Tau Electroweak Couplings

Heavy Flavours 8, Southampton, UK, 1999

PROCEEDINGS

Alan J. Weinstein∗ California Institute of Technology 256-48 Caltech Pasadena, CA 91125, USA E-mail: [email protected]

Abstract: We review world-average measurements of the tau lepton electroweak couplings, in both 0 + − − − decay (including Michel parameters) and in production (Z → τ τ and W → τ ντ ). We review the searches for anomalous weak and EM dipole couplings. Finally, we present the status of several other tau lepton studies: searches for lepton ﬂavor violating decays, neutrino oscillations, and tau neutrino mass limits.

1. Introduction currents. This will reveal itself in violations of universality of the fermionic couplings. Most talks at this conference concern the study Here we review the status of the measure- of heavy quarks, and many focus on the diffi- ments of the tau electroweak couplings in both culties associated with the measurement of their production and decay. The following topics will electroweak couplings, due to their strong inter- be covered (necessarily, briefly, with little atten- actions. This contribution instead focuses on the tion to experimental detail). We discuss the tau one heavy flavor fermion whose electroweak cou- lifetime, the leptonic branching fractions (τ → plings can be measured without such difficulties: eνν and µνν), and the results for tests of uni- the tau lepton. Indeed, the tau’s electroweak versality in the charged current decay. We then couplings have now been measured with rather turn to measurements of the Michel Parameters, high precision and generality, in both produc- which probe deviations from the pure V − A tion and decay. In all cases, the couplings of structure of the charged weak current. Next we the tau are identical, to high precision, to those review the charged current couplings in tau pro- − − of the electron and the muon. The leptonic cou- duction via W → τ ντ decay. Then we turn to plings thus form a standard against which the hy- neutral current couplings in tau production via pothesis of universality of all fermionic (including Z0 → τ +τ −. We review searches for anomalous quark) couplings can be tested. weak dipole moment couplings in Z0 → τ +τ −, Because the tau lepton is so massive, it de- and anomalous electromagnetic dipole moment cays in many different ways. The daughter decay couplings in Z0 → τ +τ −γ. We briefly review the products can be used to analyze the spin polar- searches for flavor changing neutral currents in ization of the parent tau. This can then be used lepton flavor violating (neutrinoless) tau decays, to study the spin dependence of the tau elec- and searches for neutrino oscillations involving troweak couplings. Further, since the tau is the the tau neutrino ντ . We present the current heaviest known lepton and a member of the third limits on the ντ mass. Finally, we summarize family of fermions, it may be expected to be more and review the prospects for further progress in sensitive to physics beyond the Standard Model τ physics in the coming years. (SM), especially to mass-dependent (Higgs-like) Most of these high-precision measurements ∗For the CLEO Collaboration. Work supported by US and sensitive searches for anomalous (non-SM) DOE Grant DE-FG03-92-ER40701. couplings have been performed, and refined, over Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein the last few years. There have been no dra- To test the hypothesis that all of the charged matic new results since the last Heavy Flavors weak current couplings are equal (ge = gµ = conference, only updated results with higher pre- gτ ), we must measure the muon lifetime, the cision. There are updated leptonic branching branching fraction B(µ → eνν), the tau lifetime, fractions from LEP; updated Michel parameter and the branching fractions B(τ → eνν)and measurements from LEP and CLEO; final re- B(τ→µνν). The muon properties are well mea- sults on tau polarization measurements and measured [1]. surements of the Z0 couplings from LEP; limits on neutral weak dipole moments from LEP and 2.1 Tau Lifetime SLD; new measurements of the rate for W → τν The tau lifetime has been measured by many ex- from LEP II, results on electromagnetic dipole periments with many different methods [2]. There moments from LEP, new m(ντ ) limits from CLEO; are recent measurements from L3 [3] and DEL- and new limits on lepton flavor violating (neutri- PHI [4]. noless) decays from CLEO. I draw heavily from An example of a decay length distribution, the presentations at the Fifth Workshop on Tau from DELPHI [4], is shown in figure 1. A sum- Lepton Physics (TAU’98), from September 1998. mary of recent measurements is given in figure 2. Other than neutrino oscillation observations The world average from 6 experiments, each with < which may involve νµ → ντ oscillations, all re- ∼ 1% precision, is ττ = (290.5 1.0) fs. cent measurements confirm the minimal Stan- dard Model predictions to ever increasing pre- 2.2 Leptonic Branching Fractions cision. Nevertheless, new physics may be just There are recent results on the tau leptonic branch- around the corner, waiting to be revealed by even ing fractions from ALEPH [5], DELPHI [6] and higher precision studies. OPAL [7]. Measurements from 5 experiments [8] are shown in figure 3, leading to the world aver- 2. Leptonic branching fractions, tau age values: − − lifetime, universality B(τ → e νeντ )=(17.81 0.07)% (2.5) B − → − The rate for tau decays to leptons is given by (τ µ νµντ )=(17.37 0.09)% (2.6) the universal charged weak current decay rate The branching fractions Be and Bµ are now formula for pointlike massive fermions: measured to 0.4% accuracy, i.e., at the level of the radiative corrections (equation 2.3). These precise results already provide limits Γ(τ → ντ µνµ)=ττB(τ→ντµνµ) (2.1) on simple extensions to the Standard Model, us- 2 2 2 5 GF gτ gµmτ ing equation 2.1. The η parameter (to be dis- = fµτ REW hη (2.2) 192π3 cussed in section 3 below) is inferred to be Here, the Fermi coupling constant GF is mea- η =0.013 0.022 (η = 0 in SM). (2.7) sured in µ decay, assuming gµge is 1. Here, we let them vary, in order to test the assumption of 700 universality. The phase space correction fµτ = DELPHI 2 2 600 preliminary f mµ/mτ is 0.9726 for τ → µνν and ≈ 1for

events / 0.25 mm 500 τ→eνν. The electroweak correction is 400 2

3 mτ α 25 2 300 REW = 1+ 2 1+ − π 5mW π 4 200 − +0.03% 0.4% (2.3) 100

-1 -0.5 0 0.5 1 1.5 2 and the correction due to possible scalar currents decay length (cm) is, in terms of the Michel parameter η, Figure 1: Tau ﬂight length distribution from DEL- hη =1/(1 + 4ηm`/mτ ) = 1 in SM. (2.4) PHI [4].

2 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

2 In addition, the ντ mass must be less than 38 =(1.000 0.003) (2.11) 2 MeV [9]. One can also put limits on mixing with gµ Bµ th ≡ a4 generation, anomalous electromagnetic com- ge fµτ Be plings, and compositeness [9]. 2 =(1.000 0.003) (2.12) B → 2.3 (τ `ννγ) from CLEO 99 We see that the strength of the charged cur- CLEO has made precision measurements of tau rent couplings (irrespective of their Lorentz struc- leptonic decays in the presence of a radiative ture) are equal to each other within 0.25%. (decay) photon [10], ﬁnding branching fractions in good agreement with Standard Model predic- 2.5 What Could Cause Lepton Universal- tions: ity Violation? Many extensions to the Standard Model predict B − (e νeντ γ)=(1.75 0.06 0.17)% violation of lepton universality. In fact, lepton SM =(1.86 0.01)% (2.8) universality is put in to the SM by hand, so that − → B(µ νµντ γ)=(0.361 0.016 0.035)% non-universal W `ν couplings can naturally SM =(0.368 0.002)% (2.9) appear if the model is not so constrained. In the Minimal Supersymmetric SM (MSSM), ∗ for Eγ > 10 MeV in the τ center of mass. decays via a charged Higgs (which couples more strongly to the heavy tau than to the lighter lep- 2.4 Lepton Universality tons) can interfere either constructively or de- structively with the W -mediated decay, enhanc- From the measurements of the tau lifetime and ing or suppressing the decay rate [11]. leptonic branching fractions, we can extract ra- If a fourth-generation massive ν4 or sterile νs tios which test the universality hypothesis ge = exists, and mixes with ντ , it will suppress all the gµ = gτ : decay rates and thus the total tau lifetime. The current accuracy of the measurements 2 5 gτ τµ mµ do not yield signiﬁcant limits on any of these ≡Be gµ ττ mτ models, illustrating the need to further improve =(1.000 0.003)2 (2.10) their precision. 2 B 5 gτ ≡ µ τµ mµ ge fµτ ττ mτ

Figure 2: Summary of recent tau lifetime measure- Figure 3: Summary of recent tau leptonic branching ments. fraction measurements.

3 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

3. Michel Parameters The tau Michel parameter measurements are now precision physics, although they are still far Although the strength of the charged weak in- from the precision obtained with muons [1]. They teraction in decays of the muon and tau are well are consistent with being entirely V −A in struc- measured, the Lorentz structure in tau decays is ture (left-handed vector couplings). They strongly − not as well established as it is for the purely V A limit the probability of right-handed τ couplings structure seen in muon decays. In general, the τ to the weak charged current PR; for example, couplings can have scalar (S), pseudoscalar (P), τ CLEO [19] sets the the limit PR < 0.044 at and tensor (T) terms as well as the vector (V) 90% CL. However, for left-handed τ couplings, it and axial vector (A) contributions built into the is currently not possible to distinguish between SM. Using a general ansatz for the couplings, in- scalar, vector, and tensor contributions. Inde- cluding all the lowest-order S, P, V, A, T terms, pendent information (e.g., from the cross section Michel [12] derived a form for the diﬀerential de- − − σ(ντ e → τ νe)) is needed to distinguish be- cay rate of the muon (and the tau), integrating tween the possible left-handed τ couplings. over the unobserved ν momenta and daughter ` spin. In terms of scaled energy x = E`/Emax, The limit on right-handed couplings can be 2 2 interpreted in terms of limits on right-handed with Emax =(m` +mτ)/2mτ, one has: h WR bosons. In Left-Right symmetric models [20], dΓ x2 4ρ =Γ 12(1 − x)+ (8x − 6) two charged boson mass eigenstates M1, M2 mix dxd cos θ 0 2 3 to give the “light” WL of the SM, and a heavy m`(1 − x) +24η WR. The parameters in these models are α = mτ x i 4 M(W1)/M (W2 ), and the mixing angle ζ;both − ξcos θ 4(1 − x)+ δ(8x − 6) (3.1) 3 are zero in the SM. The heavy right-handed WR ∝ x2 [I(x|ρ, η) A(x, θ|ξ,δ)] (3.2) will contribute to the decay of the tau, inter- − where Γ0 is given in equation 2.1. fering with the left-handed W , and producing The spectral shape Michel parameters, and deviations from the Standard Model values for their SM (V − A) values, are: the Michel parameters ρ and ξ.CLEO[19]ob- ! 2 tains limits on α and ζ in these models, shown 3 |gV | 3 ρ ' LL = (SM) (3.3) in ﬁgure 4. For mixing angle ζ = 0, they obtain V 2 V 2 2 4 |gLL| + |gLR| 4 MR > 304 GeV/c at 90 % CL, and for free mix- 2 V S∗ 2 η ∝<(gLLgRR + ···)= 0 (SM). (3.4) ing angle ζ, they obtain M > 260 GeV/c at 90 %CL. The spin polarization-dependent Michel parameters are: The consistency of the Michel parameters with ! V V 2 SM predictions permits a limit to be set on the |gLL|−3|gLR| ξ '− 2 = −1 (SM) (3.5) mass of a (scalar) charged Higgs boson, in the |gV | + |gV |2 LL LR ! context of the MSSM [11]. For the η parameter, 2 3 |gV | 3 δ ' LL = (SM). (3.6) V 2 V 2 4 |gLL| +3|gLR| 4 3100497-005 2 M (GeV / c ) 2 3.1 Michel Parameter measurements 800 400 200 0.2

There are updated results from LEP [13, 14, 15, 3 0.1 2 16] and CLEO [17]. The world averages, com- 1

0 piled for TAU’98 [18], assuming lepton univer- min tan sality, are: I 0.1

ρτ =0.750 0.011 (SM =3/4) (3.7) I 0.2 0 0.1 0.2 0.3 0.4 0.5 ητ =0.048 0.035 (SM = 0) (3.8) ξτ =0.988 0.029 (SM = 1) (3.9) Figure 4: Limits on the mass ratio α and the mixing ξτ δτ =0.735 0.020 (SM =3/4).(3.10) angle ζ of a Left-Right symmetric model [19].

4 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein the dependency is: 4.1 W → τν at LEP II

2 2 η ≈− mτmµtan β/(2mH ), (3.11) All four LEP II experiments use the reaction e+e− → W +W − to measure the ratio of rates with similar formulas for ξ and ξδ. Using the (W → τν): (W →µν): (W →eν). The re- world average measurements of η, ξ,andξδ com- sults are summarized [21] in figure 6. There is bined, one obtains: excellent consistency between experiments, final state leptons, and SM predictions. Charged cur- 2 mH > 2.5tanβ GeV/c at 90% CL. (3.12) rent universality is confirmed to 4.0% via these measurements. This is competitive with other direct and indirect search limits (shown in figure 5) for two-Higgs- > 4.2 W → τν from pp¯ doublet mixing angles tan β ∼ 30. DELPHI has taken the analysis one step fur- Real W bosons are also produced at pp¯ colliders, ther, by probing derivative terms in the inter- via the reaction pp¯ → W X, W → `ν. There are action Lagrangian (beyond the Michel ansatz). measurements of the coupling ratio gτ /ge from DELPHI measures [16] the anomalous tensor cou- UA1, UA2, CDF, and D0. The world average [22] pling κ by analyzing the tau leptonic decays with is gτ /ge =1.003 0.025, confirming charged cur- the usual Michel parameters fixed to their SM rent universality at the 2.5% level. As seen in values. They measure Section 2 above, charged current universality is tested in tau leptonic decays to 0.25%. κ = −0.029 0.036 0.018, (3.13) in agreement with the SM expectation of κ =0. 5. Z0 Couplings Once again, many extensions to the SM predict deviations of these parameters from their The weak neutral current couplings of the tau SM values. It is thus worth improving the preci- are directly measured in tau pair production via sion of these measurements, to push the limits on e+e− → Z0 → τ +τ −. All four LEP experiments, contributions from charged Higgs, right-handed and SLD, measure a large number of relevant ob- W ’s, and other anomalous couplings. servables.

4. W → τν W Leptonic Branching Ratios ALEPH W→eν 11.20 ± 0.85 DELPHI W→eν 9.90 ± 1.21 The strength of the weak charged current cou- L3 W→eν 10.50 ± 0.92 → ν ± pling to the τ can also be measured in τ produc- OPAL W e 11.70 0.97 LEP W→eν 10.92 ± 0.49 tion from real W decays. ALEPH W→µν 9.90 ± 0.84 DELPHI W→µν 11.40 ± 1.21 L3 W→µν 10.20 ± 0.92 OPAL W→µν 10.10 ± 0.86 LEP W→µν 10.29 ± 0.47 160 140 ALEPH W→τν 9.70 ± 1.06 DELPHI W→τν 11.20 ± 1.84 120 L3 W→τν 9.00 ± 1.24 →τν ± 100 OPAL W 10.30 1.05 LEP W→τν 9.95 ± 0.60 80 60 LEP W→lν 10.40 ± 0.26 40 -1 2 10 1 10 10 81012 Br(W→lν) [%]

Figure 5: Direct and indirect search limits for Figure 6: Branching fractions B(W → `ν`)mea- charged Higgs mass versus tan β. sured by the four LEP II experiments [21].

5 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

5.1 Rτ and AFB the SLC [26]. These are shown in figure 9. From these measurements, they form the asymmetry The LEP experiments measure the ratio Rτ = τ Γ(Z → hadrons)/Γ(Z → ττ), and the forward- ALR(cos θ). This allows them to extract values 0 + − for Ae and Aτ of relatively high precision, despite backward asymmetry AFB(Z → τ τ ). The LEP averages for these quantities [23] and for low statistics. They obtain [26] the analogous quantities for the light leptons, are Aτ =(14.21.9)%; Ae =(15.00.7)%. (5.3) shown in figure 7. All three lepton species have values consistent with each other and with the SM prediction (assuming universality of the weak 5.4 NC Lepton Universality neutral current). In particular, the equality Re = The measurements discussed in this section can Rµ = Rτ is tested to a precision of 0.3%. be combined to extract the vector and axial vector weak neutral current coupling constants gv 0 5.2 τ polarization at Z and ga for the tau (and the other leptons). The All four LEP experiments measure the tau polar- results from LEP and SLD for all three charged ization Pτ (cos θ) as a function of the τ produc- leptons is summarized [27] in figure 10. tion angle θ, using the decay modes eνν, µνν, πν, There is fine agreement between experiments, ρν,and3πν. From the measured Pτ (cos θ) dis- and all the leptonic couplings are consistent with tributions (see example in figure 8), they extract each other and with the SM prediction. The lat- the asymmetry parameters ter depends on the SM Higgs mass, and it can be seen that a low-mass Higgs is favored. Non- A ≡ ` ` ` 2 ` 2 ` (2gvga)/((gv) +(ga) ) (5.1) SM contributions, as measured by the model- independent S and T parameters [28] are strongly for ` = e and τ. A summary of the results from constrained [27]. LEP [25] is also shown in figure 8. The world Since all measurements are consistent with average results are the SM predictions, they can be used to extract 2 Aτ =(14.31 0.45)%; Ae =(14.79 0.51)%. the value of the SM parameter sin θeff . This (5.2) can then be compared with the value, and er- rors, for this parameter obtained from studies τ 0 5.3 ALR(cos θ) from SLD of Z → qq¯. This comparison [27] is shown SLD measures the tau polarization as a function in figure 11. We see that the measurement of τ provides one of the most precise methods for of the τ production angle θ, separately for left- 2 and right-handed beam electron polarizations at obtaining sin θeff . The LEP and SLD results are completely consistent for the lepton measure- b c ments; the LEP values for Rb, AFB, AFB pull 0.0228 + − l l Preliminary + − the LEP average away from SLD, but not very e e µ+µ− significantly so. τ+τ− 0.0188 Aτ and Ae measurements at LEP

fb ALEPH (single τ) τ 0,l 0.2 Data L3 ALEPH ( direction)

A m No Universality Aτ DELPHI t Universality 0.1 L3 α s OPAL 0.0148 0 τ P m -0.1 H ALEPH (single τ) A e ALEPH (τ direction) -0.2 DELPHI

L3 -0.3 0.0108 OPAL -1 -0.5 0 0.5 1 20.6 20.7 20.8 20.9 θ cos 10 12 14 16 18 20

Rl Figure 8: Left: Measurement of Pτ (cos θ) from L3 0 Figure 7: Measurements of Rτ and AFB for Z → [24]; Right: summary of the results from LEP on Aτ + − ` ` , from LEP [27]. and Ae from tau polarization [25].

6 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

6. Dipole Moments Predictions for the values of these weak dipole moments, in the SM and beyond, are [30, 32]: The pure vector nature of the electromagnetic W − × −6 couplings is modified due to radiative corrections, aτ = (2.1+0.6i) 10 (SM) (6.3) −5 which induce magnetic dipole tensor couplings. → 10 (MSSM) (6.4) If the lepton or quark is composite, and if CP is → 10−3 (composite) (6.5) violated, electric dipole couplings also appear. W −37 dτ =3×10 e·cm (SM-CKM) (6.6) Analogous couplings also appear for the weak → few × 10−20 (MSSM, LQ).(6.7) interactions. In addition to the SM Lagrangian 0 for Z ττ, which includes vector and axial vec- The → symbol denotes that predictions can range tor couplings, it is natural to consider extensions up to values as large as those shown. that add tensor couplings, corresponding to weak Weak magnetic dipole couplings produce parity- electric and weak magnetic dipole moment cou- odd azimuthal asymmetries [31]. For example, in + + plings [29]. τ → π ντ , the expectation value for < pˆτ + × W · + w 2 pê+ pˆπ > is proportional to aτ .Ifitisanoma- 1 eF2 (q ) µν L = LSM + · ψσ¯ ψZµν lously large, it would be measurable at LEP. L3 2 2mτ w 2 has measured this azimuthal asymmetry using i eF3 (q ) µν → − · ψσ¯ γ5ψZµν . (6.1) τ πν and ρν. Seeing no significant asymme- 2 2mτ try, it sets the limits [30] Here, ψ is the quantum field of the tau, Zµν is the W × −3 0 w 2 w 2 Re(aτ )=(0.0 1.6 2.3) 10 (6.8) Z field strength tensor, and F2 (q )andF3 (q ) Im(aW )=(−1.03.64.3) × 10−3 (6.9) are the weak magnetic and weak electric form τ factors, respectively. The anomalous weak mag- 6.1 CP violating Weak-Electric Dipole Mo- netic moment, and the CP-violating weak electric ment dipole moment, of the tau are: A non-zero weak electric dipole moment (weak w 2 EDM) of the tau would be evidence for both w ≡ w 2 w≡eF3 (mZ ) aτ F2 (mZ ),dτ (6.2) substructure and CP violation in the lepton sec- 2mτ tor. It would induce modifications to the spin structure in e+e− → Z0 → τ +τ − [29]. The sub- sequent tau decays can be used to analyze the

-0.031 68% CL contours Preliminary

t + t - -0.035 mH Vl

g mt +- ALR (SLD) ll -0.039 e+ e-

m + m - -0.043 -0.503 -0.502 -0.501 -0.500

gAl

Figure 9: The τ production angle distribution for Figure 10: Extracted values for the weak neutral left- and right-handed beam electron polarizations current couplings gv and ga for the leptons, from LEP from SLD [26]. and SLD [27], compared with SM predictions.

7 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein spins of both taus in an event, and seach for CP- its [34]: odd spin polarizations and correlations. These Re(aW ) < 2.47 × 10−3 (6.13) also take the form of triple product observables τ W × −3 which are CP-odd. Im(aτ ) < 1.25 10 (6.14) W −17 A set of optimized CP-violating observables Re(dτ ) < 1.35 × 10 e · cm (6.15) W −17 have deen defined [29], and have been measured Im(dτ ) < 0.87 × 10 e · cm (6.16) by the LEP experiments [33], using most tau which are quite competitive with the LEP aver- decays (`, π, ρ, a1) as spin analyzers. Simulated spectra, illustrating the effect for non-zero weak ages, despite much smaller statistics. EDM, are shown in figure 12. The measurements W W 6.3 EM dipole moments of Re(dτ ), Im(dτ ) from LEP are shown in fig- 0 ure 13, and the limits from the combined data Despite the dominance of the Z over the virtual are [32]: photon at LEP I, the electromagnetic dipole moments can be measured using radiative events, W −18 + − → 0 → + − |Re(dτ )| < 3.0 × 10 e · cm (6.10) e e Z τ τ γ. Anomalously large elec- W −18 tromagnetic dipole moments will produce an ex- |Im(dτ )| < 9.2 × 10 e · cm (6.11) cess of events with a high energy photon, away | W | × −18 · dτ < 9.4 10 e cm (6.12) from both the beam e+ and τ + momentum axes [35]. L3 [36] and OPAL [37] compare the observed spectra in Eγ vs cos θγ for radiated photons to 6.2 Weak Dipole Moments: SLD predictions from the SM with the addition of The electron beam longitudinal polarization avail- anomalously large electromagnetic dipole moments, γ γ able at the SLC collider enhances the ability of and set limits on aτ and dτ . The L3 spectra are the SLD detector to measure the weak dipole mo- shown in figure 14. The resulting limits are [38]: W ments, especially Im(dτ ). They do an unbinned γ α |aτ | < 0.06 (SM : =0.011) (6.17) likelihood fit to the full event kinematics, using 2π γ −16 tau pairs which decay to (`, π, ρ). This allows |dτ | < 3.1 × 10 (SM :0(CP))6 . (6.18) them to measure the real and imaginary parts For comparison, the limit on the electric dipole of both weak dipole moments, and set the lim- γ −25 moment of the electron is |de | < 5 × 10 e · cm [1]. Preliminary

0,l ± Afb 0.23117 0.00054 A 0.23202 ± 0.00057 7. Other searches for new couplings τ Average Aτ− ± Ae 0.23141 0.00065 0,b ± Afb 0.23225 0.00038 Searches have also been made for other non-SM A 0,c 0.2322 ± 0.0010 fb currents such as the ﬂavor-changing neutral cur- 0.2321 ± 0.0010 fb ↔ ↔ Average(LEP) 0.23189 ± 0.00024 rents (FCNC) τ e and τ µ in neutrinoless χ2/d.o.f.: 3.3 / 5 ↔ ↔ ± tau decay, and ντ νe and ντ νµ in neutrino Alr(SLD) 0.23109 0.00029 Average(LEP+SLD) 0.23157 ± 0.00018 oscillation experiments. χ2/d.o.f.: 7.8 / 6

10 3 ] GeV [

H 2 1/α= 128.896 ± 0.090 m 10 α ± s= 0.119 0.002 ± mt= 173.8 5.0 GeV 0.230 0.232 0.234 2θlept sin eff Figure 12: Simulation of the distribution of optimal CP-violating observables in Z0 → τ +τ −, for the case 2 Figure 11: Extracted values for sin θeff from mea- of no WEDM (left), and for non-zero WEDM (right) surements at the Z0 [27]. [32].

8 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

7.1 Neutrinoless tau decay which will push below the 10−7; they will be rare τ decay experiments. All known tau decays proceed via the weak charged − − current: τ → ντ W . Flavor changing neu- 7.2 Neutrino oscillations tral current decays such as τ − → e−X0 and τ − → µ−X0,whereX0 is some neutral cur- If one or more of the three neutrino flavor eigen- 0 rent such as the photon, Z , or some new cur- states (νe, νµ, ντ ) have mass and can couple to rent, violate Lepton Flavor conservation. Lepton the others, they will mix and induce neutrino os- Flavor Violating (LFV) decays include: τ − → cillations, or (effective) flavor changing neutral `−γ, `−`+`− Z0 → τ −e+, τ −µ+ τ − → `−M 0, currents. − + − 0 ` P1 P2 . Here, ` is e or µ, M is a neutral me- Evidence for neutrino oscillations comes from son, and P is a charged pseudoscalar meson. several different experiments [43]. If the solar, Another class of decays violate Lepton Num- atmospheric, and LSND observations are all cor- th ber conservation, as well. Lepton Number Vio- rect, it seems to require a 4 (sterile? very mas- − + − − lating (LNV) decays include: τ ` P1 P2 ,and sive?) neutrino [43]. pX¯ 0. The latter conserves the difference between Only the atmospheric neutrino anomaly, in baryon number and lepton number (B − L). which a deficit of muon neutrinos is observed SUSY, GUTS, Left-Right symmetric models, from cosmic ray showers, is likely to involve the and superstring models all predict LFV, LNV, ντ . The Super-Kamiokande experiment sees ev- and violations of the universality of the dominant idence for νµ → νX oscillations [44], where νX th current couplings [39] The effects are small, of the may be a ντ or a sterile 4 generation neutrino order of 10−6 or smaller, and are only now within νs; however, some evidence favors νµ → ντ over the reach of experiment [40]. νµ → νsterile [45]. The deficit is consistent with 2 ∼ The most sensitive search for neutrinoless de- maximal neutrino mixing (sin 2θ 1), and mass- 2 ∼ −2 2 cays has been by the CLEO Collaboration, which squared difference ∆mµX 10 eV . searches for τ → µγ with 12.6 million pro- This observation has spawned a host of mid- duced tau pairs, and sets the limit [41]: B(τ → and long-baseline accelerator experiments, in which µγ) < 1.1 × 10−6 at 90% CL, which is in the a νµ neutrino beam from pion decay travels some range of model parameters for some supersymmetric models [39]. 500 (a) L3 CLEO also searched for 28 different neutri- 400 Data noless decay modes, using 4.4 million produced MC (all) 300 MC (non-ττγ) tau pairs [42]. The limits on the branching frac- aτ = 0.1 / 2GeV −6 γ 200 tions are on the order of few ×10 or greater. N 100 The present bounds are approaching or reach- 0 ing levels where some model parameter spaces 0 1020304050 E (GeV) can be excluded. The models can also be pushed γ 250 above the present limits; so we are already begin- (b) L3 200 Data ning to exclude such efforts. The current limits MC (all) will be improved by the B Factory experiments, 150 MC (non-ττγ) aτ = 0.1

/ 0.1rad 100 γ N w [ −18 ⋅ ] w [ −17 ⋅ ] Re (dτ ) 10 e cm Im (dτ ) 10 e cm 50

ALEPH(*) −0.29 ± 2.59 ± 0.88 DELPHI(*) −1.48 ± 2.64 ± 0.27 DELPHI(*) −0.44 ± 0.77 ± 0.13 0 OPAL 0.72 ± 2.46 ± 0.24 OPAL 0.35 ± 0.57 ± 0.08 0 0.5 1 1.5 2 2.5 3 −4.4 ± 8.8 ± 13.3 L3 ψγ (rad)

LEP −0.34 ± 1.50 LEP 0.07 ± 0.46 + − -10 0 10 -2 0 2 Figure 14: Spectra of Eγ and cos θγ from L3 τ τ γ events, compared with MC predictions with and Figure 13: Summary of recent measurements of the without an anomalously large magnetic dipole mo- weak electric dipole moment of the tau [32]. ment [36].

9 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein distance, allowing it to oscillate into a neutrino The technique that has yielded the best lim- of different flavor, which is then detected by a de- its on the ντ mass in the tens-of-MeV region tector capable of distinguishing νµ → µX from is the study of the two-dimensional mass and νµ → ντ → τX. Two mid-baseline experiments energy spectrum of the nπ final state in τ → − at CERN, CHORUS [46] and NOMAD [47], have (nπ) ντ , n ≥ 3. A deficit of events in the corner completed their run. Having failed to observe of mnπ, Enπ space indicates the recoil of a mas- the latter reaction, they exclude νµ → ντ for sive neutrino. However, the spectrum is falling > > ∆m2 ∼ 40 eV2,sin22θ∼2×10−4,asshown sharply there, leading to very limited statistics; in figure 15. and the spectral function governing that spec- In order to reach the small ∆m2 suggested trum is not precisely known. The best limits ob- by Super-K, a new generation of long-baseline tained so far [49] are listed in Table 1. experiments are being prepared [48], including 0 K2K, FNAL to MINOS, and CERN to Gran Sasso. ALEPH 5π(π ) 22.3 MeV These experiments will probe the region down to ALEPH 3π 30 MeV > ∆m2 ∼ 10−3 eV2,sin22θ∼10−1, as illustrated ALEPH both 18.2 MeV in figure 16. The understanding of these flavor OPAL 5π 39.6 MeV changing neutrino couplings is one of the major DELPHI 3π 28 MeV goals of particle physics in the next decade. OPAL 3π − vs − 3π 35 MeV CLEO (98) 5π,3π2π0 30 MeV CLEO (98) 4π 28 MeV

8. Limits on mντ Table 1: Summary of limits on mντ from τ → − ≥ Requiring the mass density of neutrinos to be (nπ) ντ , n 3. less than that required to over-close the universe excludes stable neutrinos with masses larger than It is interesting to note that the limits from 65 eV [49]. However, if neutrinos decay, they can CLEO [50] are not as tight as those from LEP, evade that limit. For lifetimes in the range of ∼1 despite much larger statistical samples. Indeed, there are many subtle issues involved in making day <τντ <∼few years, neutrino masses on the these measurements, regarding resolution, back- order of ∼ 5

CHORUS NOMAD CCFR

E531

CHORUS (Aim)

CDHS

Figure 16: Exclusion limits for νµ → ντ in 2 2 Figure 15: Exclusion limits for νµ → ντ in the space the space of ∆mν versus sin 2θmix, expected 2 2 of ∆mν versus sin 2θmix, from recent mid-baseline from the ICARUS long-baseline experiment. The experiments. [46]. Kamiokande observation is shown in yellow.

10 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

2 potentially improve the limits to the 10 MeV/c [3] A.P. Colijn for the L3 Collaboration, in the range. proceedings of Tau ’98, Nucl. Phys. 76 (Proc. Suppl.) (1999) 101. 9. Future prospects, and conclusions [4] A. Andreazza et al., DELPHI Collaboration, DELPHI-99-133, submitted to HEP’99, Tam- Experiments at LEP, SLD, and CLEO have pro- pere, Finland, July 1999. duced a wealth of rather precise measurements [5] H. Videau et al., ALEPH Collaboration, of the electroweak couplings, including limits on ALEPH 99-014, submitted to HEP’99, Tam- a range of potential couplings beyond the Stan- pere, Finland, July 1999. dard Model ones. But new physics may (hope- [6] P. Abreu et al., DELPHI Collaboration, Eur. fully) be just around the corner, and higher pre- Phys. J. C10(1999) 201. cision in these very fundamental measurements [7] K. Ackerstaff et al., OPAL Collaboration, Phys. may reveal it. The fact that the tau is the heavi- Lett. B 447 (1999) 134. est known lepton, free of uncertainties from non- [8] B. Stugu, in the proceedings of Tau ’98, Nucl. perturbative physics, makes it a particularly sen- Phys. 76 (Proc. Suppl.) (1999) 123. sitive probe of new, high mass scale physics. [9] M.T. Dova, J. Swain and L. Taylor, in the 0 The LEP Z program is now over, but the B proceedings of Tau ’98, Nucl. Phys. 76 (Proc. Factories now coming on line (CLEO III, BaBar, Suppl.) (1999) 101. 7 + − and Belle) will produce on the order of 10 τ τ [10] T. Bergfeld et al., CLEO Collaboration, per year. This will permit a wealth of new mea- hep-ex/9909050, submitted to Phys. Rev. D. surements, including: rare decays (7πν, ηππν, [11] A. Stahl, Phys. Lett. B 324 (1994) 121. etc.); forbidden (ν-less) decay (limits?); mντ to < ∼ 10 MeV; greater precision on universality tests; [12] L. Michel, Proc. Phys. Soc. London A 63 (1950) 514; T. Kinoshita and A. Sirlin, Phys. Rev. 108 greater precision on Michel Parameters, probing (1957) 844; C. Bouchiat and L. Michel, Phys. Higgs and WR couplings; weak and EM dipole Rev. 106 (1957) 170; L. Okun and A. Rudik, moments, CP violation; and deeper studies of J. Expt. Theor. Phys. (USSR) 32 (1957) 627 low-mass meson dynamics. We may also see the [Sov. Phys. JETP 6 (1957) 520]. observation of νµ ↔ ντ oscillations in the long- [13] M. Wunsch for the ALEPH Collaboration, in baseline experiments now in preparation. the proceedings of Tau ’98, Nucl. Phys. 76 We can expect continued progress in τ physics (Proc. Suppl.) (1999) 159. in the coming years, and maybe (someday) some [14] M. Acciarri et al.,L3Collaboration,Phys. Lett. surprises! B 438 (1998) 405. [15] K. Ackerstaff et al., OPAL Collaboration, Eur. Acknowledgments Phys. J. C8(1999) 3. [16] P. Seager et al., DELPHI Collaboration, The author acknowledges many fruitful conver- DELPHI-99-129, submitted to HEP’99, Tam- sations with M. Davier. Thanks go also to the pere, Finland, July 1999. members of the LEP and SLD collaborations who [17] A.J. Weinstein for the CLEO Collaboration, provided their latest results. Finally, the author in the proceedings of Tau ’98, Nucl. Phys. 76 thanks the organizers of Heavy Flavors 8 for a (Proc. Suppl.) (1999) 165. very enjoyable, fruitful, and well-run conference. [18] A. Stahl, in the proceedings of Tau ’98, Nucl. Phys. 76 (Proc. Suppl.) (1999) 173. References [19] J. Alexander, et al., CLEO Collaboration, Phys. [1] C. Caso et al., the Particle Data Group, Eur. Rev. D56(1997) 5320. Phys. J. C3(1998) 1. [20] M.A.B. Bég, R. V. Budny, R. Mohapatra and [2] SR Wasserbaech, in the proceedings of Tau ’98, A. Sirlin, Phys. Rev. Lett. 38 (1977) 1252. Santander, Spain, September 1998, Nucl. Phys. [21] T. Moulik, in the proceedings of Tau ’98, Nucl. 76 (Proc. Suppl.) (1999) 107. Phys. 76 (Proc. Suppl.) (1999) 173.

11 Heavy Flavours 8, Southampton, UK, 1999 Alan J. Weinstein

[22] S. Protopopescu, in the proceedings of Tau ’98, [36] M. Acciarri et al., L3 Collaboration, Phys. Lett. Nucl. Phys. 76 (Proc. Suppl.) (1999) 91. B 434 (1998) 169. [23] R.J. Sobie, in the proceedings of Tau ’98, Nucl. [37] K. Ackerstaff et al., OPAL Collaboration, Phys. Phys. 76 (Proc. Suppl.) (1999) 75. Lett. B 431 (1998) 188. [24] M. Acciarri et al.,L3Collaboration,Phys. Lett. [38] L. Taylor, in the proceedings of Tau ’98, Nucl. B 429 (1998) 387. Phys. 76 (Proc. Suppl.) (1999) 237. [25] R. Alemany, in the proceedings of Tau ’98, Nucl. [39] R. Barbieri and L.J. Hall, Phys. Lett. B 338 Phys. 76 (Proc. Suppl.) (1999) 55. (1994) 212; J. Hisano et al., Phys. Lett. B 357 (1995) 579; J. Hisano and D.Nomura, Phys. Rev. [26] P.L. Reinertsen for the SLD Collabora- D59(1999) 116005; K.S. Babu, B. Dutta and tion, in the proceedings of Tau ’98, Nucl. R.N. Mohapatra, Phys. Lett. B 458 (1999) 93; Phys. 76 (Proc. Suppl.) (1999) 45. See also S.F. King and M. Oliveira, Phys. Rev. D60 hep-ex/9908006, 1999. (1999) 035003. [27] LEP and SLD Electroweak Working Group, [40] R. Stroynowski, in the proceedings of Tau ’98, CERN-EP.99-15 (1999). Nucl. Phys. 76 (Proc. Suppl.) (1999) 185, and [28] M.E. Peskin and T. Takeuchi, Phys. Rev. D46 references therein. (1992) 381. [41] S. Ahmed et al., CLEO Collabora- [29] W. Bernreuther, U. Löw, J.P. Ma, and tion, hep-ex/9910060, Submitted to O. Nachtmann, Z. Physik C43(1989) 117; Phys.Rev.Lett. (1999). W. Bernreuther and O. Nachtmann, Phys. [42] D.W. Bliss et al., CLEO Collaboration, Phys. Rev. Lett. 63 (1989) 2787; W. Bernreuther, Rev. D57(1998) 5903; and R. Godang et al., G.W. Botz, O. Nachtmann, and P. Overmann, CLEO Collaboration, Phys. Rev. D59(1999) Z. Physik C52(1991) 567; W. Bernreuther, 091303. O. Nachtmann, and P. Overmann, Phys. Rev. D [43] For a review, see, for example, MC. Gonzalez- 48 (1993) 78; W. Bernreuther and P. Overmann, Garcia, in the proceedings of Tau ’98, Nucl. Z. Physik C73(1997) 647; W. Bernreuther, Phys. 76 (Proc. Suppl.) (1999) 185; and P. Lan- A.Brandenburg, and P. Overmann, Phys. Lett. gacker, in Nucl. Phys. 77 (Proc. Suppl.) (1999) B 391 (1997) 413. 241. [30] J. Bernabéu, G.A. González-Sprinberg, [44] Y. Fukuda et al., Super-Kamiokande Collabora- M. Tung, J. Vidal, Nucl. Phys. B 436 (1995) tion, Phys. Rev. Lett. 81 (1998) 1562. 474; W. Hollik, J.I. Illana, C. Schappacher, D. Stöckinger, S. Rigolin, KA-TP-10-1998, [45] T. Kajita, Super-Kamiokande Collaboration, in hep-ph/9808408 (1998). the proceedings of Neutrino ’98, Nucl. Phys. 77 (Proc. Suppl.) (1999) 123. [31] J. Vidal, J. Bernabeu and G. Gonzalez- Sprinberg, hep-ph/9812373 and in the proceed- [46] E. Eskut et al., CHORUS Collaboration, Phys. ings of Tau ’98, Nucl. Phys. 76 (Proc. Suppl.) Lett. B 434 (1998) 205. (1999) 165. [47] P. Astier et al., NOMAD Collaboration, Phys. Lett. B 453 (1999) 169. [32] A. Zalite, in the proceedings of Tau ’98, Nucl. Phys. 76 (Proc. Suppl.) (1999) 229. [48] See, for example, contributions from NuMi and MINOS (S.G. Wojcicki, P. 182); CERN-LNGS [33] M. Acciarri et al., L3 Collaboration, Phys. (P. Picchi, p. 187); K2K (K. Nishikawa, p. 198); Lett. B 426 (1998) 207; K. Ackerstaff et al., in the proceedings of Neutrino ’98, Nucl. Phys. OPAL Collaboration, Z. Physik C74(1997) 77 (Proc. Suppl.) (1999) 401. 403; D. Busilic et al., ALEPH Collaboration, Phys. Lett. B 346 (1995) 371; M.C. Chen et al., [49] R. McNulty, in the proceedings of Tau ’98, Nucl. DELPHI Collaboration, DELPHI 97-70 CONF Phys. 76 (Proc. Suppl.) (1999) 409, and refer- 56 (1997). ences therein. [34] K. Abe et al., SLD Collaboration, SLAC-PUB- [50] R. Ammar et al., CLEO Collaboration, Phys. 8163, Submitted to Phys.Rev.Lett. (1999). Lett. B 431 (1998) 209; M. Athanas et al., CLEO Collaboration, hep-ex/9906015, submit- [35] S.S. Gau, T. Paul, J. Swain, L. Taylor, Nucl. ted to Phys. Rev. Lett. (1999). Phys. B 523 (1998) 439.