CLNS 95/1347 CLEO 95-11

Measurements of the decays τ^{−} → h^{−}h^{+}h^{−}ν_{τ} and τ^{−} → h^{−}h^{+}h^{−}π^{0}ν_{τ}

R. Balest,^{1} K. Cho,^{1} W.T. Ford,^{1} M. Lohner,^{1} H. Park,^{1} P. Rankin,^{1} J.G. Smith,^{1} J.P. Alexander,^{2} C. Bebek,^{2} B.E. Berger,^{2} K. Berkelman,^{2} K. Bloom,^{2} T.E. Browder,^{2}^{∗} D.G. Cassel,^{2} H.A. Cho,^{2} D.M. Coffman,^{2} D.S. Crowcroft,^{2} M. Dickson,^{2} P.S. Drell,^{2} D.J. Dumas,^{2} R. Ehrlich,^{2} R. Elia,^{2} P. Gaidarev,^{2} M. Garcia-Sciveres,^{2} B. Gittelman,^{2} S.W. Gray,^{2} D.L. Hartill,^{2} B.K. Heltsley,^{2} S. Henderson,^{2} C.D. Jones,^{2} S.L. Jones,^{2}

J. Kandaswamy,^{2} N. Katayama,^{2} P.C. Kim,^{2} D.L. Kreinick,^{2} T. Lee,^{2} Y. Liu,^{2} G.S. Ludwig,^{2} J. Masui,^{2} J. Mevissen,^{2} N.B. Mistry,^{2} C.R. Ng,^{2} E. Nordberg,^{2}

J.R. Patterson,^{2} D. Peterson,^{2} D. Riley,^{2} A. Soffer,^{2} P. Avery,^{3} A. Freyberger,^{3} K. Lingel,^{3} C. Prescott,^{3} J. Rodriguez,^{3} S. Yang,^{3} J. Yelton,^{3} G. Brandenburg,^{4} D. Cinabro,^{4} T. Liu,^{4}

M. Saulnier,^{4} R. Wilson,^{4} H. Yamamoto,^{4} T. Bergfeld,^{5} B.I. Eisenstein,^{5} J. Ernst,^{5} G.E. Gladding,^{5} G.D. Gollin,^{5} M. Palmer,^{5} M. Selen,^{5} J.J. Thaler,^{5} K.W. Edwards,^{6} K.W. McLean,^{6} M. Ogg,^{6} A. Bellerive,^{7} D.I. Britton,^{7} E.R.F. Hyatt,^{7} R. Janicek,^{7} D.B. MacFarlane,^{7} P.M. Patel,^{7} B. Spaan,^{7} A.J. Sadoff,^{8} R. Ammar,^{9} P. Baringer,^{9} A. Bean,^{9} D. Besson,^{9} D. Coppage,^{9} N. Copty,^{9} R. Davis,^{9} N. Hancock,^{9} S. Kotov,^{9} I. Kravchenko,^{9} N. Kwak,^{9} Y. Kubota,^{10} M. Lattery,^{10} M. Momayezi,^{10} J.K. Nelson,^{10} S. Patton,^{10} R. Poling,^{10} V. Savinov,^{10} S. Schrenk,^{10} R. Wang,^{10} M.S. Alam,^{11} I.J. Kim,^{11}

Z. Ling,^{11} A.H. Mahmood,^{11} J.J. O’Neill,^{11} H. Severini,^{11} C.R. Sun,^{11} F. Wappler,^{11} G. Crawford,^{12} R. Fulton,^{12} D. Fujino,^{12} K.K. Gan,^{12} K. Honscheid,^{12} H. Kagan,^{12} R. Kass,^{12} J. Lee,^{12} M. Sung,^{12} C. White,^{12} A. Wolf,^{12} M.M. Zoeller,^{12} X. Fu,^{13}

B. Nemati,^{13} W.R. Ross,^{13} P. Skubic,^{13} M. Wood,^{13} M. Bishai,^{14} J. Fast,^{14} E. Gerndt,^{14} J.W. Hinson,^{14} T. Miao,^{14} D.H. Miller,^{14} M. Modesitt,^{14} E.I. Shibata,^{14} I.P.J. Shipsey,^{14} P.N. Wang,^{14} L. Gibbons,^{15} S.D. Johnson,^{15} Y. Kwon,^{15} S. Roberts,^{15} E.H. Thorndike,^{15} T.E. Coan,^{16} J. Dominick,^{16} V. Fadeyev,^{16} I. Korolkov,^{16} M. Lambrecht,^{16} S. Sanghera,^{16} V. Shelkov,^{16} T. Skwarnicki,^{16} R. Stroynowski,^{16} I. Volobouev,^{16} G. Wei,^{16} M. Artuso,^{17} M. Gao,^{17} M. Goldberg,^{17} D. He,^{17} N. Horwitz,^{17} S. Kopp,^{17} G.C. Moneti,^{17} R. Mountain,^{17} F. Muheim,^{17} Y. Mukhin,^{17} S. Playfer,^{17} S. Stone,^{17} X. Xing,^{17} J. Bartelt,^{18} S.E. Csorna,^{18}

V. Jain,^{18} S. Marka,^{18} D. Gibaut,^{19} K. Kinoshita,^{19} P. Pomianowski,^{19} B. Barish,^{20} M. Chadha,^{20} S. Chan,^{20} D.F. Cowen,^{20} G. Eigen,^{20} J.S. Miller,^{20} C. O’Grady,^{20}

J. Urheim,^{20} A.J. Weinstein,^{20} F. Würthwein,^{20} D.M. Asner,^{21} M. Athanas,^{21} D.W. Bliss,^{21} W.S. Brower,^{21} G. Masek,^{21} H.P. Paar,^{21} J. Gronberg,^{22} C.M. Korte,^{22} R. Kutschke,^{22} S. Menary,^{22} R.J. Morrison,^{22} S. Nakanishi,^{22} H.N. Nelson,^{22} T.K. Nelson,^{22} C. Qiao,^{22}

J.D. Richman,^{22} D. Roberts,^{22} A. Ryd,^{22} H. Tajima,^{22} and M.S. Witherell^{22}

(CLEO Collaboration)

1University of Colorado, Boulder, Colorado 80309-0390 2Cornell University, Ithaca, New York 14853 3University of Florida, Gainesville, Florida 32611 4Harvard University, Cambridge, Massachusetts 02138 5University of Illinois, Champaign-Urbana, Illinois, 61801

6Carleton University, Ottawa, Ontario K1S 5B6 and the Institute of Particle Physics, Canada 7McGill University, Montréal, Québec H3A 2T8 and the Institute of Particle Physics, Canada

8Ithaca College, Ithaca, New York 14850 9University of Kansas, Lawrence, Kansas 66045 10University of Minnesota, Minneapolis, Minnesota 55455 11State University of New York at Albany, Albany, New York 12222 12Ohio State University, Columbus, Ohio, 43210 13University of Oklahoma, Norman, Oklahoma 73019 14Purdue University, West Lafayette, Indiana 47907 15University of Rochester, Rochester, New York 14627 16Southern Methodist University, Dallas, Texas 75275 17Syracuse University, Syracuse, New York 13244 18Vanderbilt University, Nashville, Tennessee 37235

19Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 20California Institute of Technology, Pasadena, California 91125 21University of California, San Diego, La Jolla, California 92093 22University of California, Santa Barbara, California 93106

(October 3, 1995)

Abstract

We use a data sample of 2.8 million produced τ-pair events, obtained with the CLEO II detector, to measure B(τ^{−} → h^{−}h^{+}h^{−}(π^{0})ν_{τ}), where h refers to either a charged π or K. These branching fractions are measured with samples of lepton-tagged and 3 vs. 3 events. We find B(τ^{−} → h^{−}h^{+}h^{−}ν_{τ}) = 0.0951±0.0007±0.0020 and B(τ^{−} → h^{−}h^{+}h^{−}π^{0}ν_{τ}) = 0.0423±0.0006±0.0022. We also measure B(τ^{−} → ωh^{−}ν_{τ}) = 0.0195 ± 0.0007 ± 0.0011.

PACS numbers: 13.35.Dx, 14.60.Fg

Typeset using REVTEX

∗Permanent address: University of Hawaii at Manoa

During the past few years, a consistent picture of tau decays has emerged, particularly for decays to a single charged particle; however, discrepancies remain among measurements with three charged particles in the final state. In particular, there is a large variation among previous measurements of B(τ → 3h^{±}ν_{τ}), where h refers to either a π or K; results range from 0.06 to 0.10, with uncertainties less than 0.01 [1]. This decay is dominated by τ → 3π^{±}ν_{τ}, proceeding predominantly through the a_{1} resonance [1]. The branching fraction of the charged a_{1} is constrained by isospin to be the same (except for small phase-space corrections) for the 3π^{±} and π^{±}2π^{0} decay modes. A precise test of the equivalence of these two modes tests these expectations.

Though previous measurements of B(τ → 3h^{±}π^{0}ν_{τ}) have been in reasonable agreement, they are not very precise. Most of these used photon counting rather than π^{0} reconstruction and thus are more sensitive to unexpected feed-across backgrounds, such as the recently measured τ → 3h2π^{0}ν_{τ} decay mode [2]. Since the τ → 3hπ^{0}ν_{τ} mode proceeds through the vector current, e^{+}e^{−} → 4π data and the conserved-vector-current (CVC) hypothesis have been used to predict a branching fraction for this decay [3] [4]. The fraction of the 4π state which proceeds through ωπ also has been predicted with CVC [4].

We employ two methods to measure the branching fractions B(τ → 3h^{±}ν_{τ}) and B(τ → 3h^{±}π^{0}ν_{τ}), using tau pairs produced in the reaction e^{+}e^{−} → τ^{+}τ^{−}. In the first method, we select a sample, denoted ℓ-3h (ℓ-3hπ^{0}), in which one τ is required to decay via τ → ℓνν̄ and the other via τ → 3h^{±}ν_{τ} (τ → 3h^{±}π^{0}ν_{τ}). This method has the advantage that the background from qq̄ events (e^{+}e^{−} → qq̄, q = udsc) is quite low. In the second approach, we select events in which both τ’s decay to three charged tracks, with the samples denoted 3h-3h and 3h-3hπ^{0}. The method for the 3h-3h analysis has not been used previously and is possible only with a very large data sample. There are two main advantages: many systematic errors are reduced by a factor of two since one measures the square of the branching fraction; and the technique is independent of direct knowledge of any other τ decay modes. We measure B(τ → 3h^{±}π^{0}ν_{τ}) with the 3h-3hπ^{0} sample, since the sample with π^{0}’s in both hemispheres is small.

The data used in this analysis have been collected with the CLEO II detector [5], operating at a center-of-mass energy, E_{cm}≈10.6 GeV at the e^{+}e^{−} Cornell Electron Storage Ring. The total integrated luminosity of the sample is 3.0 fb^{−1}, corresponding to 2.8×10^{6} τ-pairs. CLEO II is a general purpose spectrometer. Showers are reconstructed from energy deposited in a 7800-crystal CsI(Tl) calorimeter, and charged particles are measured with three cylindrical drift chambers inside a 1.5-T superconducting solenoidal magnet. Electrons are identified from specific-ionization (dE/dx) information from the main drift chamber and energy deposited in the calorimeter. Muons are identified with proportional-tube muon chambers embedded in the magnet return iron.

Events are selected for the ℓ-3h (3h-3h) analysis by requiring four (six) charged tracks. The event is divided into hemispheres by the charged-particle thrust axis; leptons are required to be at least 90^{∘} from each of the 3-prong tracks. The net charge in each hemisphere is required to be ±1 and the total charge of the event must be zero. For each track, we require the polar angle θ to lie in the central region of the detector, | cos θ| < 0.81, and the momentum to be greater than 0.05E_{b}, where E_{b} is the beam energy. To suppress secondary decays such as K_{S} → ππ, we veto events if there are any tracks which miss the interaction point by more than 15 mm in the plane normal to the beams. We reject events if an identified electron, when paired with another track, is consistent with arising from a photon conversion.

We suppress qq̄ background and feed-across from other τ decay modes by vetoing events with calorimeter showers which have energy greater than 100 MeV, are more than 30 cm from the nearest hadronic charged track and have a lateral profile consistent with that of photons. Events containing showers with energy greater than 800 MeV are rejected regardless of the shower location and shape. For the ℓ-3h (3h-3h) analysis, background from qq̄ events is reduced further by requiring 3π invariant masses to be less than 1.777 (1.50) GeV. We remove contamination to the ℓ-3h sample from radiative μ-pair and Bhabha events with a photon conversion by vetoing events for which the scalar sum of the momenta of the three hadron tracks exceeds 0.95E_{b}. To reject 2-photon background, we require that the polar angle of the missing momentum satisfy | cos θ_{miss}| < 0.90(0.98) for the ℓ-3h (3h-3h) sample, and for the 3h-3h analysis we require the scalar sum of the momenta of the six tracks to be at least 0.45E_{cm}.

The requirements for the 3hπ^{0} analyses are the same except: we omit the last three mentioned above, since QED backgrounds are insignificant; for the 3h-3hπ^{0} analysis we make a 3π (4π) mass cut of 1.5 (1.7) GeV; the energetic-shower veto is applied only after forming π^{0} candidates. These π^{0} candidates are formed from the two most energetic photons with energy greater than 50 MeV and | cos θ| < 0.71. In Fig. 1 we show the normalized deviation from the π^{0} mass for π^{0} candidates from the ℓ-3hπ^{0} analysis. This quantity, in contrast with m_{γγ} itself, is independent of the energy of the photons. We select π^{0}’s and statistically remove fake π^{0}’s by using the signal and sideband regions indicated in the figure.

FIG. 1. Normalized mass of π^{0} candidates for the ℓ-3hπ^{0} analysis. Points are data and histogram is MC. Signal and sideband regions are indicated by arrows.

Tagging leptons must satisfy: | cos θ| < 0.71, p_{e} > 0.10E_{b} and p_{μ} > 0.26E_{b}. Muons are required to penetrate at least 3 interaction lengths of iron and electrons to have dE/dx within 2σ of the expected value and E_{sh}/p > 0.85, where E_{sh} is the energy of the calorimeter shower matched to the track. The lepton-identification efficiency is measured with radiative Bhabha and μ-pair events. The hadron-misidentification probabilities are measured with independent τ data samples. Based on this, we determine that the final 3h (3hπ^{0}) sample contains 0.35 ± 0.03% (0.44 ± 0.06%) fake tag electrons and 4.5 ± 0.1% (4.4 ± 0.3%) fake muons.

To determine the efficiencies of the analyses and to estimate the amount of τ feed-across and non-τ backgrounds, we have generated samples of τ-pair, qq̄, and Υ(4S) using Monte Carlo (MC) techniques. For τ-pairs we use the KORALB generator [6], for qq̄ events the Lund generator [7], and for Υ(4S) events the CLEO QQ generator [8], which is appropriate for threshold production. The GEANT code [9] is used to simulate the detector response.

We find agreement between data and MC for all variables which are used in the analyses. The 3π masses for the two analyses are shown in Fig. 2, with MC histograms normalized to the measured branching fractions.

FIG. 2. The mass for 3h candidates, assuming m_{h} = m_{π}, for (a) the ℓ-3h analysis; and (b) the 3h-3h analysis (2 entries/event). We show data (points with error bars), signal plus background MC (solid line) and background MC (dashed line). Arrows indicate the location of cuts.

In Table I we summarize information for each analysis: the number of data events (N_{d}), the fraction of τ (f_{b}^{τ}) and non-τ (f_{b}^{qq̄}) backgrounds and the efficiency (ϵ). Errors in the backgrounds and efficiency include systematic errors as discussed below.

For the 3h-3h (3h-3hπ^{0}) analysis, we estimate the amount of qq̄ background from MC, scaled by 1.2±0.2 (1.1±0.1) to agree with data in regions where qq̄ background dominates. We estimate 2-photon background from distributions sensitive to this background and Υ(4S) background from MC and find that both are negligible. For the lepton-tag analysis, we find that qq̄ backgrounds are small, as is evident from the region above m_{τ} in Fig. 2a, and all other non-tau backgrounds are negligible.

TABLE I. Summary of the numbers of observed events, background fractions and efficiencies.

\begin{matrix}Sample & N_{d} & f_{b}^{τ} (%) & f_{b}^{qq̄} (%) & ϵ(%) \\ e-3h & 18815 & 7.5 ± 0.2 & 0.2 ± 0.2 & 20.0 ± 0.4 \\ μ-3h & 13985 & 12.8 ± 0.2 & 0.3 ± 0.3 & 14.4 ± 0.3 \\ 3h-3h & 4877 & 16.8 ± 1.3 & 6.5 ± 1.3 & 14.8 ± 0.4 \\ e-3hπ^{0} & 3227 & 4.5 ± 0.4 & 0.3 ± 0.3 & 7.9 ± 0.3 \\ μ-3hπ^{0} & 2335 & 10.3 ± 0.4 & 0.7 ± 0.7 & 5.6 ± 0.2 \\ 3h-3hπ^{0} & 1681 & 13.6 ± 0.6 & 12.3 ± 1.4 & 5.4 ± 0.6 \end{matrix}

The largest backgrounds are from feed-across of other τ decays, which we calculate with our measured branching fractions and those from a recent review [11]. Feed-across is dominated by modes with an extra π^{0}: 3hπ^{0} and 3h2π^{0}, depending on analysis and tag method. Uncertainties in f_{b}^{τ} are estimated by comparing MC and data in regions where feed-across background is large. The lepton-fake contributions are included in the feedacross background.

We calculate branching fractions from

B_{3h(π^{0})} = \frac{N_{d}(1 − f_{b}^{qq̄} − f_{b}^{τ})}{2σ_{ττ} L ϵ B_{ℓ}} (ℓ − 3h(π^{0}))
B_{3h}^{2} = \frac{N_{d}(1 − f_{b}^{qq̄} − f_{b}^{τ})}{σ_{ττ} L ϵ} (3h − 3h)
B_{3hπ^{0}} = \frac{N_{d}(1 − f_{b}^{qq̄} − f_{b}^{τ})}{2σ_{ττ} L ϵ B_{3h}} (3h − 3hπ^{0}),

where σ_{ττ} is the radiatively-corrected τ-pair cross section and L the integrated luminosity. We determine σ_{ττ} and L, each with a precision of 1%, by using, respectively, KORALB, and events from the processes e^{+}e^{−} → e^{+}e^{−}, e^{+}e^{−} → γγ and e^{+}e^{−} → μ^{+}μ^{−} [10]. For the leptonic branching fractions, B_{ℓ}, we use world averages from Ref. [12]. Branching fraction results are given in Table II.

TABLE II. Summary of branching fraction measurements.

Sample  B(τ → 3h^{±}ν_{τ})  B(τ → 3h^{±}π^{0}ν_{τ})
e-tag  0.0951 ± 0.0008 ± 0.0029 0.0424 ± 0.0008 ± 0.0021
μ-tag  0.0948 ± 0.0008 ± 0.0031 0.0417 ± 0.0010 ± 0.0021
3-3  0.0952 ± 0.0009 ± 0.0021 0.0439 ± 0.0017 ± 0.0033
Combined 0.0951 ± 0.0007 ± 0.0020 0.0423 ± 0.0006 ± 0.0022

We have considered many contributions to the systematic errors, as summarized in Table III. Uncertainty in the absolute tracking efficiency is estimated by studying a sample of events with a lepton and at least two additional tracks. These are predominantly ℓ-3h(π^{0}) events. We successfully reconstruct the fourth track in 97% of the events, but the reconstruction efficiency is larger in the MC than in the data by 0.4 ± 0.2%. We correct for this difference, though we conservatively assign a systematic error of 0.4%/track, since the origin of the difference is not fully understood. The τ-background systematic error includes uncertainty in the branching fractions of feed-across modes and also the Kππ and KKπ signal since ϵ is ∼15% larger for these modes. Uncertainty in ϵ is determined by varying all selection criteria and adding in quadrature estimates of the individual variations. The uncertainty in π^{0} reconstruction efficiency is found by variation of the π^{0} criteria and includes uncertainty in the probability for photon-conversions.

TABLE III. Fractional systematic errors for the measured B’s (%).

Source  3h  3hπ^{0}
e-tag μ-tag 3-3 e-tag μ-tag 3-3π^{0}
Luminosity  1.0 1.0 0.5 1.0 1.0 1.0
Tau cross section  1.0 1.0 0.5 1.0 1.0 1.0
Tracking efficiency 1.6 1.6 1.2 1.6 1.6 1.2
Non-τ backgrounds 0.6 0.4 0.7 0.4 0.8 2.0
τ backgrounds  0.2 0.2 0.8 0.4 0.4 0.8
Efficiency  2.2 2.2 1.3 3.3 3.3 5.6
MC statistics  0.4 0.5 0.4 1.0 1.2 1.5
Lepton ID 0.2 0.8 - 0.2 0.8 -
Tag B  0.5 0.5 - 0.5 0.5 2.3
π^{0} reconstruction  -  -  - 3.0 3.0 3.0
Total  3.1 3.3 2.2 5.0 5.2 7.1

To determine the combined results, shown in Table II, we form a weighted average, where the weights are calculated from the statistical and systematic errors, taking into account correlations. The correlated systematic errors are typically somewhat larger than the uncorrelated errors. The weights are 0.24 (0.76) for the combined ℓ-3h (3h-3h) measurement and 0.88 (0.12) for the ℓ-3hπ^{0} (3h-3hπ^{0}) analysis.

We also explore the spectral function [13] and the ωπ component of the 3hπ^{0} final state, where interference with the ρππ components is relatively unimportant. In Fig. 3a, we plot the mass of the two π^{+}π^{−}π^{0} combinations for the ℓ-3hπ^{0} sample. The solid curve is a fit to the data with a MC signal shape and a quadratic background function. From the fit result of 2223 ± 74 signal events, we find the fraction of all 3hπ^{0} decays which come from an ωh final state to be 0.412±0.014±0.015. The systematic error comprises 2% from uncertainties in the spectral function and 3% from variations of the fitting method, including uncertainties in the Breit-Wigner shape used in KORALB. Most other systematic errors cancel in this ratio. Using the ℓ-3hπ^{0} result for B(τ → 3h^{±}π^{0}ν_{τ}) from Table II and accounting for B(ω → π^{+}π^{−}π^{0}) [1], we find B(τ → ωhν_{τ}) = 0.0195 ± 0.0007 ± 0.0011. This result is in agreement with, but considerably more precise than, previous measurements [1], and also in agreement with the CVC prediction, 0.0179 ± 0.0014 [4]. In Fig. 3b, for the 3hπ^{0} final state and the ωh component, we show data histograms of the spectral function

v(m) = \frac{m_{τ}^{8}}{12π|V_{ud}|^{2}} \frac{1}{F (m)} \frac{B_{3hπ^{0}}}{B_{e}} \frac{1}{N} \frac{dN}{dm} ,

FIG. 3. (a) Invariant mass of π^{+}π^{−}π^{0} combinations (2 entries/event) with the fit (solid histogram) to a MC ω signal shape and quadratic background function (dashed curve). (b) Calculated spectral function for the 3hπ^{0} final state (open squares) along with the ωπ component (open circles). The corresponding spectral functions derived from low-energy e^{+}e^{−} data are shown with solid and dashed histograms, respectively.

where m is the 4π mass, F (m) = m · (m_{τ}^{2} − m^{2})^{2}(m_{τ}^{2} + 2m^{2}), the quark-mixing matrix element V_{ud} is taken from Ref. [1], and dN/dm is the background- and efficiency-corrected mass distribution for the data. Also shown in this figure are the spectral functions derived from e^{+}e^{−} → 4π data (see Ref. [4]). The agreement between our measurements and this e^{+}e^{−} data is good, as expected from CVC, except above 1.4 GeV for the ωh component. The CVC data in this region are dominated by measurements from the DM2 collaboration [14].

In conclusion, we have measured

B(τ → 3h^{±}ν_{τ}) = 0.0951 ± 0.0007 ± 0.0020
B(τ → 3h^{±}π^{0}ν_{τ}) = 0.0423 ± 0.0006 ± 0.0022.

The measurement for the 3h decay is larger, by 4.0 standard deviations, than that in a recent ARGUS publication [15], but in agreement with recent reports from LEP [16]. Subtracting the Kππ and KKπ modes [11] from this result yields 0.0891 ± 0.0024, in good agreement with the world average for τ → π2π^{0}ν_{τ}, 0.0909 ± 0.0014. Our measurement for the 3hπ^{0} decay is more precise and smaller than previous measurements but in good agreement with the CVC prediction, 0.042 ± 0.003 [4]. Since our data indicate that decays with more than 2π^{0}’s are negligible, we determine the total 3-prong branching fraction to be B_{3} = 0.1422 ± 0.0010 ± 0.0037, by combining these 3h and 3hπ^{0} measurements with the CLEO measurement for the τ → 3h^{±}2π^{0}ν_{τ} decay [2]. All results in this paper exclude contributions from known decay modes involving K^{0} mesons and assume that decays not included in Ref. [11] are negligible. This value of B_{3} is in good agreement with other recent measurements and the world average, B_{3} = 0.1432 ± 0.0027 [1].

We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. We thank K. Hayes and S. Eidelman for many useful discussions. This work was supported by the National Science Foundation, the U.S. Dept. of Energy, the Heisenberg Foundation, the Alexander von Humboldt Stiftung, the Natural Sciences and Engineering Research Council of Canada, and the A.P. Sloan Foundation.

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