CLNS 93/1240 CLEO 93-15 September 7, 1993

Measurement of Charmless Semileptonic Decays of B Mesons

J. Bartelt,^{1} S.E. Csorna,^{1} Z. Egyed,^{1} V. Jain,^{1} D.S. Akerib,^{2} B. Barish,^{2} M. Chadha,^{2} S. Chan,^{2} D.F. Cowen,^{2} G. Eigen,^{2} J.S. Miller,^{2} C. O’Grady,^{2} J. Urheim,^{2} A.J. Weinstein,^{2}

D. Acosta,^{3} M. Athanas,^{3} G. Masek,^{3} H. Paar,^{3} M. Sivertz,^{3} A. Bean,^{4} J. Gronberg,^{4} R. Kutschke,^{4} S. Menary,^{4} R.J. Morrison,^{4} S. Nakanishi,^{4} H.N. Nelson,^{4} T.K. Nelson,^{4}

J.D. Richman,^{4} A. Ryd,^{4} H. Tajima,^{4} D. Schmidt,^{4} D. Sperka,^{4} M.S. Witherell,^{4} M. Procario,^{5} S. Yang,^{5} R. Balest,^{6} K. Cho,^{6} M. Daoudi,^{6} W.T. Ford,^{6} D.R. Johnson,^{6}

K. Lingel,^{6} M. Lohner,^{6} P. Rankin,^{6} J.G. Smith,^{6} J.P. Alexander,^{7} C. Bebek,^{7} K. Berkelman,^{7} D. Besson,^{7} T.E. Browder,^{7} D.G. Cassel,^{7} H.A. Cho,^{7} D.M. Coffman,^{7} P.S. Drell,^{7} R. Ehrlich,^{7} M. Garcia-Sciveres,^{7} B. Geiser,^{7} B. Gittelman,^{7} S.W. Gray,^{7} D.L. Hartill,^{7} B.K. Heltsley,^{7} C.D. Jones,^{7} S.L. Jones,^{7} J. Kandaswamy,^{7} N. Katayama,^{7} P.C. Kim,^{7} D.L. Kreinick,^{7} G.S. Ludwig,^{7} J. Masui,^{7} J. Mevissen,^{7} N.B. Mistry,^{7} C.R. Ng,^{7} E. Nordberg,^{7} M. Ogg,^{7}^{∗} J.R. Patterson,^{7} D. Peterson,^{7} D. Riley,^{7} S. Salman,^{7} M. Sapper,^{7}

H. Worden,^{7} F.Würthwein,^{7} P. Avery,^{8} A. Freyberger,^{8} J. Rodriguez,^{8} R. Stephens,^{8} J. Yelton,^{8} D. Cinabro,^{9} S. Henderson,^{9} K. Kinoshita,^{9} T. Liu,^{9} M. Saulnier,^{9} F. Shen,^{9} R. Wilson,^{9} H. Yamamoto,^{9} B. Ong,^{10} M. Selen,^{10} A.J. Sadoff,^{11} R. Ammar,^{12} S. Ball,^{12} P. Baringer,^{12} D. Coppage,^{12} N. Copty,^{12} R. Davis,^{12} N. Hancock,^{12} M. Kelly,^{12} N. Kwak,^{12}

H. Lam,^{12} Y. Kubota,^{13} M. Lattery,^{13} J.K. Nelson,^{13} S. Patton,^{13} D. Perticone,^{13} R. Poling,^{13} V. Savinov,^{13} S. Schrenk,^{13} R. Wang,^{13} M.S. Alam,^{14} I.J. Kim,^{14} B. Nemati,^{14} J.J. O’Neill,^{14} H. Severini,^{14} C.R. Sun,^{14} M.M. Zoeller,^{14} G. Crawford,^{15} M. Daubenmeir,^{15}

R. Fulton,^{15} D. Fujino,^{15} K.K. Gan,^{15} K. Honscheid,^{15} H. Kagan,^{15} R. Kass,^{15} J. Lee,^{15} R. Malchow,^{15} F. Morrow,^{15} Y. Skovpen,^{15}^{†} M. Sung,^{15} C. White,^{15} J. Whitmore,^{15} P. Wilson,^{15} F. Butler,^{16} X. Fu,^{16} G. Kalbfleisch,^{16} M. Lambrecht,^{16} W.R. Ross,^{16}

P. Skubic,^{16} J. Snow,^{16} P.L. Wang,^{16} M. Wood,^{16} D. Bortoletto,^{17} D.N. Brown,^{17} J.Fast,^{17} R.L. McIlwain,^{17} T. Miao,^{17} D.H. Miller,^{17} M. Modesitt,^{17} S.F. Schaffner,^{17} E.I. Shibata,^{17}

I.P.J. Shipsey,^{17} P.N. Wang,^{17} M. Battle,^{18} J. Ernst,^{18} H. Kroha,^{18} S. Roberts,^{18} K. Sparks,^{18} E.H. Thorndike,^{18} C.H. Wang,^{18} V. Chelkov,^{19} J. Dominick,^{19} S. Sanghera,^{19} T. Skwarnicki,^{19} R. Stroynowski,^{19} I. Volobouev,^{19} P. Zadorozhny,^{19} M. Artuso,^{20} D. He,^{20} M. Goldberg,^{20} N. Horwitz,^{20} R. Kennett,^{20} G.C. Moneti,^{20} F. Muheim,^{20} Y. Mukhin,^{20}

S. Playfer,^{20} Y. Rozen,^{20} S. Stone,^{20} M. Thulasidas,^{20} G. Vasseur,^{20} and G. Zhu^{20}

(CLEO Collaboration)

1Vanderbilt University, Nashville, Tennessee 37235 2California Institute of Technology, Pasadena, California 91125 3University of California, San Diego, La Jolla, California 92093 4University of California, Santa Barbara, California 93106 5Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 6University of Colorado, Boulder, Colorado 80309-0390 7Cornell University, Ithaca, New York 14853 8University of Florida, Gainesville, Florida 32611 9Harvard University, Cambridge, Massachusetts 02138 10University of Illinois, Champaign-Urbana, Illinois, 61801 11Ithaca College, Ithaca, New York 14850 12University of Kansas, Lawrence, Kansas 66045 13University of Minnesota, Minneapolis, Minnesota 55455 14State University of New York at Albany, Albany, New York 12222 15Ohio State University, Columbus, Ohio, 43210 16University of Oklahoma, Norman, Oklahoma 73019 17Purdue University, West Lafayette, Indiana 47907 18University of Rochester, Rochester, New York 14627 19Southern Methodist University, Dallas, Texas 75275 20Syracuse University, Syracuse, New York 13244 (September 7, 1993)

Abstract

Using the CLEO-II detector and a sample of 955000 Υ(4S) decays we have confirmed charmless semileptonic decays of B mesons. In the momentum interval 2.3 − 2.6 GeV/c we observe an excess of 107 ± 15 ± 11 leptons which we attribute to b→uℓν. This result yields a model-dependent range of values for |V_{ub}/V_{cb}| that is lower than has been obtained in previous studies. For the inclusive spectator model of Altarelli et al. we find |V_{ub}/V_{cb}| = 0.076 ± 0.008. Models that describe b→uℓν with a limited set of exclusive final states give |V_{ub}/V_{cb}| = 0.06 − 0.10.

PACS numbers: 13.20.Jf, 12.15.Ff, 14.40.Jz

Typeset using REVTEX

∗Permanent address: Carleton University, Ottawa, Canada K1S 5B6

†Permanent address: INP, Novosibirsk, Russia

The measurement of the Cabibbo-Kobayashi-Maskawa matrix element V_{ub} is among the principal goals of b-quark physics. A nonzero value for V_{ub} is essential for the Standard Model description of CP violation, and a precise determination will significantly enhance our understanding of the weak interaction. CLEO [1] and ARGUS [2] demonstrated the existence of b→uℓν transitions by observing B-meson decays with leptons that were too energetic to originate from b→cℓν. These measurements established a value of |V_{ub}/V_{cb}| of approximately 0.1. Subsequently ARGUS [3] presented preliminary evidence for the exclusive decay B^{−}→ρ^{0}ℓ^{−}\overline{ν}, but this has not been confirmed by CLEO [4]. Thus, the inclusive results are the only undisputed evidence that V_{ub} is nonzero.

In this Letter we describe a study of B-meson semileptonic decays in the lepton momentum range 2.3 − 2.6 GeV/c. Our data sample was obtained with the CLEO-II detector at the Cornell Electron Storage and consisted of 924 pb^{−1} of e^{+}e^{−} annihilations at the Υ(4S) resonance (ON), and 416 pb^{−1} at total energies ∼ 55 MeV below the Υ(4S) (OFF). Our total of 955000 ± 18000 B\overline{B} events represented a more than fourfold increase over previous inclusive measurements of b→uℓν. The contribution of continuum processes to our ON yields was estimated the by scaling the OFF yields by 2.20 ± 0.01, the ratio of the ON and OFF luminosities, corrected for the energy dependence of the continuum cross section.

The CLEO-II detector has been described in detail [5]. The crucial components for this study are charged particle tracking and lepton detection. The tracking system, which measures both the momentum and specific ionization (dE/dx) of charged particles, consists of a 67-layer drift chamber system inside a 1.5-T solenoidal magnet. Electromagnetic energy is measured with a 7800-crystal cesium iodide calorimeter, located inside the magnet. Muons are identified with proportional counters embedded in an iron absorber.

Hadronic event-selection requirements were based on standard CLEO-II criteria for event multiplicity, visible energy and a reconstructed event vertex consistent with the nominal interaction point. Electron candidates were required to have both an energy deposit in the calorimeter approximately equal to the measured momentum, and a dE/dx which was consistent with that expected for an electron. The efficiency for identifying a 2.3−2.6 GeV/c electron was 92±4% (70±5%) in the polar angular range |cosθ| < 0.71 (0.71 ≤ |cosθ| < 0.85). The probability of misidentifying a hadron as an electron was 0.3 ± 0.1%. Muon candidates were identified as charged tracks with matching muon-detector hits at absorber depths of at least seven nuclear interaction lengths. The detection efficiency for a 2.3−2.6 GeV/c muon with |cosθ| < 0.85 was 85 ± 4%, and the misidentification probability per hadron track was 0.7 ± 0.3%.

The observation of leptons in Υ(4S) decays with momenta above the b→cℓν kinematic limit (∼2.46 GeV/c) provides model-independent evidence for b→uℓν. We restricted our lepton sample to |cosθ| < 0.85, and we applied stringent track-quality requirements, to eliminate contamination from mismeasured tracks. The momentum resolution was investigated with μ-pair events, and by embedding isolated tracks from QED processes into hadronic events. No appreciable non-Gaussian behavior in the momentum resolution function was found.

Lepton production at the Υ(4S) resonance is dominated by b→cℓν. For momenta above 2.3 GeV/c, however, the dominant source of leptons is continuum production. To eliminate τ^{+}τ^{−} events and other QED processes, we required at least five charged tracks, or four tracks and six or more photon showers. Additional QED background, and other events with a sizable momentum component along the beam axis, were eliminated by demanding the cosine of the polar angle of the missing momentum to be between −0.9 and 0.9. We eliminated events with a track of momentum greater than 3.5 GeV/c, or a shower with energy above 3.5 GeV, since these indicate mismeasurement or continuum production.

We suppressed leptons from continuum hadronic processes by using the differences in event shape between these events and B\overline{B} events. Our selection criteria were optimized in a Monte Carlo study of b→uℓν signal events and the continuum background. To simulate the signal we used the models of Isgur et al. (ISGW) [6], Körner and Schuler (KS) [7], and Wirbel, Stech and Bauer (WSB) [8]. These models include a limited set of exclusive final states consisting of single resonances recoiling against a lepton-neutrino pair. Our main continuum-suppression tool was the Fox-Wolfram parameter [9] R_{2} = H_{2}/H_{0}, which discriminates between more spherical B\overline{B} events and more jet-like continuum events. We found the optimal requirement to be R_{2} ≤ 0.2, with a signal efficiency of 44%, and a continuumsuppression factor of 25. The missing momentum, p_{miss}, provided additional discrimination against continuum processes. This quantity should be large for b→uℓν events, in which a neutrino carries off appreciable momentum. By requiring p_{miss} ≥ 1 GeV/c, we reduced the continuum by a factor of 2.3, while losing less than 10% of the efficiency for the b→uℓν decays considered. Since the energetic lepton and neutrino are produced roughly back-to-back, we required the lepton and missing momentum to point into opposite hemispheres. This cut rejected 25% of the remaining continuum with a negligible loss of b→uℓν signal. Overall, relative to the case of no continuum suppression, these criteria (henceforth the “strict cuts”) reduced continuum background by a factor of 70, while providing an efficiency for the b→uℓν Monte Carlo sample of 38%.

There is considerable uncertainty about the detailed properties of B-meson decays mediated by b→uℓν. In the exclusive models most of the leptons above 2.3 GeV/c are produced in decays with final states ρℓν and ωℓν (∼ 70% for ISGW). These models also predict that most decays will have large values of q^{2} = (p_{l} + p_{ν})^{2}, which measures the mass squared of the virtual W. In contrast, both the inclusive model of Altarelli et al. (ACCMM) [10], and the hybrid approach suggested by Ramirez et al. (RDB) [11], yield more events at low q^{2} than the exclusive models, which ignore nonresonant multipion final states. Since the efficiency of stringent continuum-suppression cuts depends on q^{2}, we must assess possible model dependence in our selection efficiency. To do this we have also analyzed our data with a cut of R_{2} < 0.3 and no requirements on either the magnitude or direction of the missing momentum. This cut suppressed the continuum by a factor of 7, while giving an efficiency of 72% for the exclusive b→uℓν Monte Carlo sample described above.

Figure 1 shows the momentum spectra for the ON and scaled OFF samples. Both continuum-suppression procedures give clear signals for lepton production beyond the b→cℓν end point. We estimated the remaining continuum background by fitting the OFF spectra to smooth functions. Good fits were obtained for a variety of functions and fit intervals. The fit results were consistent with directly measured yields. The systematic uncertainty in the continuum subtraction was estimated from the spread among the results of these fits.

The yields of lepton candidates in the 2.4−2.6 GeV/c momentum range are summarized in Table I. Background from misidentified hadrons (fakes) was estimated by multiplying the observed numbers of hadron tracks by the misidentification probabilities. High-momentum leptons from B→J/ψX were suppressed by excluding any lepton which was accompanied by an oppositely charged track with which it formed a mass within 60 MeV of the J/ψ. We used Monte Carlo, normalized by our observed J/ψ yield, to estimate both the leakage through the J/ψ veto and the contribution of B→ψ′X.

We calculated the contribution of b→cℓν decays by fitting the spectra below the endpoint region to models of b→cℓν [6,8]. Theoretical spectra were corrected for QED effects [12], boosted into the lab using B-momentum measurements from fully reconstructed decays, and smeared to account for the detector momentum resolution. We fitted our electron and muon spectra to the theoretical predictions over the momentum intervals 1.6−2.2 and 1.9−2.2 GeV/c, respectively. The small contribution of b→uℓν was ignored. From the fit results we determined the b→cℓν contributions to the signal bins, with systematic uncertainties reflecting differences among the models considered, as well as reasonable variations in radiative corrections, boost, and momentum resolution. We have considered several other sources of leptons from B decays, including B→D→ℓ and leptonic decays of vector mesons. These processes make a very small contribution to the observed yields of high-momentum leptons, and have been included with the b→cℓν entries.

In the momentum range 2.4 − 2.6 GeV/c the strict-cut analysis yields an excess of 43.0 ± 10.2±6.7 leptons which we attribute to b→uℓν. For the R_{2} < 0.3 analysis, the b→uℓν signal is 128.4±26.3±15.3 leptons. This is a model-independent demonstration of b→uℓν, since the contribution of b→cℓν above 2.4 GeV/c is extremely small. We have also measured the lepton yield between 2.3 and 2.4 GeV/c to increase our efficiency in measuring |V_{ub}|. While this bin has appreciable b→cℓν background, the procedure described above allows this background to be calculated reliably. The observed lepton totals and background estimates are given in Table II. For our strict cuts, the total yield due to b→uℓν in the 2.3 − 2.6 GeV/c range is 107 ± 15 ± 11 leptons.

Several models were used to extract |V_{ub}/V_{cb}| from the b→uℓν signal (Table III). In addition to the exclusive models, we used an inclusive calculation based on ACCMM and a simple fragmentation model [13]. We determined efficiencies for detecting b→uℓν with fully simulated Monte Carlo samples for each model. Sources of systematic uncertainty in the efficiencies include track finding (5%), lepton detection (5%), and the continuum-suppression procedures (5% for the strict cuts and 2.5% for R_{2} < 0.3). Averaging over electrons and muons, we determined ΔB_{ub}(p), the partial branching ratio for b→uℓν decays in the specific momentum interval. This was used to calculate |V_{ub}/V_{cb}|^{2} by

|\frac{V_{ub}}{V_{cb}} |^{2} = \frac{ΔB_{ub}(p)}{d(p)B_{cb}},

where B_{cb} is the b→cℓν branching ratio (10.8±0.6% [14]), and d(p) is a theoretical parameter [15].

Table III shows reasonable consistency between the results for the 2.3 − 2.4 and 2.4 − 2.6 GeV/c momentum bins. The small differences between strict-cut and R_{2} < 0.3 results are consistent with being statistical fluctuations, but could also hint at inadequacies in the theoretical models. The relative consistency of the two continuum-suppression procedures demonstrates that our strict-cut analysis does not introduce severe model dependence into the determination of |V_{ub}/V_{cb}|. A much more significant source of uncertainty is the modelto-model variation of d(p), reflecting inconsistent predictions for the b→uℓν decay rate and spectral shape.

The final results of our strict-cut analysis for the full 2.3−2.6 GeV/c momentum range are summarized in Table IV. For the ACCMM model, we find ΔB_{ub}(p) = (154±22±20)×10^{−6}, and |V_{ub}/V_{cb}| = 0.076±0.008. The exclusive models give |V_{ub}/V_{cb}| = 0.06−0.10. The limited set of final states included in the exclusive models raises concerns about their appropriateness for extracting |V_{ub}/V_{cb}|. The inclusive approach provides an average over all b→uℓν decays, but does not explicitly include the single-meson final states which must contribute in the endpoint region. Reference [11] proposed a hybrid model using exclusive techniques when the hadronic recoil energy is small, and an inclusive description when the recoil energy is large. We constructed such a hybrid from our ISGW and ACCMM Monte Carlo samples. There is some sensitivity to the choice of parameters, and we found values of |V_{ub}/V_{cb}| between 0.065 and 0.075. Because most of the model dependence is in the quantity d(p), one can use our measurements of ΔB_{ub}(p) to estimate |V_{ub}/V_{cb}| with models besides those discussed here. Ball et al. have used QCD sum rules and our results to obtain |V_{ub}/V_{cb}| ≈ 0.08 [16].

Our measurements of |V_{ub}/V_{cb}| are consistent with upper limits from an exclusive search for b→uℓν [4]. The new |V_{ub}/V_{cb}| values are considerably smaller than those of previous inclusive studies. Using the ISGW model, CLEO [1] reported |V_{ub}/V_{cb}|^{2} measurements of (3.6 ± 1.0) × 10^{−2} and (2.2 ± 0.6) × 10^{−2}, for the momentum intervals 2.4 − 2.6 and 2.2 − 2.6 GeV/c, respectively. Correcting these measurements to use the B_{cb} value of Ref. [14], we find that our new results differ by 1.5 to 2.5 standard deviations. While comparisons with ARGUS [2] are more difficult, we estimate that our results are smaller by approximately 2.5 standard deviations.

In conclusion, we have confirmed charmless semileptonic decays of B mesons. The values of |V_{ub}/V_{cb}| which we find are smaller than those obtained in previous inclusive studies. Extraction of |V_{ub}/V_{cb}| continues to be limited by theoretical uncertainties. As the CLEO-II data sample grows, more detailed studies of the b→uℓν signal events should allow some discrimination among the theoretical alternatives.

We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. This work was supported by the National Science Foundation, the U.S. Dept. of Energy, the Heisenberg Foundation, the SSC Fellowship program of TNRLC, and the A.P. Sloan Foundation.

REFERENCES

[1] R. Fulton et al., Phys. Rev. Lett. 64, 16 (1990).

[2] H. Albrecht et al., Phys. Lett. B234, 409 (1990); H. Albrecht et al., Phys. Lett. B255, 297 (1991).

[3] M. Paulini, Proceedings of the Joint International Symposium & Europhysics Conference on High Energy Physics, edited by S. Hegarty, K. Potter, and E. Quercigh, World Scientific, Singapore (1992).

[4] A. Bean et al., Phys. Rev. Lett. 70, 18 (1993).

[5] Y. Kubota et al., Nucl. Instrum. Methods A320, 66 (1992).

[6] N. Isgur et al., Phys. Rev. D39, 799 (1989).

[7] J. Körner and G. Schuler, Zeit. Phys. C38, 511 (1988); ibid. C41, 690 (1988).

[8] M. Wirbel et al., Zeit. Phys. C29, 637 (1985).

[9] G. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978).

[10] G. Altarelli et al., Nucl. Phys. B208, 365 (1982).

[11] C. Ramirez et al., Phys. Rev. D41, 1496 (1990).

[12] D. Atwood and W. Marciano, Phys. Rev. D41, 1736 (1990).

[13] M. Artuso, Phys. Lett. B311, 307 (1993).

[14] S. Henderson et al., Phys. Rev. D45, 2212 (1992).

[15] For any model, Γ(b → uℓν) = |V_{ub}|^{2}γ_{u} and Γ(b → cℓν) = |V_{cb}|^{2}γ_{c}, where Γ is the total width for the given semileptonic decay. If f_{u}(p) is the fraction of the b→uℓν momentum spectrum in the specified momentum interval, then d(p) = f_{u}(p)γ_{u}/γ_{c}.

[16] P. Ball et al., Heidelberg reports HD-THEP-92-35 and HD-THEP-92-35A (to be published).

FIGURES

FIG. 1. Lepton momentum spectra after the (a) strict and (b) R_{2} < 0.3 continuum-suppression criteria have been applied. The filled points are the ON data, and the open points are scaled OFF. The dashed curves are fits to the OFF data. The solid curves show the predicted b→cℓν contribution added to the fits to the OFF data.

TABLES

TABLE I. Lepton yields and backgrounds in the momentum interval 2.4 to 2.6 GeV/c.

Strict Cuts  R_{2} < 0.3
N_{ON}  80  463
N_{OFF}(Direct)  16  161
N_{OFF}(Fit)  14.8 ± 2.2 ± 3.0  143.9 ± 6.8 ± 6.8
Excess  47.4 ± 10.2 ± 6.6  146.4 ± 26.2 ± 15.0
Fakes  1.7 ± 0.7 ± 0.5  3.7 ± 2.1 ± 0.9
J/ψ, ψ′  1.4 ±  0.4  8.1 ±  1.8
b→cℓν  1.3 ±  0.6  6.2 ±  2.0
b→uℓν  43.0 ± 10.2 ± 6.7  128.4 ± 26.3 ± 15.3

TABLE II. Lepton yields and backgrounds in the momentum interval 2.3 to 2.4 GeV/c.

Strict Cuts  R_{2} < 0.3
N_{ON}  122  474
N_{OFF}(Direct)  7  114
N_{OFF}(Fit)  10.1 ± 1.2 ± 1.4  107.1 ± 4.0 ± 4.2
Excess  99.8 ± 11.4 ± 3.1  238.4 ± 23.5 ± 9.2
Fakes  5.2 ± 0.6 ± 1.8  22.7 ± 1.6 ± 8.0
J/ψ, ψ′  2.2 ±  0.5  11.7 ±  2.3
b→cℓν  28.1 ±  2.5  105.9 ±  8.3
b→uℓν  64.3 ± 11.4 ± 4.4  98.1 ± 23.6 ± 14.9

TABLE III. Calculated values of d(p) for various theoretical models and the corresponding efficiencies, partial branching fractions, and values of |V_{ub}/V_{cb}|^{2}.

p = 2.4−2.6 GeV/c Strict Cuts R_{2} < 0.3
Model  d(p) Efficiency 10^{6}ΔB_{ub}(p) 10^{2}|V_{ub}/V_{cb}|^{2} Efficiency 10^{6}ΔB_{ub}(p) 10^{2}|V_{ub}/V_{cb}|^{2}
ISGW  0.05 0.21±0.02 53±12±9 0.94±0.28 0.41±0.03 82±17±11 1.46±0.37
KS  0.19 0.22±0.02 51±12±9 0.25±0.07 0.43±0.03 78±16±11 0.39±0.10
WSB  0.11 0.20±0.02 56±13±10 0.47±0.14 0.40±0.03 83±17±12 0.69±0.18
ACCMM 0.12 0.16±0.01 70±16±12 0.53±0.16 0.37±0.03 89±18±12 0.68±0.17
p = 2.3−2.4 GeV/c Strict Cuts R_{2} < 0.3
Model  d(p) Efficiency 10^{6}ΔB_{ub}(p) 10^{2}|V_{ub}/V_{cb}|^{2} Efficiency 10^{6}ΔB_{ub}(p) 10^{2}|V_{ub}/V_{cb}|^{2}
ISGW  0.06 0.25±0.02 67±12±7 1.07±0.23 0.44±0.04 57±14±10 0.90±0.27
KS  0.16 0.27±0.03 62±11±7 0.37±0.08 0.44±0.04 57±14±10 0.34±0.10
WSB  0.10 0.26±0.03 64±11±7 0.58±0.13 0.44±0.04 57±14±10 0.51±0.15
ACCMM 0.13 0.20±0.02 82±15±9 0.60±0.13 0.42±0.03 59±15±10 0.43±0.13

TABLE IV. Partial branching fractions and corresponding values of |V_{ub}/V_{cb}|^{2} and |V_{ub}/V_{cb}| for the strict-cut analysis in the momentum interval 2.3 to 2.6 GeV/c.

Model  10^{6}ΔB_{ub}(p)  10^{2}|V_{ub}/V_{cb}|^{2}  |V_{ub}/V_{cb}|
ISGW  121 ± 17 ± 15  1.02 ± 0.20  0.101 ± 0.010
KS  115 ± 16 ± 15  0.31 ± 0.06  0.056 ± 0.006
WSB  122 ± 17 ± 16  0.53 ± 0.11  0.073 ± 0.007
ACCMM  154 ± 22 ± 20  0.57 ± 0.11  0.076 ± 0.008