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Tau Electroweak Couplings Heavy Flavours 8, Southampton, UK, 1999 PROCEEDINGS Tau Electroweak Couplings 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 mea- sured [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).
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