CLNS 94/1286 CLEO 94–16 June 23, 1994

Semileptonic Branching Fractions of Charged and Neutral B Mesons

M. Athanas,^{1} W. Brower,^{1} G. Masek,^{1} H.P. Paar,^{1} J. Gronberg,^{2} R. Kutschke,^{2} S. Menary,^{2} R.J. Morrison,^{2} S. Nakanishi,^{2} H.N. Nelson,^{2} T.K. Nelson,^{2} C. Qiao,^{2} J.D. Richman,^{2} A. Ryd,^{2} H. Tajima,^{2} D. Sperka,^{2} M.S. Witherell,^{2} R. Balest,^{3} K. Cho,^{3} W.T. Ford,^{3} D.R. Johnson,^{3} K. Lingel,^{3} M. Lohner,^{3} P. Rankin,^{3} J.G. Smith,^{3} J.P. Alexander,^{4} C. Bebek,^{4} K. Berkelman,^{4} K. Bloom,^{4} T.E. Browder,^{4}^{∗} D.G. Cassel,^{4} H.A. Cho,^{4} D.M. Coffman,^{4} D.S. Crowcroft,^{4} P.S. Drell,^{4} D. Dumas,^{4} R. Ehrlich,^{4} P. Gaidarev,^{4}

M. Garcia-Sciveres,^{4} B. Geiser,^{4} B. Gittelman,^{4} S.W. Gray,^{4} D.L. Hartill,^{4} B.K. Heltsley,^{4}

S. Henderson,^{4} C.D. Jones,^{4} S.L. Jones,^{4} J. Kandaswamy,^{4} N. Katayama,^{4} P.C. Kim,^{4} D.L. Kreinick,^{4} G.S. Ludwig,^{4} J. Masui,^{4} J. Mevissen,^{4} N.B. Mistry,^{4} C.R. Ng,^{4} E. Nordberg,^{4} J.R. Patterson,^{4} D. Peterson,^{4} D. Riley,^{4} S. Salman,^{4} M. Sapper,^{4} F. Würthwein,^{4} P. Avery,^{5} A. Freyberger,^{5} J. Rodriguez,^{5} S. Yang,^{5} J. Yelton,^{5} D. Cinabro,^{6} T. Liu,^{6} M. Saulnier,^{6} R. Wilson,^{6} H. Yamamoto,^{6} T. Bergfeld,^{7} B.I. Eisenstein,^{7} G. Gollin,^{7} B. Ong,^{7} M. Palmer,^{7} M. Selen,^{7} J. J. Thaler,^{7}

K.W. Edwards,^{8} M. Ogg,^{8} A. Bellerive,^{9} D.I. Britton,^{9} E.R.F. Hyatt,^{9} D.B. MacFarlane,^{9} P.M. Patel,^{9} B. Spaan,^{9} A.J. Sadoff,^{10} R. Ammar,^{11} P. Baringer,^{11} A. Bean,^{11} D. Besson,^{11}

D. Coppage,^{11} N. Copty,^{11} R. Davis,^{11} N. Hancock,^{11} M. Kelly,^{11} S. Kotov,^{11} I. Kravchenko,^{11} N. Kwak,^{11} H. Lam,^{11} Y. Kubota,^{12} M. Lattery,^{12} M. Momayezi,^{12}

J.K. Nelson,^{12} S. Patton,^{12} R. Poling,^{12} V. Savinov,^{12} S. Schrenk,^{12} R. Wang,^{12} M.S. Alam,^{13} I.J. Kim,^{13} Z. Ling,^{13} A.H. Mahmood,^{13} J.J. O’Neill,^{13} H. Severini,^{13}

C.R. Sun,^{13} F. Wappler,^{13} G. Crawford,^{14} C. M. Daubenmier,^{14} R. Fulton,^{14} D. Fujino,^{14} K.K. Gan,^{14} K. Honscheid,^{14} H. Kagan,^{14} R. Kass,^{14} J. Lee,^{14} R. Malchow,^{14} Y. Skovpen,^{14}^{†} M. Sung,^{14} C. White,^{14} M.M. Zoeller,^{14} F. Butler,^{15} X. Fu,^{15} B. Nemati,^{15} W.R. Ross,^{15} P. Skubic,^{15} M. Wood,^{15} M. Bishai,^{16} J. Fast,^{16} E. Gerndt,^{16} R.L. McIlwain,^{16} T. Miao,^{16} D.H. Miller,^{16} M. Modesitt,^{16} D. Payne,^{16} E.I. Shibata,^{16} I.P.J. Shipsey,^{16} P.N. Wang,^{16}

M. Battle,^{17} J. Ernst,^{17} L. Gibbons,^{17} Y. Kwon,^{17} S. Roberts,^{17} E.H. Thorndike,^{17} C.H. Wang,^{17} J. Dominick,^{18} M. Lambrecht,^{18} S. Sanghera,^{18} V. Shelkov,^{18} T. Skwarnicki,^{18}

R. Stroynowski,^{18} I. Volobouev,^{18} G. Wei,^{18} P. Zadorozhny,^{18} M. Artuso,^{19} M. Gao,^{19} M. Goldberg,^{19} D. He,^{19} N. Horwitz,^{19} R. Kennett,^{19} R. Mountain,^{19} G.C. Moneti,^{19}

F. Muheim,^{19} Y. Mukhin,^{19} S. Playfer,^{19} Y. Rozen,^{19} S. Stone,^{19} G. Vasseur,^{19} X. Xing,^{19} G. Zhu,^{19} J. Bartelt,^{20} S.E. Csorna,^{20} Z. Egyed,^{20} V. Jain,^{20} D. Gibaut,^{21} K. Kinoshita,^{21}

P. Pomianowski,^{21} B. Barish,^{22} M. Chadha,^{22} S. Chan,^{22} D.F. Cowen,^{22} G. Eigen,^{22} J.S. Miller,^{22} C. O’Grady,^{22} J. Urheim,^{22} and A.J. Weinstein^{22}

(CLEO Collaboration)

1University of California, San Diego, La Jolla, California 92093 2University of California, Santa Barbara, California 93106 3University of Colorado, Boulder, Colorado 80309-0390 4Cornell University, Ithaca, New York 14853 5University of Florida, Gainesville, Florida 32611 6Harvard University, Cambridge, Massachusetts 02138 7University of Illinois, Champaign-Urbana, Illinois, 61801

8Carleton University, Ottawa, Ontario K1S 5B6 and the Institute of Particle Physics, Canada 9McGill University, Montréal, Québec H3A 2T8 and the Institute of Particle Physics, Canada

10Ithaca College, Ithaca, New York 14850 11University of Kansas, Lawrence, Kansas 66045 12University of Minnesota, Minneapolis, Minnesota 55455 13State University of New York at Albany, Albany, New York 12222 14Ohio State University, Columbus, Ohio, 43210 15University of Oklahoma, Norman, Oklahoma 73019 16Purdue University, West Lafayette, Indiana 47907 17University of Rochester, Rochester, New York 14627 18Southern Methodist University, Dallas, Texas 75275 19Syracuse University, Syracuse, New York 13244 20Vanderbilt University, Nashville, Tennessee 37235

21Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 22California Institute of Technology, Pasadena, California 91125

Abstract

An examination of leptons in Υ(4S) events tagged by reconstructed B decays yields semileptonic branching fractions of b_{−} = (10.1 ± 1.8 ± 1.4)% for charged and b_{0} = (10.9 ± 0.7 ± 1.1)% for neutral B mesons. This is the first measurement for charged B. Assuming equality of the charged and neutral semileptonic widths, the ratio b_{−}/b_{0} = 0.93 ± 0.18 ± 0.12 is equivalent to the ratio of lifetimes.

14.40.Nd, 13.20.Jf

Typeset using REVTEX

∗Permanent address: University of Hawaii at Manoa

†Permanent address: INP, Novosibirsk, Russia

Semileptonic B decay proceeds through a coupling of the b-quark to a c- or u-quark and a l^{−}ν̄ pair (via a virtual W^{−}). This is known as a spectator process because the accompanying quark plays no direct role. In the naïve spectator model for hadronic decays, the relationship between semileptonic and hadronic widths, and thus the semileptonic branching fraction, is readily predicted [1]. Unfortunately, this simple picture does not seem to hold; for the past decade, the measured average branching fraction, b̄, of B’s in Υ(4S) events [2–4] has been ∼15% lower than predictions [1].

The hadronic width may be altered by contributions from nonspectator diagrams or by interference among final state quarks in spectator processes. Both mechanisms carry intrinsic dependences on the flavor of the spectator and do not apply to semileptonic decays. They may therefore result in unequal charged and neutral semileptonic branching fractions, b_{−} and b_{0}. The asymmetry is predicted to be less than 10% [1].

Previous measurements in Υ(4S) events carried several uncertainties. If the Υ(4S) decays to final states other than BB̄, there will be an apparent shift in b̄ [5]. Rates of exclusive decay determine (b_{−}f_{+−})/(b_{0}f_{00}), where f_{+−} and f_{00} are the production fractions of neutral and charged BB̄ events [6]. This gives b_{−}/b_{0} if f_{+−}/f_{00} = 1, but the uncertainty on this assumption is a major source of systematic error. These uncertainties are minimized in tagged measurements where the number of B mesons in the event sample is counted directly rather than being inferred from the number of Υ(4S) events. We report here the measurements via tagging of b_{−}, b_{0} and their ratio. This is a first measurement of b_{−}. If there is no asymmetry in semileptonic widths, then the ratio b_{−}/b_{0} is equal to the ratio of lifetimes, which is measured at higher energies [7].

The data were collected with the CLEO II detector [8] at the Cornell Electron Storage Ring (CESR) and consist of integrated luminosities of 1.35 fb^{−1} on the Υ(4S) resonance and 0.64 fb^{−1} taken at a CM energy which is lower by 60 MeV (continuum). All events considered in this report are required to pass our standard hadronic criteria, which require at least 3 well-fitted charged tracks, a measured energy at least 0.15 times the CM energy and an event vertex consistent with the known interaction point.

B decays are reconstructed using three methods, (A) full reconstruction of all decay products, (B) partial reconstruction of semileptonic decay, and (C) partial reconstruction of a hadronic decay. Tag (A) gives the only measurement of b_{−}. All three yield b_{0}, where method (B) dominates statistically. Each analysis is performed both with and without a requirement that events contain a hard lepton consistent with being a primary decay product of the other B. For B^{−}, we need only consider leptons with charge corresponding to B^{+} [9]. For B̄^{0}, since B^{0} mixes with B̄^{0}, we accept leptons of either sign.

In tag (A), we reconstruct hadronic B decays [10] in eight modes: Dπ^{−}, D^{∗}π^{−}, Dρ^{−}, D^{∗}ρ^{−}, Da_{1}^{−}, D^{∗}a_{1}^{−}, ψK and ψK^{∗}, with charm mesons in the channels:

\begin{aligned}D^{∗+} & → & D^{0}π^{+}, D^{+}π^{0} \\ D^{∗0} & → & D^{0}π^{0} \\ D^{0} & → & K^{−}π^{+}, K^{−}π^{+}π^{0}, K^{−}π^{+}π^{+}π^{−}, K_{S}^{0}π^{0}, K_{S}^{0}π^{+}π^{−} \\ D^{+} & → & K^{−}π^{+}π^{+}, K_{S}^{0}π^{+} \\ J/ψ & → & e^{+}e^{−}, μ^{+}μ^{−} \end{aligned}

and light mesons reconstructed in the channels π^{0}→γγ, K_{S}^{0}→π^{+}π^{−}, K^{∗+}→K^{+}π^{0}, K^{∗+}→K_{S}^{0}π^{+}, K^{∗0}→K_{S}^{0}π^{0}, K^{∗0}→K^{+}π^{−}, ρ^{+}→π^{0}π^{+}, ρ^{0}→π^{+}π^{−} and a_{1}^{+}→ρ^{0}π^{+}.

All events must contain at least four well-fitted charged tracks and have a ratio R_{2} of second and zeroth Fox-Wolfram moments [11] less than 0.45. Leptons are required to have momentum 1.4–2.4 GeV, to be within the barrel region of the detector, and to be consistent with originating at the interaction point. Muons must penetrate at least five nuclear absorption lengths in the muon detector. Electron identification utilizes primarily the ratio of calorimetric energy to momentum and specific ionization in the drift chamber. Except in the case of direct slow pions from D^{∗}, both the time-of-flight and dE/dx systems are used for hadron identification. Photons must be detected in regions of good calorimeter resolution and exceed a minimum energy, equal to 30 MeV for most of the detector acceptance. Candidates for π^{0}, K_{S}^{0}, D, D^{∗}, and J/ψ are required to have an invariant mass (for D^{∗} a (D^{∗} − D) mass difference) consistent with the nominal mass [12]. The K^{∗}, ρ and a_{1}^{+} masses are each required to be within one full decay width of the nominal mass.

From the measured components, we obtain a candidate momentum p_{B} = ∑ p_{i} and energy E_{B} = ∑ E_{i}. We calculate δ(ΔE) = (Ebeam − E_{B})/σ(ΔE) = ΔE/σ(ΔE) and the beam-constrained mass M_{B} = [Ebeam^{2} − (∑ p_{i})^{2}]^{1/2}, where Ebeam is the beam energy and σ(ΔE) is calculated from the error matrices of daughter particles. To be considered further a candidate must satisfy |δ(ΔE)| < 7.0, M_{B} > 5.2 GeV. We consider charged and neutral B’s separately, but all modes are otherwise combined. At most one charged and one neutral B candidate per event are allowed; for each, a χ^{2} is constructed based on the agreement of its component π^{0}, K_{S}^{0}, D, D^{∗} and charged hadron candidates to their hypotheses, and the candidate with the highest likelihood is selected.

Due to the spin orientation of the Υ(4S) produced in e^{+}e^{−} annihilation, the angle θ_{B} of the B momentum with the beam axis is distributed as sin^{2} θ_{B}. We require | cos θ_{B}| < 0.95. The “thrust angle” θthr, between the thrust axes of the B candidate and of the remainder of the event, is also examined. The distribution in cos θthr is uniform for B decays and peaks near | cos θthr| = 1 for continuum. We require | cos θthr| < 0.9 (0.8,0.7) for B→Xπ (B→Xρ, B→Xa_{1}) where X is D or D^{∗}.

We define two regions in |δ(ΔE)|, “signal” (|δ(ΔE)| < 2.5) and “sideband” (4.0 < |δ(ΔE)| < 6.5). Looking both at data on the continuum and simulations of BB̄ background, the signal and sideband regions are found to give similar distributions in M_{B}. We require that the difference between M_{B} and the nominal B mass be less than 6 MeV and count candidates, subtracting directly the sideband from the signal sample. We find 834 ± 42 B^{−} and 515 ± 31 B̄^{0} mesons. The same technique is used in events containing an identified lepton. Figure 1 (a) and (b) show the sideband superimposed on the signal for both samples. Details of this analysis are given in ref. [13].

The method (B) of partial B̄^{0}→D^{∗+}ℓ^{−}ν̄ reconstruction, where the decay D^{∗+}→D^{0}π^{+} is identified using only the π^{+}, has been used by CLEO II to measure B̄^{0} mixing [14]. This approach yields a large sample and exploits the extremely low energy of the D^{∗+} decay; the momentum of the π^{+} is scaled to obtain an approximate four-momentum (Ẽ_{D^{∗}}, p̃_{D^{∗}}) for the D^{∗+}. The squared missing mass,

M̃_{ν}^{2} ≡ (Ebeam − Ẽ_{D^{∗}} − E_{ℓ})^{2} − (p̃_{D^{∗}} + p_{ℓ})^{2}

approximates the squared mass of the neutrino.

The pion and lepton momenta p_{π} and p_{ℓ} are required to satisfy p_{π} < 0.19 GeV and 1.8 < p_{ℓ} < 2.4 GeV. Pion candidates are required to have a consistent specific ionization.

Background from charged B’s arising from B^{−} → D^{∗∗0}ℓν (D^{∗∗0} → D^{∗+}π^{−}) is suppressed by demanding a high lepton momentum.

We examine the M̃_{ν}^{2} distribution and select candidates in the signal region (M̃_{ν}^{2} > −2 GeV^{2}). The continuum contribution is estimated using the data collected at energies off resonance, corrected for luminosity and energy differences. Background from BB̄ events is estimated via Monte Carlo. Its shape in M̃_{ν}^{2} is largely defined by the phase space, and the simulation is in agreement with data in the nonsignal regions and for combinations where the lepton and pion carry the same charge. Its normalization is obtained by fitting to data in the sideband region, −20 < M̃_{ν}^{2} < −4 GeV^{2}. We find 7119 ± 139 tags [15]. The same procedure is applied to tagged events with a lepton. We require that the cosine of the angle between the two leptons in these events be less than 0.99, to eliminate multiply reconstructed tracks. The M̃_{ν}^{2} distributions obtained after continuum subtraction are shown in Fig. 1, (c) and (d).

The decay chain B̄^{0}→D^{∗+}π^{−}, D^{∗+}→D^{0}π^{+} produces a hard π^{−} and a soft π^{+}, which are used in method (C) to identify the chain without detecting the D^{0} [3]. Briefly, the energy E_{D} of the D^{0} is obtained by energy conservation. Since the D^{0} and π^{+} must form a D^{∗+}, defining their energies fixes the angle θ between them as well as the decay angle θ^{∗} of the π^{+} in the D^{∗+} rest frame relative to the D^{∗+} direction in the lab. If one then calculates the maximum possible D^{∗+}π^{−} invariant mass M_{B} under these constraints, it must for a signal candidate lie in the narrow region between the actual B mass and the beam energy. Details are given in ref. [16].

Taking events with R_{2} < 0.45, we select pairs of oppositely charged tracks compatible with the tagging mode, i.e., for which values of E_{D} and cos θ are physical. The fast track must have specific ionization consistent with being a pion and not be identified as an electron or muon. Because the D^{∗+} is fully polarized, the π^{+} decay angle is distributed as cos^{2} θ^{∗}, and we require |cos θ^{∗}| > 0.5.

Each event is partitioned approximately into the tag B and the other B by including with the candidate the two particles (charged tracks or isolated neutral clusters) with the largest momentum component opposite the fast pion. The angle θthr is then calculated as in tag (A). We require |cos θthr| < 0.7.

The distribution in M_{B} is fitted to a Gaussian plus background. The signal mean and width are obtained via Monte Carlo simulation. We define a signal region M_{B} > 5.276 GeV and a mass sideband M_{B} < 5.26 GeV. Uncorrelated track pairs from BB̄ events give a flat distribution. Correlated pairs from B→D^{∗∗}π^{−} (D^{∗∗}→D^{∗+}π, D^{∗+}→D^{0}π^{+}) produce a broad peak in the signal region. The fitted background shape is the sum of this shape plus a first order polynomial. We find 822 ± 53 tags. The number of tagged events with an additional lepton is determined by counting candidates in the signal region, subtracting backgrounds from continuum, random BB̄ combinations and B→D^{∗∗}π^{−}. To exclude secondary leptons from the undetected D^{0}, which are nearly opposite to the fast pion, we require the cosine of the angle between the fast pion and lepton to be greater than −0.85.

For all three tag types, additional leptons are selected in the range 1.4 − 2.4 GeV. Background occurs when the reconstructed decay is correct but the lepton is fake (a hadron passing lepton identification) or, for neutral B’s, a secondary from charmed meson decay. Fakes are assessed separately for each type of tag. In each case, events which contain candidates in the signal regions are selected. Excluding those which comprise each candidate, all tracks within the acceptances of lepton identification which fail the identification criteria are considered. These tracks, each weighted by the appropriate fake rate per track, are summed. The contribution from background candidates is estimated using events selected from the various sidebands. The fake rate as a function of momentum is determined using data taken at the Υ(1S), which produces very few leptons. Of all leptons from B decay with momentum above 1.4 GeV, the fraction from secondaries is found to be 0.028 ± 0.008. The fraction among detected leptons is 0.027 ± 0.008(0.022 ± 0.007) for electrons (muons). For tags (B), these factors are twice as large because the undetected D^{0} may also contribute. These corrections are applied to the neutral B tags.

The efficiency for geometric acceptance, track reconstruction and identification is found to be 65.1% (50.7%) for electrons (muons). Requirements on dilepton opening angle and event characteristics result in effective adjustmentments of −1.7%, −1.1% and −12% for (A), (B) and (C), respectively. Dependences of tagging efficiencies on the decay charge multiplicity of the other B in an event result in effective increases of 6% for (A) and 3% for (B) and (C). To extrapolate the spectrum to lower momenta, we use the model of Isgur et al. (ISGW), [17] which predicts that three exclusive modes dominate, B→Dℓν, B→D^{∗}ℓν and B→D^{∗∗}ℓν. Based on our fit to the inclusive lepton spectrum, [4] we take their proportions to be 24.5/54.5/21. For electrons (muons) the fraction of the spectrum above 1.4 GeV is found to be 48.1% (51.4%). Assuming e − μ universality, we average the electron and muon totals. Shown in Table I are the raw numbers of tags with and without leptons, corrections, and branching fractions.

The systematic uncertainties in efficiencies for tracking, lepton identification and lepton spectrum extrapolation are common to all of the analyses and are found to be 2.0%, 2.5% and 8%, respectively. The effect of the lepton spectrum is simulated by varying the percentage of B→D^{∗∗}ℓν from 0% to 30% in the ISGW model. Uncertainties due to fitting methods and functions are determined by varying the techniques and shapes used to fit signals and backgrounds. Selection of events and candidates add uncertainties which are estimated via Monte Carlo. The uncorrelated systematic uncertainties are summarized in Table II.

We average the B̄^{0} measurements, using the quadratic sum of statistical and uncorrelated systematic errors to determine relative weights. The results are

b_{−} = (10.1 ± 1.8 ± 1.4)%,
b_{0} = (10.9 ± 0.7 ± 1.1)%.

Both are consistent with the CLEO II average inclusive branching fraction, (10.9±0.1±0.3)% [4]. The ratio is

\frac{b_{−}}{b_{0}} = 0.93 ± 0.18 ± 0.12.

The error due to uncertainty in f_{+−}/f_{00} is less than 1%. This result is in agreement with our other result and with that of ARGUS [6], which assume that f_{+−}/f_{00} = 1. It is consistent with the world average lifetime ratio of 1.10±0.11 [7] as well as with theoretical expectations, and is of comparable significance to existing individual measurements.

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] I. I. Bigi, et al., CERN Report Number CERN-Th.7132/94, to appear in B Decays, 2nd edition, S. Stone, ed. (World Scientific 1994).

[2] H. Albrecht et al., (ARGUS), Phys. Lett. B 249, 359 (1990).

[3] S. Henderson et al., (CLEO), Phys. Rev. D 45, 2212 (1992).

[4] J. Bartelt et al. (CLEO), “Inclusive Measurement of B Meson Semileptonic Branching Fractions,” CLEO CONF93-19.

[5] A. Khodjamirian, S. Rudaz and M. Voloshin, Phys. Lett. B 242, 489 (1990).

[6] H. Albrecht et al., (ARGUS), Phys. Lett. B 232, 554 (1989); R. Fulton et al., (CLEO), Phys. Rev. D 43, 651 (1991).

[7] W. Venus, in Lepton and Photon Interactions, XVI Int. Symp. P. Drell and D. Rubin, eds. (AIP, New York, 1994).

[8] Y. Kubota et al., (CLEO), Nucl. Instrum. Methods A 320, 66 (1992).

[9] Throughout this paper, mention of a specific particle and decay mode implies also its charge conjugate.

[10] B candidates are selected using the CABS high level programming language, described in: N. Katayama, in Proc. XXVI Int. Conf. on High Energy Physics, Dallas, 1992, J.R. Sanford, ed. (AIP, New York, 1993)

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

[12] Review of Particle Properties, Phys. Rev. 45 S1 (1992).

[13] M.A. Lambrecht, Ph.D. thesis, University of Oklahoma 1993 (unpublished).

[14] J. Bartelt et al., Phys. Rev. Lett. 71, 1680 (1993).

[15] About 5% of tags are found to be identified more than once because the soft pion curls and is multiply reconstructed. We account for this by increasing our statistical error by 2.5%.

[16] R. Giles et al., Phys. Rev. D 30, 2279 (1984).

[17] N. Isgur, D. Scora, B. Grinstein, and M. Wise, Phys. Rev. D 39, 799 (1989).

TABLES

TABLE I. Numbers of tags without (all) and with (e, μ) additional leptons. Tag types are described in the text. Subtraction of estimated fakes (a) and secondaries (b) yields the number of detected primary leptons (c), which is corrected for efficiency to obtain (d). The electron and muon values are averaged to obtain N_{ℓ}, and the branching fraction B.

B^{−} (A)  B̄^{0} (A)  B̄^{0} (B)  B̄^{0} (C)
all  834 ± 42  515 ± 31  7119 ± 139  822 ± 53
e  32.0 ± 6.8  23.0 ± 5.3  271.9 ± 22.1  25.8 ± 6.2
(a)  0.17 ± 0.05  0.13 ± 0.04  1.5 ± 0.4  0.1 ± 0.02
(b)  —  0.7 ± 0.2  14.6 ± 4.3  0.7 ± 0.2
(c)  31.8±6.8  22.3±5.3  255.8 ± 22.5  25.0±6.2
(d)  97.2 ± 20.8  68.0 ± 16.2  826.0 ± 72.7  90.9 ± 22.5
μ  21.0 ± 5.4  21.0 ± 5.4  197.7 ± 20.2  19.6 ± 5.5
(a)  1.1 ± 0.3  0.9 ± 0.3  8.3 ± 2.5  0.5 ± 0.1
(b)  —  0.5±0.2  8.3 ± 2.7  0.4 ± 0.1
(c)  19.9±5.4  19.7±5.4  181.1 ± 20.5  18.7±5.5
(d)  73.0 ± 19.8  72.1 ± 19.9  702.5 ± 79.6  81.7 ± 24.0
N_{ℓ}  84.6 ± 14.3  69.6 ± 12.5  767.5 ± 53.5  86.6 ± 16.3
B  10.1 ± 1.8  13.5 ± 2.6  10.5 ± 0.8  10.2 ± 1.9

TABLE II. Uncorrelated systematic errors, given as percent of signal.

B^{−} (A)  B̄^{0} (A)  B̄^{0} (B)  B̄^{0} (C)
Event selection  1.7  1.7  0.5  4.1
Single tag/event  7.2  5.0  –  –
# tags  4.8  6.5  2.6  4.6
# tags with leptons  3.4  5.1  7.1  5.6
Tagging efficiency  6.0  6.0  3.0  3.0
Secondary leptons  –  0.8  1.6  0.8
Fake leptons  0.1  0.2  0.2  0.2
Total uncorrelated  11.2  11.5  8.3  8.9

FIGURES

FIG. 1. Tag samples, without and with additional lepton required. (a), (b): B^{−}, method (A), M_{B} distributions; (c), (d): B̄^{0}, method (B), M̃_{ν}^{2} distributions.