Improved measurement of the Pseudoscalar Decay Constants fDS from D∗+ γµ+ ν data sample s → Abstract

+ − Determination of fDS using 14 million e e cc¯ events obtained with the CLEO → II and CLEO II.V detector is presented. New measurement of the branching ratio gives Γ (D+ µ+ν)/Γ (D+ φπ+) = 0.137 0.013 0.022. Using Γ (D+ µ+ν) = 0.036 S → S → ± ± S → 0.09, fDS was calculated and found to be (247 12 20 31) MeV. Comparison ± ± ± ± of these results with other theoretical and experimental results are also presented.

1 Introduction

Purely leptonic decay modes of heavy mesons predict their decay constants, which is connected with measured quantities such as CKM matrix elements. Currently it is not possible to measure fB experimentally, but measurements of the Cabibbo-flavor pseudoscalar decay constants such as fDS is possible. This measurement provides a check of these theoretical calculations and helps to establish different theoretical models. + The decay width of Ds is given by [1]

2 2 + + GF 2 2 mℓ 2 Γ(Ds ℓ ν)= fDS mℓ MDS 1 2 Vcs (1) → 6π − MDS ! | | where MDS is the Ds mass, mℓ is the mass of the final state lepton, Vcs is a CKM matrix element equal to 0.974 [2] and GF is the Fermi coupling constant. Various theoretical predictions of fDS range from 190 MeV to 350 MeV. The relative widths of three lepton flavors are 10 : 1 : 10−5 for tau, muon and electron respectively. Helicity suppression reduces smaller width for low mass electron. Largest branching mode τν is very difficult to use for experimental measurement due to more than one missing neutrino in the final state of events. So the only choice is the µν mode.

In previous publications [3, 4] CLEO reported the measurements of fDS = (280 19 ∗+ + + + ± 28 34) MeV, using the decay chain Ds γ Ds , Ds µ ν. Four other groups ± ± → → + + also published their results of fDS on the basis of their observations of Ds µ ν. + → WA75 published fDS = (232 45 20 48) MeV using muons from Ds leptonic ± ± ± +150 decay in emulsion [5], BES published a value of (430 −130 40) MeV, using fully + ± ±+ − reconstructed Ds mesons close to the production threshold in e e collisions [6], E653 measured a value of (194 35 20 14) MeV from one prong decays into muons in ± ± ± an emulsion target [7] and WA92 reported a value (323 44 12 34) MeV from ± ± ± the visible kink Ds to µ [8]. ∗+ + This paper describe an improved CLEO analysis of the decay chain Ds γ Ds , + + + − → Ds µ ν which included 15 million e e c c¯ events collected with the CLEO II → → −1 [9] and CLEO II.V [10] at CESR. The integrated luminosity is 13.7 fb of which 4.8 fb−1 was taken at CLEO II configuration and previous CLEO results based on that subsection of data sample. This analysis includes better neutrino reconstruction algorithms, more data hence improved statistics, and more precise measurement of lepton fake rates which reduces systematic error.

1 There are several sources of background for the D∗+ γµ+ ν process. The main s → physics background comes from semileptonic decay of heavy mesons. Due to lepton universality, contribution of electron and muon samples are nearly the same. Thus applying exactly same selection criteria as for electrons, one can get a qualitative estimation of background level from real leptons. D+ µ+ ν and D+ µ+ ν are the s → → only physics processes which produce significantly more muons than electrons with high momentum lepton in the continuum e+e− annihilation near Υ(4S) region. D+ µ+ ν → is highly suppressed by the CKM parameter (Eq. 1), and by the small branching fraction of D∗0 γ D0, 1.7 0.4 0.3% [11]. → ± ± Another source of background is the misidentification of hadron as a lepton. As CLEO has more fake muons than electrons, their relative contribution is taken care of from total samples. ∗+ + Besides the above two backgrounds, there are backgrounds arising from Ds γ DS , + + → Ds µ ν samples where true photon in decay chain is replaced by another photon → + + of the event and combination of spurious photons with D µ ν event samples. The s → shape of the second component of these backgrounds is determined by using the fully reconstructed D∗+ π+ D0, D0 K− π+ data samples and normalization is deter- → ∗+ + → mined from the ratio of Ds /Ds production ratio.

2 Event Selection

The analysis presented here is based on previous CLEO measurements of fDS [4], i.e. ∗+ + + + ∗+ search for the decay chain Ds γ Ds , Ds µ ν. The photon from Ds and muon + → → + from Ds are directly measured, where as neutrino from Ds are measured indirectly ∗ from missing momenta of the events. Mass difference between reconstructed Ds + and + Ds are looking as a signal of the event,

∆ M = M(γµ+ ν) M(µ+ν) (2) − such that most of the relatively large error of missing momenta is canceled out. Data and MC samples of decay chains, D∗0 γ D0, D0 K− π+ and D∗+ π+ D0, D0 K− π+ → → → → are used to verify this missing momenta calculation and the shape of backgrounds.

2.1 Global event A collection of purely hadronic events is selected for further analysis by requiring at least 5 good tracks in the tracking system or at least 3 tracks with 3 isolated shower in calorimeter (definition of good tracks and isolated showers are given in Appendix A). Each event hemisphere should have more than 2 particles (tracks or shower). Visible energy of the event should be more than half of the center of mass energy (√S) and less than √S. All these criteria are used to eliminate low multiplicity source of leptons i.e. two photon processes and τ + τ − pairs. To reduce the background process where particles escaped in the beam direction, a criteria used such that the missing momentum direction should be away from the beam pipe, cos θmiss < 0.85. | |

2 2.2 Lepton identification Dominant background component of lepton from semileptonic decay mode of heavy flavor mesons is removed using the criteria that the momentum of lepton should be greater than 2.4 GeV, which is 36% efficient for signal events. Muons are required to penetrate at least 7 interaction lengths of material and have to be away from beam pipe, Cos θ < 0.85. Muon efficiency is measured with e+e− µ+µ− γ events and has | | → a flat efficiency at 85.88 0.8 % beyond a momentum of 2.4 GeV [12]. Electrons are ± also confined within Cos θ < 0.85. Energy deposit of electrons in the electromagnetic | | calorimeter should be close to the fitted track momentum, dE/dx measurement of track in the tracking system expected as an electron track and most importantly calorimeter shower profile should be matched with an electromagnetic shower. The electron iden- tification efficiency is calculated by embedding tracks from radiative Bhabha events to hadronic events. For momentum of more than 2.4 GeV, the efficiency is 80 2% [13]. ± 2.3 Photon selection Photons are selected only from showers in the barrel calorimeter with energy greater than 200 MeV (details are given in Appendix A). For D∗+ γ D+ event sample, s → s photon acceptance efficiency including this energy cut is 36%. The shower must be isolated from any charged track by more than 20◦ and have a shower shape for which the probability that the energy deposition is due to a single photon is greater than 99%. Pion veto is used to reject photons from π0 decay, which are a dominant source of electromagnetic showers. Photons combination with invariant masses within 2σ (σ = 5 MeV) of the π0 mass are rejected.

2.4 Missing momenta (ν) calculation Neutrino 4-momenta were calculated by using the near-hermetic property of the CLEO detector. An Event is divided into two hemispheres by bisecting the thrust axis of the event. Loop over all particles (here particles are the ensemble of charged tracks in the tracking system and isolated neutral shower in the calorimeter) in both hemispheres is taken to calculate the 4-momenta separately. Next we take the direction of the 3- momenta of opposite hemispheres (hemisphere opposite to lepton), divide the event into two hemispheres by bisecting that direction and loop over all particles to get a new 4-momenta for the two hemispheres. This iteration is continued until we get two stable hemispheres. Though CLEO is a near hermetic detector, a particle might be undetectable when it passes through a crack or goes in the forward direction. The average loss is calculated from MC signal events. As shown in the figure 1 the visible energy in CLEO is less than the energy of generated stable particles (except ν), similarly reconstructed 3-momenta are different from true 3-momenta. Therefore, the true 4-momenta of each hemisphere are taken as a function of visible 4-momenta. So, the missing energy and momentum are found according to

Emiss = Ebeam f1(Ehem) (3) − ~pmiss = ~popp f2(~phem) (4) − −

3 Figure 1: MC generated 4-momenta in the lepton hemisphere is plotted as a function of visible 4-momenta (a) Energy (b) 3-momenta

where Ebeam is the CESR beam energy, Ehem is the visible energy in lepton hemisphere, direction of ~popp is given by momentum vector of opposite hemisphere and magnitude is 2 2 given by ~popp = Ebeam mjet. mjet is the average mass of charm quark jet, measured − 2 2 to be 3.2 GeV [4].q Events with M < 2 GeV and Cos θmiss < 0.85 are processed miss | | for further analysis using event shape variables. Figure 2 compare the neutrino reconstruction momentum and direction with its MC generated value.

2.5 Event shape variables Various kinematic variables are used mainly to reduce the background from random photons in the events. Definition of those variables and cut values are given in Appendix B. ∆M distribution of events in the MC sample, which pass through all selection criteria, are shown in figure 3. This distribution is fitted with an asymmetric Gaussian (for signal) with σ of 14 MeV in the lower side and σ of 22 MeV in upper side and a half integer polynomial 1 (for background). Figure 4 justifies the choice of one important variable and its cut value. The efficiency of selecting signal events is (2.381 0.038)%. ± 3 Cross-check of neutrino reconstruction

Monte Carlo signal shape (distribution of ∆ M) and efficiency are calculated using missing momentum calculation. There is a doubt that missing momentum calculation

1yα√x x e( (p0 (x x ))) − 0 − − 0

4 Figure 2: Reconstructed neutrino momentum is compared with generator level. (a) Differ- ence in direction, (b) Difference in absolute momentum

∗+ + Figure 3: Mass difference of the reconstructed Ds and Ds . Solid points represent the MC samples, solid line is a fit of signal distribution combined with background component and dotted line is the background distribution

5 ∗+ ∗+ Figure 4: Cosine of the angle between photon in Ds frame and Ds in lab frame is shown as a cut variable which reduces background level in the signal distribution. Left plots show its distribution for Signal MC, data sample with muons and data sample with electrons. Right plots show the its power to reduce the tail of signal distribution

6 in MC might differ in Data samples. To verify that missing momentum calculation in Data and MC work in exactly the same fashion, a collection of Data and MC samples of D∗0 γ D0, D0 K− π+ are used. → → ∗0 0 Figure 5 show the fully reconstructed ∆M = M(γ K π) M(γ K π) of D γ D , 0 − + − → D K π MC event samples. For this distribution, a kaon is required to have → momentum greater than 2.4 GeV and be within Cosθ < 0.85, similar to that used + + − + | | for muon selection in Ds µ ν events. K π invariant mass is also kept within → ∗0 0 ≈ 25 MeV (this window is dependent on D momentum) of D mass. There are clear signals in the ∆M distribution, but having a substantial background. Next we eliminate π+ from the signal events and treat K− as muon to recon- struct π+ momenta from missing momenta calculation as used in D+ µ+ ν signal s → events. Reconstructed ∆M = M(γπpmiss) M(πpmiss) is shown in figure 6 for − ∆M = M(γ K π) M(γ K π) within 10 MeV of its peak value and within mass differ- − ence window(wrt it peak values) from 15 MeV to 25 MeV. Bin-by-bin subtraction ± ± is used to get the signal events. Bin-by-bin subtracted M(γπpmiss) M(πpmiss) is − shown in figure 6, the distribution is fitted with asymmetric Gaussian (signal) with σ of 14 MeV in the lower side and σ of 22 MeV in upper side and half integer polynomial (background). The neutrino reconstructed efficiency is 54.95 0.68. ∗0 0 0 − + ± In a similar way D γ D , D K π data samples are used to reconstruct → → ∆M = M(γπpmiss) M(πpmiss) distribution. Figure 5 shows these distributions − for ∆M = M(γ K π) M(γ K π) peak region and side band region. Bin-by-bin sub- − tracted distributions are again fitted with the same function for signal and background. Neutrino reconstructed efficiency in data is found to be 53.76 0.77. ∗+ ± ∗0 Ds has different fragmentation with an s quark rather than u quark as in D . ∗+ + So, in principle resolution and efficiency for Ds γDs is somewhat different from ∗0 0 ∗0 0 → D γD . But, as MC sample of D γD accurately represents its data sample, → → one can rely on this missing neutrino reconstruction procedure.

4 Background shape for replaced/random pho- ton

Figure 3 shows the ∆M = M(γµ+ ν) M(µ+ ν) distribution from Monte Carlo stud- − ies. This distribution contains an asymmetric Gaussian part for signal and plus a background part which occurs when a true photon is replaced by another random pho- ton of the event. The Gaussian part has σ 14 MeV in the lower side and 22 MeV in the upper side. + + The shape of ∆M distribution for random photons combined with Ds µ ν or + + + → D µν samples are modeled with the MC sample of Ds µ ν. Reconstruction → ∗0 0 0 − + → is done in the same way as D γ D , D K π samples, for the combination → → of M(Kpmiss) with random photons of the events (photon has the same criteria as in D∗+ γµ+ ν signal). D∗+ π+ D0, D0 K− π+ data sample is used to model this s → → → distribution. Distributions of these two samples are consistent with each other. Figure 7 shows the shape of random photon components which is again parametrized with a half integer polynomial function.

7 Figure 5: The ∆M = M(γK−π+) M(K−π+) mass difference distribution for fully re- constructed events of D∗0 γD0,D−0 K−π+ (solid points). Solid line is a fit of signal → → distribution combined with the background component and dot line is the background dis- tribution. (a) D∗0 Monte carlo and (b) data

8 − − Figure 6: The ∆M = M(γK pmiss) M(K pmiss) mass difference distribution for miss- ing momentum analysis using fully reconstructed− events of D∗0 γD0,D0 K−π+ (solid → → points). Solid line is a fit of signal distribution combined with background component and dot line is the background distribution. (a) D∗0 Monte carlo and (b) data

9 Figure 7: Backgrounds shape for the combination of random photon with D+ µ+ ν. s → + + 5 Measurement of the DS∗ ans DS production rate

∗+ + The total background from a random photon is calculated using DS /Ds production ∗+ + ratio. The relative rates of DS and Ds above momentum 3.0 GeV is done with D+ φπ+, φ K+ K− and D∗+ γD+, D+ φπ+, φ K+ K− decay chains. A s → → s → s s → → photon is required to have the same criteria as in µν signals. The detection efficiencies ∗+ + of Ds and Ds in these decay chains are 4.17 0.07% and 14.84 0.13% respectively. ± + ± Figure 8(a,b) shows the mass distribution of φπ for Data and MC samples and (c,d) shows the distribution of ∆ M = M(γφπ+) M(φπ+) with φπ+ mass within + −+ 20 MeV (depends on the momentum of Ds ) of Ds mass. ∼ 2 Fitting the data with modified Gaussian signal shapes, whose width are predeter- mined by MC event sample 1691 41 and 10265 101, event of data samples are found ∗+ + ± ± for Ds and Ds respectively. Taking into account of relative efficiencies, the relative ∗ production ratio of D +and D+ is 1.31 (0.017). S s ± 6 Lepton fake background calculation

Strict criteria are used to get high purity electron/muon samples with momentum greater than 2.4 GeV. Even after strict lepton criteria, a significant number of hadrons show up as fake leptons because of the abundance of fast hadron tracks in CLEO data. Muon fake rate is more than electron fake rate. A precise measurement of excess of muon to electron fake rate is needed to correct the hadronic background

2 p5 2y = e−0.5((x−p0)/p2) for x p0 0 and y = e−0.5((x−p0)/p4) for x p0 0 − ≥ − ≤

10 Figure 8: The φπ+ mass distribution for data (a) and for MC (b) and the mass difference ∆M = M(γφπ+) M(φπ+) for data (c) and MC (d) are shown with the requirement that + − + + M(φπ ) is close to Ds mass. φπ distributions are fitted with Gaussian signal and 1st order polynomial. ∆M distributions are fitted with a modified Gaussian signal and 1st order polynomial. Solid dots represent data, solid lines are Fitting curve (combination of signal and background) and dotted lines are background.

11 level. The D∗ decay chains provide well tagged kaon and pion samples. In this anal- ysis, D∗+ π+D0, where D0 has three different decay modes K−π+, K−π+π0 and − + − →+ K π π π are used to collect a good sample of well tagged kaon and pion events ∗0 0 0 0 − + + − with D π D , D K π and KS π π event samples. Figure 9(a) shows a − + →+ − →+ → − + 0 M(K π π ) M(K π ) distribution after a cut on K π invariant mass close to D − + + mass where a kaon (or pion) has all leptonic kinematic criteria as in the D µ ν s → sample, except for a lepton tag. Figure 9(b) shows a subsample, where kaon (or pion) satisfies the lepton tag criteria. All the distributions are fitted with asymmetric Gaus- sian for the signal and half integer polynomial for background. Signal and background shapes are derived from all samples without any lepton identification criteria. In a similar way, the fake rates are calculated from all other four channels. Fake rates cal- culated from different channels are summarized in table 1 and the weighted average fake rates are also shown there which are used for fake rate calculation.

Data samples # of Fake rates(%) π K π/e π/µ K/e K/µ π+π− 120706 0.13 0.01 0.43 0.02 - - k−π+π− 16704 22917 0.05±0.02 0.51±0.06 0.06 0.02 1.09 0.07 − + 0 ± ± ± ± k π π 6113 8254 0.07 0.03 0.44 0.09 0.01 0.01 1.41 0.13 k−π+π−π+π− 615 1469 ±- 0.35±0.22± - 0.66±0.21 k−π+π0π+ 9210 18512 0.34 0.06 0.92±0.10 0.21 0.03 1.34±0.08 ± ± ± ± Average 0.09 0.01 0.45 0.03 0.02 0.01 1.19 0.09 ± ± ± ±

Table 1: Eletron/muon fake rates from track momentum greater than 2.4 GeV

The total number of hadronic tracks is calculated using the same D+ µ+ ν s → selection criteria after removing the tagged leptons. The fraction of pions, kaons and protons are 67%, 20% and 13% respectively [4]. The effective fake rates from protons and antiprotons are very small 0.1% and nearly equal for electrons and muons. ∼ The contributions of the lepton fake rates from hadron decay in flight are not included in the above calculation. A correction factor 1.18 0.06 is included for muonic ± fake rate [4]. Subtraction of the electron data sample from the muon data sample needs precise measurements of muon to electron normalization. Detector material causes different interaction with electrons and muons, phase space of semileptonic decay mode of D mesons also contributes to electron to muon decay width deviates from unity. A cor- rection factor of 1.01 0.03 is used to multiply electron samples to take into account ± detector effects and physics backgrounds [4].

7 Results

The ∆M distributions for the muon and electron data samples are shown in figure 10(a). Effective excess of muon fakes over electron is also shown therein. The histogram + is the sum of signal events, random photon contribution in Ds events and excess muon fake rates over electron.

12 Figure 9: Distribution of ∆M = M(K−π+π+) M(K−π+) of D∗+ D0π+ data samples for the case of hadrons identified as leptons. Top− left to bottom rig→ht are (π) total pion sample, (K) Total kaon sample, (π e) subsample of π which fake as electron, (π µ) π fakes to muon, (K e) kons fakes→ as electron and (K µ) kaon fakes as muon. → → →

13 The explicit distribution of the signal is shown in figure 10(b), which is the ∆M distribution after the electron and excess fakes are subtracted. The fitted curve has ∗+ the same shape and ratio of signal and background as it was in the Ds MC signal. ∗+ 3 The fit of explicit Ds signal distribution provides 266 26 events, which is nor- ± ∗+ + + + malized to the efficiency corrected number of reconstructed Ds γ Ds , Ds φπ →+ → events, 80481 2005 1453. Efficiencies of reconstructed γφπ are obtained from ± ± Monte Carlo samples. Thus the ratio of these two decay widths is

+ + Γ(Ds µ ν) + → + + = 0.135 0.013 0.022 (5) Γ(Ds φ π ) ± ± → The first error is the statistical error on the number of µ+ν and φ+π+ events. The second one is the total systematic error. All individual systematic errors are given + + + in table 2. Third error is due to uncertainty in the absolute Ds φ π branching + → ratio. Though total lifetime measurements of Ds [2] provide precise measurement of total width, the absolute φπ+ branching ratio has a large error. Using the values of + + −13 B (D φπ ) of 3.06 0.9% and τDS = (4.96 0.1) 10 s, the pseudo scalar decay s → ± ± × constant is calculated as

fDS = (247 12 20 31)MeV (6) ± ± ± which has 8% of systematic error better than previous cleo publication (10%).

Sourceoferror value Variation error Electron fake rate 0.09 0.01,0.02 0.01 σ oferror 0.004 Muonfakerate 0.45±0.03,1.19±0.09 σ oferror 0.014 ± ± π/K/p fractions 67%/20%/13% 70%/20%/10% 0.004 µ/e normalisation 1.01 0.03 σ oferror 0.013 ± Signal efficiency 2.38 0.04 σ oferror 0.006 ∗+ + ± Ds /Ds ratio 1.31 0.042 σ oferror 0.001 φπ+ normalisation 82481± 2005 1453 σ oferror 0.004 ± ± Table 2: Systematic error

3Statistical error is not calculated explicitly, This number is estimated from [4] with improved statistics.

14 Signal Fake 400 Eletron

(a)

200

0 0 0.05 0.1 0.15 0.2 0.25 0.3 M(γ µ ν) - M(µ ν)

50

(b)

0

0.05 0.1 0.15 0.2 0.25 M(γ µ ν) - M(µ ν)

∗+ Figure 10: (a) The ∆M distribution for Ds candidates. Excess muon fake rates are shown as cross hatch. Top of that, electron data samples are shown as parallel hatch histograms. ∗+ Total muon data are shown as solid dots. (b) The ∆M mass distribution for Ds candidates after removing electron samples and excess fakes. The fitting parameters are taken from MC samples except global normalisation. Hatched area is the remaining background due to random photons.

15 Appendix A

Definition of good tracks and isolated showers: KINCD = 0 • TNG 0 • ≥ not DREDGE • not Z ESCAPE • p 5.3 GeV • ≤ DBCD 0.005 • ≤ Z0CD 0.05 • ≤ Hit fraction 0.3 • ≥ RESIDUAL 0.0006 • ≤ Electron candidate • – R2ELEC 3.0 ≥ – Cosθ 0.85 | |≤ Muon candidate • – MUTR INDEX = 0 6 – Cosθ 0.85 | |≤ – MU DEPTH 7.0 ≥ Pion candidate • – Cosθ 0.90 | |≤ – SGPIDI leq SGKADI, SGPIDI 3 (p 0.9 GeV) ≤ ≤ Kaon candidate • – Cosθ 0.90 | |≤ – SGKADI leq SGPIDI, SGKADI 3 (p 0.9 GeV) ≤ ≤ Definition of isolated shower EBUMP 50 MeV • ≥ ANGCRT 10◦ • ≥ Photon candidate for D∗ reconstruction • – EBUMP 200 MeV ≥ – ANGCRT 20◦ ≥ – IBSTOP = 0 – E925U C92501 ≥ – NBCREG = 1

– Cosθγ 0.707 | |≤ – Mγ γ M 0 10 MeV | − π |≥

16 Appendix B

Event shape variables and their cut values :

Lepton Momentum 2.4 GeV • ≥ CosθLepton 0.85 •Missing | momentum| ≤ 0.3 GeV • M 2 ≥ 2.0 GeV2 • | mass | ≤ Cosθmiss 0.85 • | +| ≤ Mass of Ds 1.5 GeV • ∗+ ≥ Momentum of Ds 3.0 GeV • ∗+ ∗+ ≥ Cosine of the angle between photon in Ds frame and Ds -0.4 • in lab frame ≥

Table 3: List of event shape variables and their cut values

References

[1] J. L. Rosner, in Particles and Fields 3, Proceeding of the 1988 Banff Summer Inst., Bnaff, Alberta, Canada, Edited by A. N. Kamal and G. F. Khanna, World Scientific, Singapore, 1989, p395. [2] D. E. Groon et. al.,(Particle Data Group), The European Physics Journal C 15 [3] D. Acosta et. al.,Phys. Rev. D49 (1994) 5690. [4] M. Chadha et. al.,Phys. Rev. D58 (1998) 032002. [5] S. Aoki et. al.,Progress of Theoretical Physics 89 (1993) 131. [6] J. Z. Bai et. al.,Phys. Rev. Lett. 74 (1995) 4599. [7] K. Kodoma et. al.,Phys. Lett B382 (1996) 299. [8] Y. Alexandrov et. al.,Phys lett. bf B478 (2000) 31. [9] Y. Kobuta et. al.,(CLEO collaboration) Nuclear Instruments & Methods A320 (1992) 66. [10] T. S. Hill Nuclear Instruments & Methods A418 (1998) 32. (CLEO II Precision tracking layers are replaced by Silicon detector) [11] J. Barlett et. al.,Phys. Rev. Lett. 80 (1998) 4127. [12] M. Artuso et. al.,, Muon Identification Efficiencis for full cleo II.V data, CBX 00-39. [13] Bernard Gitelman, private communication

17