to account for this cross-feed contribution, and the background from partially reconstructed B þ → DðÃÞ0 ρ þ decays is parametrized by an exponential p.d.f.convolved with the same resolution functions as used for the signal.
In the fit, the parameters τ B 0 , τ B þ , and Δm d are fixed to the world averages [49], and the Dalitz plot amplitude model parameters are fixed to the results of the D 0 → K 0 S π þ π − Dalitz plot fit described above.The signal and background fractions are evaluated on an event-by-event basis from the three-dimensional fit of the M 0 bc , ΔE, and C 0 NN out observables.The only free parameters are sin 2β and cos 2β, and the results are sin 2β ¼ 0.80 AE 0.14ðstatÞ AE 0.06ðsystÞ AE 0.03ðmodelÞ; The second quoted uncertainty is the experimental systematic error, and the third is due to the D 0 → K 0 S π þ π − decay amplitude model.The evaluation of these uncertainties is described in detail in Ref. [20].The linear correlation between sin 2β and cos 2β is 5.1%.The result deviates by less than 1.0 standard deviation from the trigonometric constraint given by sin A separate fit is performed to measure directly the angle β using the signal p.d.f.constructed from Eq. ( 1), and the result is The proper-time interval distributions and projections of the fit for sin 2β and cos 2β are shown in Fig. 3 for two different regions of the D 0 → K 0 S π þ π − phase space.Figure 3(a) shows a region predominantly populated by CP eigenstates, B 0 → ½K 0 S ρð770Þ 0 ðÃÞ D h 0 .For these decays, interference emerges between the amplitude for direct decays of neutral B mesons into these final states and those following B 0 − B0 oscillations.The time evolution exhibits mixing-induced CP violation governed by the CPviolating weak phase 2β, which manifests as a sinusoidal oscillation in the signal yield asymmetry. Figure 3(b) shows a region predominantly populated by quasi-flavor-specific decays, B 0 → ½K Ã ð892Þ AE π ∓ ðÃÞ D h 0 .For these decays, the time evolution exhibits B 0 − B0 oscillations governed by the oscillation frequency, Δm d , which appears as an oscillation proportional to cosðΔm d ΔtÞ in the corresponding asymmetry.
The measurement procedure is validated by various cross-checks.The B 0 → DðÃÞ0 h 0 decays with the CKMfavored D0 → K þ π − decay have very similar kinematics and background composition as B 0 → D ðÃÞ h 0 with D → K 0 S π þ π − decays and provide a high-statistics control sample.Using the same analysis approach, the timedependent CP violation measurement of the control sample S π þ π − decays, and for the control sample without flavor-tagging applied, yield τ B 0 ¼ ½1.500 AE 0.052ðstatÞ ps and τ B 0 ¼ ½1.535 AE 0.028ðstatÞ ps, respectively, which are in agreement with the world average τ B 0 ¼ ð1.520 AE 0.004Þ ps [49].In addition, we have performed all measurements for data separated by experiment yielding consistent results [20].
The significance of the results is determined by a likelihood-ratio approach that accounts for the experimental systematic uncertainties and the Dalitz plot amplitude model uncertainties by convolution of the likelihood curves.The measurement of sin 2β agrees within 0.7 standard deviations with the world average of sin 2β ¼ 0.691 AE 0.017 [49] obtained from more precise measurements using b → ccs transitions.The measurement of cos 2β excludes the hypothesis of cos 2β ≤ 0 at a p-value of 2.5 × 10 −4 , which corresponds to a significance of 3.7 standard deviations, providing the first evidence for cos 2β > 0. The measurement of β excludes the hypothesis of β ¼ 0°at a p-value of 3.6 × 10 −7 , which corresponds to a significance of 5.1 standard deviations.Hence, we report an observation of CP violation in B 0 → D ðÃÞ h 0 decays.The result for β agrees well with the preferred solution of the Unitarity Triangle, which is ð21.9AE 0.7Þ°, if computed from the world average of sin 2β ¼ 0.691 AE 0.017 [49].The measurement excludes the second solution of π=2 − β ¼ ð68.1 AE 0.7Þ°at a p-value of 2.31 × 10 −13 , corresponding to a significance of 7.3 standard deviations.Therefore, the present measurement resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle.
In summary, we combine the final BABAR and Belle data samples, totaling an integrated luminosity of more than 1 ab −1 collected at the ϒð4SÞ resonance, and perform a timedependent Dalitz plot analysis of B 0 → D ðÃÞ h 0 with D → K 0 S π þ π − decays.We report the world's most precise measurement of the cosine of the CP-violating weak phase 2β and obtain the first evidence for cos 2β > 0. The measurement directly excludes the trigonometric multifold solution of π=2 − β ¼ ð68.1 AE 0.7Þ°without any assumptions, and thus resolves an ambiguity related to the CKM Unitarity Triangle parameters.An observation of CP violation in B 0 → D ðÃÞ h 0 decays is reported.The measurement assumes no direct CP violation in B 0 → D ðÃÞ h 0 decays.
The B 0 → D ðÃÞ h 0 decays studied by the combined BABAR and Belle approach provide a probe for the CPviolating weak phase 2β that is theoretically more clean than the "gold plated" decay modes mediated by b → ccs transitions [51].Therefore, B 0 → D ðÃÞ h 0 decays can provide a new and complementary SM reference for 2β at the experimental precision achievable by the future highluminosity B factory experiment Belle II [52].FIG. 3. Distributions of the proper-time interval (data points with error bars) and the corresponding asymmetries for B 0 → D ðÃÞ h 0 candidates associated with high-quality flavor tags for two different regions of the D → K 0 S π þ π − phase space and for the BABAR and Belle data samples combined.The background has been subtracted using the s Plot technique [50], with weights obtained from the fit presented in Fig. 2.

D h 0
decays is proportional to Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license.Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Funded by SCOAP 3 . e

FIG. 1 .
FIG. 1.The Dalitz plot data distributions (points with error bars) for D 0→ K 0 S π þ π − from D Ãþ → D 0 π þ s decays reconstructed from Belle e þ e − → ccdata, and projections of the Dalitz fit.The red solid lines show the projections of the total fit function including background, and the grey regions show projections of the background.

FIG. 2 .
FIG. 2. Data distributions for (a) M 0 bc , (b) ΔE, and (c) C 0 NN out (points with error bars) for the BABAR and Belle data samples combined.The solid black lines represent projections of the total fit function, and the colored dotted lines show the signal and background components of the fit as indicated in the legend.In plotting the M 0 bc , ΔE, and C 0 NN out distributions, each of the other two observables are required to satisfy M 0 bc > 5.272 GeVc 2 , jΔEj < 100 MeV, or 0 < C 0 NN out < 8 to select signal-enhanced regions.