CLEO Contributions to Tau Physics

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a Alan. J. Weinstein ∗ aCalifornia Institute of Technology, Pasadena, CA 91125, USA Representing the CLEO Collaboration

We review many of the contributions of the CLEO experiment to tau physics. Topics discussed are: branching fractions for major decay modes and tests of lepton universality; rare decays; forbidden decays; Michel parameters and spin physics; hadronic sub-structure and resonance parameters; the tau mass, tau lifetime, and tau neutrino mass; searches for CP violation in tau decay; tau pair production, dipole moments, and CP violating EDM; and tauphysicsatCLEO-IIIandatCLEO-c.

+ + 1. Introduction and decay, e.g.,in[3]e e− Υ(nS) τ τ −. In addition to overall rate,→ one can→ search for Over the last dozen years, the CLEO Collab- small anomalous couplings. Rather generally, oration has made use of data collected by the these can be parameterized as anomalous mag- the CLEO-II detector [1] to measure many of the netic, and (CP violating) electric, dipole mo- properties of the tau lepton and its neutrino. Now + ments. With τ τ − final states, one can study that the experiment is making a transition from the spin structure of the final state; this is per- operation in the 10 GeV (B factory) region to the haps the most sensitive way to search for anoma- 3-5 GeV tau-charm factory region [2], it seemed lous couplings. We will return to this subject in to the author and the Tau02 conference organiz- section 9.1. ers to be a good time to review the contributions Measuring the production rate at 10 GeV is of the CLEO experiment to tau physics. We are only interesting if it is precise: < 1%. This has consciously omitting results from CLEO-I (data proven to be difficult at CLEO, for several rea- taken before 1989). The author has chosen to sons. take a semi-critical approach, emphasizing both First, it is desirable to do an inclusive selec- the strengths and weaknesses of tau physics at + tion of τ τ − final states, so that production rates CLEO: past, present, and future. don’t depend on decay branching fractions, which were not measured at the 1% level in the early 2. Tau Production at 10 GeV part of the last decade. It’s difficult to select taus + inclusively, because backgrounds from qq¯, e e−, We begin by discussing a topic on which CLEO + µ µ− and two-photon are less easily distinguish- has not published: tau pair production. + able from τ τ − than at LEP, and they depend on + In e e− collisions, one can study taus in pro- tau decay mode. It’s not really hard, but it’s hard duction and/or decay. The production reac- to get precise selection efficiencies. In the end, tau + + tion e e− γ∗ τ τ − is governed by well- → → selection at CLEO always had smaller efficien- understood QED. As such, it is not terribly inter- cies and/or larger backgrounds, and often also esting (or at least, nowhere near as interesting as larger systematic errors, than analogous analyses + ( ) + studying e e− γ∗/Z ∗ τ τ − at LEP I and → → at LEP. LEP II). CLEO has studied resonance production To measure the production cross-section, one needs a precise luminosity measurement, with an ∗Work supported by the US Department of Energy and National Science Foundation. error << 1%. At CLEO, we selected large angle 2

Table 1 3.1. One-prong problem Main decay modes of the τ lepton. In the early 90’s, the “tau one-prong” problem τ eνν 18% Br, univ, Michel was raging; the branching fractions for exclusively → τ ≈ τ µνν 17% Br, univ, Michel reconstructed tau decays didn’t add up to 1 [6]. → τ ≈ τ πν, Kν 12% Br, univ The resolution of this discrepancy required preci- → τ ≈ τ ππν 25% Br, ρ, ρ0,CVC,Π sion (sub-1%) branching fractions measurements. → τ ≈ τ Kπν 1.4% Br, K∗, K∗0 CLEO-II was a new detector; acceptances, → τ ≈ τ 3πν 18% Br, a , a0 , h in/efficiencies, and detector simulation needed to → τ ≈ 1 1 ντ τ Kππντ 0.8% Br, K1, K1b,W-Z be understood very well. Important issues in- → ≈ 0 τ 4πν 5% Br, ρ0,CVC cluded the detection of π ’s: they rarely merged → τ ≈ τ rare 2% 5π,6π, ηππ, ... into one shower, and CLEO obtained great m → ≈ γγ τ ηπν, b ν 1% 2nd-class currents resolution ( 6 MeV) with its CsI calorime- → 1 τ τ forbidden 1% neutrinoless decays ter. However,∼ soft photons could get lost; and → “splitoffs” from hadronic showers could fake photons. Overall, ensuring reliable detection of π0’s resulted in a detection efficiency 50(1 0.03)%. Also, CLEO had poor K/π separation∼ over± most + + + Bhabhas (e e−), µ µ−, e e− γγ with rather of the interesting momentum range. We made high statistics. To get the luminosity,→ we need 0 progress using KS, with detection efficiency accurate predictions of the cross-section times se- 50%. Because of all this, it was hard to know the∼ lection efficiency from precision Monte Carlo sim- overall detection efficiency, after backgrounds, to ulations, incorporating accurate QED radiative better than 1%. corrections. Much less effort has gone into this at Ultimately, CLEO’s branching fraction mea- 10 GeV than at LEP! Each of these measurements surements were limited by knowledge of luminos- has small statistical errors, but the systematic er- ity (1%), cross-section (computed to order α with rors are of the order of 2%. CLEO got agree- KORALB [7], 1%), and knowledge of the de- ∼ ment between the 3 QED processes at the level tection efficiency∼ and backgrounds ( 1 2%). ∼+ − of 1% but not much better; the discrepancies are However, with millions of produced τ τ −,what likely to be in the QED Monte Carlos. CLEO we lacked in efficiency we made up for in statis- quotes a 1% systematic error on luminosity [4]. tics. The moral is that further progress in this By 1995, we made (1 2)% measurements of ∼ − 0 topic requires precision QED Monte Carlos. The branching fractions to eνντ , µνντ , π/Kντ , ππ ντ , 0 0 KKMC program [5] promises precision results, πnπ ντ ,3πντ ,3ππ ντ , etc.[8–11]. These mea- but it must be validated with careful computa- surements reduced the “tau one-prong” problem tional and experimental cross-checks. Consistent to insignificance by PDG 1996 [12]. We had also + + + results for e e−, µ µ−, e e− γγ are a good tested e/µ/τ charged-current coupling universal- → first step. Further, measurements of anomalous ity at the 1% level [8]. By then, LEP was mea- moments make use of the spin correlations in tau suring branching fractions with total errors much pair production at 10 GeV, so one must validate smaller than 1%. This came as quite a shock to the correct treatment of spin-dependence in the CLEO! It helped that the LEP experiments knew Monte Carlo. Nττ = σ quite well, as a by-product of their in- crediblyL successful electroweak program. 3. Tau decay physics at CLEO 4. Rare semi-hadronic decay modes CLEO pursued a systematic study of all tau decays during the 1990’s, learning much about the Rare semi-hadronic decay modes of the tau pro- tau, its neutrino, and low-energy meson dynam- vide unique laboratories for low-energy meson dy- ics. The main decay modes are listed in Table 1. namics, and tests of conservation laws. With the 3

Table 2 The ηπ− mode is a signature for second-class Measurements of branching fractions for rare (isospin-violating) currents. The ηK− mode pro- semi-hadronic τ decay modes by CLEO-II. 0 ceeds by SU(3)f violation. The ηπ−π mode proceeds by the Wess-Zumino anomalous current. + 0 3 The η3π signals, which are rich in sub-structure, (2π−π 2π ντ )=(5.3 0.4) 10− B ± × areshowninFig.2. (3π 2π+ν )=(7.8 0.6) 10 4 − τ − CLEO also observed the radiative decay modes B + 0 ± × 4 (2π−π 3π ν )=(2.2 0.5) 10− B τ ± × τ − e−ντ γ and τ − µ−ντ γ [22], and made the + 0 4 → → + (3π−2π π ντ )=(1.7 0.3) 10− ﬁrst observation of the decays τ − e−e e−ν¯ ν B ± × → e τ 0 4 (5 events) and τ µ e+e ν¯ ν (1 event) [23]. (π−2π ων )=(1.5 0.5) 10− − − − µ τ B τ ± × → + 4 (2π−π ωντ )=(1.2 0.3) 10− B + 0 ± × 4 (3π−2π 2π ντ ) < 1.1 10− B × 50 100 0 6 45 (7π±(π )ντ ) < 2.4 10− . B × 40 80 35

60 30

40 20 Events/(50 MeV) Events/(50 MeV) Events/(50

15 Table 3 20 10

Measurements of τ decay modes involving kaons 5 0 0 from CLEO-II. 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 M(2π -π + 3π0) (GeV) M(3π-2π+π0) (GeV)

4 (ν ηπ−) < 1.4 10− at 95% CL B τ × (ν ηK )=(2.6 0.5) 10 4 τ − − Figure 1. Mass distributions from τ 6πντ .The B 0 ± × 3 → (ν ηπ−π )=(1.7 0.3) 10− data are shown as data points with error bars, the B τ ± × + 4 lower histograms show various background mod- (ντ ηπ−π π−)=(3.4 0.8) 10− B 0 0 ± × 4 els, and the open solid histogram shows the model (ν ηπ−π π )=(1.4 0.6) 10− B τ ± × of the background plus tau decay signal. Left: (ν K η)=(2.90 0.80 0.42) 10 4. + 0 + 0 τ ∗− − M(2π−π 3π ντ )inτ − 2π−π 3π ντ [15]. B ± ± × + 0 → + 0 Right: M(3π−2π π )inτ − 3π−2π π ν [16]. → τ world’s largest sample of tau pairs throughout the 1990’s, CLEO made many first and/or most pre- 4.1. Rare strange modes - XS−ντ cise measurements of rare decay modes [13–17], 0 Modes with KS are easily accessible in the listed in Table 2. CLEO data. Identifying charged kaons was prob- Decay modes like 5π,6π,7π, ηππ, η3π, are rel- lematical in CLEO-II, but even with poor K/π atively easy to reconstruct. The big problem is separation ( < 2σ), we identified and measured background from qq¯. Lepton tags can clean that branching fractions∼ for many modes containing up reasonably well, but an irreducible background kaons, listed in Table 4. During the same time remains, that can be estimated and subtracted period, LEP-I produced terrific results on modes statistically. These modes have rich and compli- with kaons, including K0 ! cated sub-structure, which we attempted to delve L into for the 5π,6π,andη3π modes. Some 6π sig- 5. Forbidden (neutrinoless) decays nals are shown in Fig. 1. Of particular interest are modes involving η Tau decays to final states with no ντ (or more mesons [18–21], listed in Table 3. precisely, no missing energy) are a clear signature 4

3350697-002 Table 4 55 30 16 ( a ) ( b ) ( c ) Measurements of τ decay modes involving kaons 12 from CLEO-II. 35 20 (K¯0π π0ν )=(0.417 0.058 0.044)% 8 − τ B + ± ± (K−π π−ν )=(0.345 0.023 0.055)% 15 10 τ B 0 0 ± ± 4 (K−π π ντ )=(0.14 0.10 0.03)% Events / 150 MeV B 0 0 ± ±

I 5 0 0 (K−K π ντ )=(0.145 0.036 0.020 )% B + ± ± 1.0 1.8 2.6 1.0 1.8 2.6 1.0 1.8 2.6 (K−K π−ντ )=(0.144 0.013 0.028 )% M (GeV)M (GeV) M (GeV) 3 3 2 0 B 0 0 ± ± (KSKSπ−ντ )=(0.023 0.005 0.003 )% B + 0 ± ± (K−π π−π ντ )=(0.075 0.026 0.017)% B + 0 ± ± (K−K π−π ν )=(0.033 0.018 0.007)% B τ ± ± Figure 2. Mass distributions from τ 3πηντ [20]. The data are shown as data points→ with error bars, the hatched histogram shows the background model (mostly from non-tau contin- Table 5 uum), and the open solid histogram shows the Measurements of neutrinoless τ decay modes involving K0 ’s, from CLEO-II [31]. model of the background plus tau decay signal. S + M((3π)−η) is plotted, for (a) 2π−π η, η γγ; + 0 0 → 0 7 (b) 2π−π η, η 3π ;(c)π−2π η, η γγ. (e K ) < 9.1 10 → → − S − B 0 × 7 (µ−KS) < 9.5 10− B 0 0 × 6 (e−KSKS) < 2.2 10− B 0 0 × 6 (µ−KSKS) < 3.4 10− for lepton-number violation, pointing directly to B × physics beyond the Standard Model. The golden mode is τ µγ, which in many models, would be → the easiest to observe in tau decays (despite the 0 strong constraint from non-observation of µ about modes containing K ’s! This has now been → corrected: New for this conference [31], based on eγ). 6 + 12.7 10 τ τ −), are the branching fraction up- CLEO-II set its ﬁrst upper limit (τ µγ) < × 6 B → per limits at 90% CL listed in Table 5. 4.2 10− (90% CL) in 1992 [24]. This was im- × 6 6 proved to 3.0 10− by 1996 (4.3 10 tau pairs) × 6 × 6 6. CLEO Michel Parameter analyses [25]; then 1.1 10− by 1999 (12.6 10 tau pairs) × × [26]. By this point, we were starting to hit back- We turn now from measurements of branch- ground events (see Fig. 3), which appear to be ing fractions to the substructure in the multi- irreducible; further progress can no longer be ex- particle decay modes. For the leptonic decays pected to scale inversely with the number of pro- τ − `−ν¯`ντ , this amounts to the measurement duced tau pairs. of the→ Michel parameters governing the Lorentz CLEO also searched for many other neutrino- structure of the decay (i.e., the search for devia- less modes, setting limits on 22 of them in 1994 tions from the Standard Model V A structure). [27], with branching fraction upper limits around Information on the Lorentz structure− of the decay, 5 10− . This was updated in 1997 [28], with 28 especially on the helicity of the tau neutrino hντ , modes, including resonances; branching fraction can also be obtained from decay distributions in 6 upper limits of a few 10− were obtained. We semi-hadronic (τ X ν ) decays. × − h− τ added 10 more modes with π0’s and/or η’s in 1997 CLEO-II has published→ four diﬀerent analyses [29]. Five more modes were added in 1998 [30], focusing on Lorentz structure: 0 containing (anti-)protons: τ − pX¯ . → + 0 0 Throughout all this, we managed to forget Select `−νν vs. π π ν ;Useπ±π as tag. • τ τ 5

decay ρ+ π+π0, the QED-predicted correla- → + tions between the spins of the τ and the τ −, and the momentum distribution of the daughter lepton in τ − `−νντ , in order to extract the spin-independent→ Michel parameters ρ and η,the spin-dependent parameters ξ and ξδ,andthetau

neutrino helicity hντ . This is illustrated in Fig. 4.

ντ

π+ ρ+ τ+ γ ντ π0 τ- νe ρ helicity spin- e- angle correlation p e + 0 + - hρ hρ τ spin τ spin hντ ξ

τ neutrino helicity hντ Figure 3. CLEO data (points) and Monte Carlo prediction (open boxes) for τ − µ−γ [26]. → Figure 4. Illustration of how to extract spin- dependent Michel parameters in the reaction + + + + e e− τ τ −, τ ρ ντ , τ − `−νντ . From the lepton energy spectrum, extract → → → the Michel parameters ρ and η [32]. Select π ν vs. π+ν ; exploit the spin cor- − τ τ The Michel parameters measured in this way • relations between the two taus in the event are compared with those from other experiments to extract the square of the tau neutrino 2 in Fig. 5. From these measurements, strong con- helicity hντ [33]. | | straints could be placed on right-handed τ ντ + 0 0 − Select `−νντ vs. π π ντ ;usetheπ±π de- couplings and the mass of a right-handed WR±. • cay as spin analyzer. Use the full event Further, the precise limit obtained on η (without kinematics to extract measurements of the making use of any constraint on η from the leptonic branching fractions) sets a constraint on the Michel parameters ρ, η, ξ, δ,and hντ [34]. | | presence of, e.g., a scalar charged Higgs mediat- Select `−νντ vs. (ρπ)−ντ . Exploit the inter- ing tau decays. • ference between the two ρπ amplitudes, and use the full event kinematics to extract the 7. Hadronic substructure in tau decays parity-violating signed tau neutrino helicity Tau semi-hadronic decays τ − X−ντ provide hντ [35]. h a uniquely clean probe of low energy→ meson dy- The third-listed analysis [34], in particular, namics. Recall that strong dynamics is the most made rather precise measurements, using a pow- poorly understood part of the Standard Model. erful technique. To make full use of kinematical The fundamental theory is QCD, but it is difficult information, a full multi-dimensional likelihood to use QCD to characterize hadronic structure in fit was performed. The fit correlated information detail. Instead, we must rely on models, symme- on the ρ+ polarization in τ + ρ+ν from the tries and conservation laws (such as isospin and → τ 6

2 ARGUS 95 ρ ARGUS 95 η extracting αS(mτ ). ALEPH 95 ALEPH 95 CLEO has studied substructure in the following L3 96 L3 96 SLD 97 SLD 97 tau decays: Average 96 Average 96 CLEO 97 CLEO 97 0 τ − π−π ν [38]; see Fig. 6. We extracted OPAL 98 OPAL 98* • → τ the mass and width of the ρ− meson and the 0.45 0.65 0.85 -1.5 -0.45 0.6 mass, width, and coupling of the ρ0− me- 2 ARGUS 95 ξ ARGUS 95 ξδ son; measured the pion form factor Fπ(q ) ; ALEPH 95 ALEPH 95 | | L3 96 L3 96 and provided tests of CVC in comparison + + SLD 97 SLD 97 with e e− π π− (see [39]). These data Average 96 Average 96 are useful in→ the evaluation of the hadronic CLEO 97 CLEO 97 OPAL 98 OPAL 98 contribution to the vacuum polarization di- 2 agrams that arise in (g 2)µ and α(q ) [36]. 0 0.75 1.5 -0.2 0.5 1.2 − 0 ARGUS 95 hν τ − π−K ντ [40], see Fig. 7. We studied ALEPH 95 • the→ mass and width of K meson, looked L3 96 ∗− SLD 97 for evidence of a K∗0−, and extracted the

Average 96 decay constant fK∗ . This work has not CLEO 97 yet been published! Of particular note is a signiﬁcant discrepancy between the mass -1.5 -1.125 -0.75 of the K∗− seen in our clean sample from τ − K∗−ντ and the world average in the PDG.→ Figure 5. Measurements of tau Michel parameters from CLEO’97 and from other experiments. τ − 3πν ; see Fig. 6. We have performed • → τ ∗The leptonic branching fractions were used to three analyses: a model-dependent analy- 0 0 further constrain the value of η in the OPAL 98 sis using the π−π π mode [35], a model- measurement. independent measurement of the structure 0 0 functions using the π−π π mode [41], and a model-dependent analysis using the + π−π π− mode [42]. We found a rich struc- SU(3)f ), the Conserved Vector Current (CVC) ture, including the presence of scalar and hypothesis, sum rules, chiral perturbation theory, tensor mesons. We measured the decay con- and results from QCD on the lattice. stant fa1 ; the signed neutrino helicity hντ ; The momentum transfer is small in τ decays; and limits on couplings to the π0(1300). we are in the region where resonances dominate, and their description relies on phenomenological τ − (Kππ)−ντ [43–45,40]; see Fig. 7. models. The dynamics of such hadronic systems • Here→ again, a rich structure can be uncov- is parameterized in tau decays via the “spectral ered. We have studied the mass, width, 2 2 2 function” v(q )(q = M(Xh) ), containing all couplings and decay branching fractions of the strong dynamics. These spectral functions the K1(1270) and K1(1400) mesons, and can be related, via CVC, to similar quantities in explored their mixing and SU(3) violating + e e− collisions and in vacuum polarization dia- couplings to the tau. More on this in sec- 2 grams that arise in (g 2)µ and α(q ) [36]. CLEO tion 7.1. can measure v(q2) using− exclusive ﬁnal states; it is more problematic to do inclusive studies such as τ − (4π)−ντ [47]. The physics that can has been done at LEP, as discussed above. Still, • be explored→ in this decay is discussed in sec- CLEO published one paper on the subject [37], tion 7.2. 7

3100999-031 τ − η(3π)−ντ [20]; see Fig. 2. This de- • cay→ was first observed by CLEO, using two 105 different modes of the η, and two different charge combinations of (3π)−.Weobserved clear evidence for τ − f (1285)π−ν , → 1 τ f1 a0(980)π, a0 ηπ and measured 104 their→ product branching→ fractions. We searched for and set upper limits on τ − 0 → η0π−ν and τ − η0π−π ν . τ → τ 103 + 0 τ − 2π−π 3π ντ [16]; see Fig. 1. We Events / 0.025 GeV • measured→ a branching fraction in good agreement with expectations from isospin, and constrained the isospin structure of the 102 decay. The branching fraction is some- + what below the CVC prediction from e e− data [39]. The decay appears to be sat- 0.3 0.5 0.7 0.9 1.1 1.3 1.5 Mass (0 ) (GeV) 0 urated by the channels τ − π−2π ωντ ,

+ → 0 -1 τ − 2π−π ηντ ,andτ − π−2π ηντ . ] → → 2 3 Notable omissions from this list include a study 10 of substructure in τ − (5π)−ντ , and the study → 0 of Lorentz structure in τ − ηπ−π ντ (which is 2 expected to proceed via the→ Wess-Zumino anoma- 10 [ 0.025 GeV/c

lous current). π 3 m

7.1. τ − K−ν structure ∆ → 1 τ 10 The decay τ − (Kππ)−ντ has particularly N/ ∆ interesting structure.→ It can be studied in the final states K π+π ν and K0 π π0ν .CLEO − − τ S − τ 1 has published results focusing on the former [45], despite the poor K±/π± separation. Results on 0.6 1 1.4 1.8 the latter mode, which is much cleaner and can be m [ GeV/c2] isolated event-by-event, are still in progress [40]. 3π The (Kππ)− final state is expected to be dom- P + inated by the axial-vector K1 (J =1 ). There are two such states; in the quark model, they are 3 Ka in the P1 octet, the strange partner of the Figure 6. Fully corrected mass distributions 1 0 a1(1260); and Kb in the P1 octet, the strange from (top) τ − π−π ντ [38]; (bottom) τ − 0 0 → → partner of the b1(1235). The Kb couples to W π−π π ντ [35]. The data are shown as data only through an SU(3)-violating “second-class” points, and the curve shows a model of the tau current. Both K1’s decay to Kππ via K∗π and decay signal. Kρ, and they mix, via virtual states, into the physically observed K1(1270), K1(1400). So, we have weak coupling, SU(3)-violation, mixing, and decays to resonances. In addition, (Kππ) fi- − We can parameterize the K1a K1b mixing nal state could proceed via a vector current, via via a mixing angle: ↔ the Wess-Zumino anomaly: K∗0 (K∗π, Kρ) Kππ . → → K (1400) = K cos θ K sin θ 1 a K − b K 8

K1(1270) = Ka sin θK + Kb cos θK

103 and the SU(3)f symmetry breaking via a parameter δ: 102 τ W K δ K → →| ai− | bi δ =(ms mu)/√2(ms + mu) 0.18. 1 | | − ≈ 10 The branching fraction of the τ to the K1’s can Events per 10 MeV then be written in terms of these parameters: 1 2 (τ K1(1270)ν) sin θK δ cos θK 0.60 0.85 1.10 1.35 1.60 B → = − Φ, π [ ] Corrected KS Mass GeV (τ K1(1400)ν) cos θK + δ sin θK × 3030200-024 B → Data Fit where Φ is some known (or estimatable) kinemat- 3000 K1 (1270) K1 (1400) ical and phase space terms. From the CLEO data [45], we obtain two pos-

2000 sible solutions, depending upon the sign of δ:

θK =(69 16 19)◦ (δ =0.18),

Number of Events ± ± 1000 θ =(49 16 19)◦ (δ = 0.18). K ± ± − These mixing angles are consistent with those ob-

0 tained using only the K1 widths and branching 0.80 1.05 1.30 1.55 1.80 M (GeV/c2) K fractions [46].

7.2. τ − (4π)−ν → τ 600 The τ 4πντ decay is expected to proceed through the→ vector current (J P =1 ), dominated N events data − 500 cleo2 MC by the ρ, ρ0, ρ00... resonances. There are many 0 π0 cleo2 KsK MC 400 cleo2 ττ background MC sub-resonances that can contribute: ωπ, ηπ, a1π. cleo2 continuum MC In the CLEO analysis [47], the spectral functions 2 2 300 v(m4π)andv(mωπ) were measured, and the ωπ contribution was modeled with interfering ρ, ρ0, 200 ρ00... resonances (see Fig. 8). The resonant sub-

100 structure was measured and modeled, showing clear evidence for ωπ and ρππ, and the latter is 0 0.6 1.0 1.4 1.8 2.2 2.6 3.0 consistent with originating from a1π, a1 ρπ. M [ GeV/c2] → Kππ The 4π spectral function must be known well in order to use this ﬁnal state to kinematically constrain the ν mass from τ 4πν data; this is τ → τ Figure 7. Mass distributions from tau decay discussed in section 8.1. The 4π spectral function modes containing kaons. Top: M(K0 π ) from can also be compared with the isospin-rotated re- S − + + + 0 0 actions e e− 2π 2π−, π π−2π as a test of τ − KSπ−ντ [40]. Middle: M(Kππ) from → → + + CVC [39]. τ − K−π π ντ [45]. Bottom: M(Kππ) from → 0 0 The 4π ﬁnal state can also proceed through the τ − KSπ−π ντ [40]. The data are shown as data→ points, and the topmost curve or histogram axial-vector current, which is expected to be dominated by the b (1235): τ b ν , b ωπ.The shows a model of the tau decay signal. 1 → 1 τ 1 → b1 has, however, the wrong G-parity to couple to the weak charged current; it is a second-class current. The resulting decay to ωπ occurs via an S- or D-wave, instead of the ρ ωπ P-wave. CLEO → 9

3350899-012 measured the angular distribution in this decay 0.06

(Fig. 8) and found complete consistency with P- (770), (1523), (1700) wave decay, setting a limit on the non-vector cur- 0.05 (770), (1523) rent contribution of less than 5.4% of the total at 90% CL. (770), (1700) 0.04 (770) 8. Tau mass and lifetime, tau neutrino mass 0.03 V (q) CLEO pioneered the use of kinematical constraints to measure the tau mass, by observing 0.02 semi-hadronic tau decays on both sides of an event, and determining for each event a maxi- 0.01 mum kinematically-allowed tau mass consistent with the observed hadronic energies and mo- 0 menta. The distribution of this maximum mass 0.8 1.2 1.6 2 exhibits a sharp drop-off near the tau mass, and q ( ) (GeV / c ) from the position of this drop-off, CLEO measured [48] mτ = (1778.2 1.4) MeV. At around the same time,± the BES experiment measured the tau mass much more accurately, through a threshold scan [49]. CLEO turned this to an advantage; the “maximum kinematically- allowed tau mass” was really a measurement of a combination of the tau mass and the ντ mass: mkin mBES m2 /m where m is a mass τ τ ντ 0 0 parameter' determined− through Monte Carlo simulation. Making use of the BES measurement, CLEO kinematically constrained the ντ mass to be m(ντ ) < 60 MeV, 95% CL. Of course, what is being constrained here is the effective mass of the linear combination of neutrino mass eigenstates which couple to the tau. CLEO-II used its vertex proportional chambers to measure the tau lifetime [50]. Using 1-v-3 and 3-v-3 events, and making use of vertex and beam + 0 position information, the tau lifetime was mea- Figure 8. Distributions from τ − π−π π−π ν → τ sured to be ττ = 289.0 2.8 4.0 fs, in good [47]. Top: The spectral function v(M(ωπ)), with ± ± agreement with more precise measurements from fits to various combinations of ρ, ρ0, ρ00... res- LEP. CLEO-II.V introduced a precision silicon onances. Bottom: Angular distribution sensi- vertex detector, but so far, that device has not tive to the polarization of the ω in X ωπ been used to re-measure the tau lifetime. (points), compared to predictions for different→ partial waves. Second-class currents would reveal 8.1. Mass of the m(ντ ) themselves as L =0, 2 partial waves. Regardless of m(ντ ) constraints from ν-mixing and cosmology, constraining it kinematically in tau decays remains a worthy goal. The ALEPH eff limit from 1998 still stands: m (ντ ) < 18.2 10

MeV (95% CL). (Again, what is being con- 1160398-004 strained here is the effective mass of the linear 1.00 ( a ) combination of neutrino mass eigenstates which 0.98 couple to the tau.) 0.96 0.94 eff CLEO-II has published 3 limits on m (ντ ), 0.92 using different decay modes and ever-larger 0.90 datasets: 0.88 eff 0 m (ν ) < 32.6 MeV, 1993, 5π, 3π2π [51], 0.86 τ Beam eff 0 m (ντ ) < 30 MeV, 1998, 5π, 3π2π [52], / E 1.00 ( b ) eff 0 X m (ντ ) < 28 MeV, 2000, 3ππ [53]. E 0.98 The last two limits used the MX versus 0.96 EX /Ebeam technique pioneered at LEP, where X 0.94 0.92 is the hadronic system in τ Xντ decay. All three of these limits used a much→ larger data sam- 0.90 ple, than the one available to ALEPH, and com- 0.88 0.86 parable or better MX , EX resolution. The data 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 2 from the second analysis listed above is shown in M (GeV / c ) Fig. 9. X If one is motivated to improve this kinematical limit appreciably, e.g. to approach the 1MeV ∼ level, one needs lots of statistics, excellent, well- Figure 9. Distribution of invariant mass MX ver- understood MX , EX resolution, good spectral sus scaled energy EX /Ebeam for τ Xντ ,where →0 function models, and most especially, a good un- (a) X =5π±,and(b)X =3π±2π ,inCLEO derstanding of statistics and systematics - there data [52] near the kinematic endpoints, with 1σ are many subtleties [54]! resolution error ellipses shown. The solid lines show the kinematical boundary for m(ντ )=0, 9. CP Violation in tau decay and the dashed contours are for m(ντ ) = 30, 60, and 100 MeV. A highlight of the recent work in tau physics from CLEO has been the search for CP violation in tau decay [55]. Of course, CP violation is not expected in leptonic decays, in the Standard Model. To man- a mechanism, in two analyses. ifest it, a process must have two or more inter- In the first, the decay τ − (Kπ)−ντ (or its fering amplitudes, with relatively complex phases charged conjugate) is reconstructed→ on one side of (as in the CKM matrix in the quark sector). In the event. The other tau decay is used only to tag + the Standard Model, the µ and τ decay via one the event as τ τ −. CP violation would manifest amplitude: τ − W −ντ , a process that has been itself if the K momentum vector lay preferentially well studied at CLEO→ and LEP. Also, the charged on one side of the plane formed by the e+τ + mo- leptons cannot undergo particle-antiparticle oscil- mentum vectors; this effect is manifestly SU(3)f lations. violating. To produce CP violation in tau decay, we can In the second, both sides of the event are re- + + add a second amplitude, such as a charged Higgs: quired to go to ρν : τ τ − (ρ−ν )(ρ ν ). The τ → τ τ τ − H−ντ . Endow it with a complex coupling τ ρντ decays are used to analyze the spin Λ with→ a phase which flips sign under CP, and orientation→ of each tau, and one looks for net a strong phase (supplied by the W ρ or K∗ transverse spin polarization; a manifestly isospin- Breit-Wigner propagator) which does→ not. CLEO violating, as well as CP-violating effect. has recently searched for CP violation due to such In both cases, maximal information about the 11 presence of CP-violating terms in the decay rate but the taus are nearly at rest. The spin corre- (in the context of a model containing a scalar lations are dominantly along the direction of the + charged Higgs with a complex coupling Λ) is ex- e e− beam axis. Again, there is no net spin po- tracted by defining an optimal CP-violating ob- larization. servable, and looking for an asymmetry in the These differences lead to significant and inter- distribution of that observable. esting differences in the way anomalous dipole No such asymmetry was seen, and (model- moments and CP violation are manifested in tau dependent) limits were set on (Λ): pair production, and different optimal observ- 0.172 < (Λ) < 0.067 at 90%= CL ables must be defined in order to best observe − =0 in the π±KSντ -vs- any-tag analysis [56], and it. 0.033 < (Λ) < 0.089 at 90% CL − + = in the ρ ν¯ -vs- ρ−ντ analysis [57]. ^ ^ z + x + 9.1. Anomalous τ τ − production: dipole τ moments y^ As mentioned in section 2, it is of interest +− + θ to search for anomalous τ τ − production at ee energies much below the Z0, parameterized by anomalous dipole moments. The best sensitivity − to anomalous dipole moments can be obtained by τ + studying the spin correlations in e e− γ∗ + → → τ τ − events. z^ Searches have recently been made by ARGUS + [58] and Belle [59]. Sadly, CLEO has not pub- τ lished on this subject. + − If the tau dipole moments are not anomalously eeθ large, then (far below the Z0 peak) the taus in + τ τ − events have very small net spin polariza- − tion. However, their spin polarizations are almost τ 100% correlated, in all three dimensions. This is interesting to measure, if only as as a test of QED. z^ The nature of spin correlations is a strong func- + tion of beam energy. At 10 GeV, tau pairs τ + + − are produced via e e− γ∗. This is parity- θ conserving, and at at energies→ where the taus are ee relativistic but not extremely so. Both longitudinal and transverse spin correlations are main- − tained, but there is no net spin polarization. τ + At LEP-I, tau pairs are produced via e e− Z0. This is parity-violating, and at energies→ where the taus are extremely relativistic. Both longitudinal and transverse spin correlations are Figure 10. Illustration of tau spin correlations in maintained, but the large boost makes it nearly e+e collisions at 10 GeV (top), near the peak of impossible to measure the transverse spin polar- − the Z0 (middle), and near threshold (bottom). izations; and there is a net longitudinal spin polarization which is well established at LEP. + Near τ τ − threshold, tau pairs are produced + via e e− γ∗. Again, this is parity-conserving, → 12

10. Tau physics at CLEO-III and at parameters, especially the low-energy parame- + CLEO-c ter η. The unique spin correlations near τ τ − threshold will permit new tests of QED, and facil- The study of tau physics continues in the itate searches for anomalous couplings. Thresh- CLEO-III era, where our RICH detector permits old scans could result in measurements of the tau a more precise study of modes containing kaons mass to a precision of 0.1 MeV. It may also be [60]. possible to limit m(ν ) kinematically at the 10 6 + τ CLEO-III has 9 10 produced τ τ − near 10 ∼ × MeV level. GeV, with good K/π separation. There is also The CLEO-c tau-charm factory has a bright 6 1 3 10 fb− collected on or near the peaks future in tau physics! ∼of the× on Υ(nS) resonances (n =1, 2, 3) which + will yield measurements of (Υ(nS) τ τ −). Other topics in tau physics whichB will be→ pursued 11. Summary include: The CLEO Collaboration has published numer- rare decays, modes with kaons, precision ous studies of the physics of the tau lepton and • measurements; its neutrino, and looks forward to continuing this work with data from the CLEO-III detector, and into the CLEO-c era. More tests of CP in τ system: hντ = hν¯τ ; • − The author would very much like to thank the Rare decays may be seen: e.g.,2ndclass organizers of Tau02 for their hospitality, but un- • currents; fortunately, he was not able to avail himself of it, because personal problems prevented him from Limits (observation?) on LFV decays; attending in person. He is grateful for the oppor- • tunity to give his presentation remotely. anomalous (e.g., CPv) couplings in weak • decay or in QED production; REFERENCES 0 exotica (e.g., τ − π−ν , e−G ); • → heavy 1. CLEO Collaboration (Y. Kubota, et al.), continued testing and development of mod- Nucl. Instr. Meth. 320, 66 (1992). • els of meson dynamics as a guide towards 2. CESR-c Taskforce, CLEO-c Taskforce, and more fundamental theory: structure of τ CLEO-c Collaboration, hep-ex/0205003, → CLNS 01/1742 (2002). 4πντ , K3πντ , η2πντ , η3πντ , etc.. 3. CLEO Collaboration (D. Cinabro et al.), Within the next year, CESR will make the Phys. Lett. B 340, 129 (1994). transition to CESR-c, operating in the Ecm 4. CLEO Collaboration (G. Crawford et al.), 3 5 GeV region. The suitably modified CLEO-c∼ Nucl. Instr. Meth. A 345, 429 (1994). experiment− will collect data on the ψ(nS)res- 5. S. Jadach et al., Comput. Phys. Com- + onances, and, hopefully, near/at τ τ − thresh- mun. 130, 260 (2000); S. Jadach et al., old. All the physics topics on the CLEO-III list Phys. Rev. D 63, 113009 (2001); See also above will also be accessible to CLEO-c, but with http://jadach.home.cern.ch/jadach/ unique kinematical constraints [2]. KKindex.html. When the taus are produced near threshold, de- 6. Particle Data Group, R.M. Barnett et al., cays like τ πντ will produce a monochromatic Phys. Rev. D 54, 1 (1994). → + pion, which will tag τ τ − events with good ef- 7. S. Jadach and Z. Was, Comput. Phys. Com- ficiency and virtually no background. It should mun. 36, 191 (1985); and ibid, 64, 267 (1991); be possible to measure branching fractions with S. Jadach, J.H. Kühn, and Z. Was, Comput. sub-1% precision. It should be possible to obtain Phys. Commun. 64, 275 (1991); ibid, 70,69 greater precision in measurements of the Michel (1992), ibid, 76, 361 (1993). 13

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