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CLEO Results on Tau Michel Parameters Alan J View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server 1 CLEO Results on Tau Michel Parameters Alan J. Weinsteina aCalifornia Institute of Technology, Pasadena, CA 91125 We present measurements of the tau Michel Parameters made by the CLEO experiment. Three different analyses are performed: a spin-independent lepton spectrum analysis and a second spin-dependent analysis using 0 + `± vs. π∓π events, and a third spin-dependent analysis using π vs. π− events. the results are used to derive limits on the general four-fermion couplings, the mass of the charged Higgs in the MSSM, and a right-handed W in left-right models. Many of these measurements are more precise than the PDG world averages. 1. INTRODUCTION spin direction [1,4]. After integration over the unobserved neutrino momenta and the spin of `, Heavy lepton (µ, τ) decays are mediated (in and neglecting radiative effects we can write the the Standard Model) by the charged weak cur- charged lepton momentum spectrum as: rent, carried by W ± force bosons with a V A Lorentz structure. As a consequence, such decays− exhibit maximal parity violation, while conserv- 1 dΓ x2 = ing CP. The couplings of all the charged leptons Γ dxd cos θ 2 × to the W ± are consistent with being exactly equal 4ρ m (1 x) 12(1 x)+ (8x 6) + 24η ` − (universality). − 3 − m x τ Many extensions to the Standard Model pre- 4 dict small deviations from the V A law, and/or Pτ ξcos θ 4(1 x)+ δ(8x 6) − ± − 3 − fermion universality. Such deviations can be ob- 2 served in sensitive measurements of the Lorentz x [I(x ρ, η) Pτ A(x, θ ξ,δ)] ∝ | ± | structure of the weak interaction. In leptonic de- cays of the µ and τ leptons, in which the out- where ρ and η are the spectral shape Michel going neutrinos are unobserved, the dynamics of parameters and ξ and δ are the spin-dependent the decay can be described in terms of the Michel Michel parameters [1]; x = E`/Emax is the parameters [1]. The precise measurement of these daughter charged lepton energy scaled to the maximum energy E =(m2+m2)/2m in the parameters can be used to search for evidence of, max τ ` τ or provide limits on, processes which go beyond τ rest frame; θ is the angle between the tau spin the pure V A structure of the charged weak direction and the daughter charged lepton mo- current. In− particular, they are sensitive to the mentum in the τ rest frame; and Pτ is the po- presence of small scalar currents (such as those larization of the τ. In the Standard Model (SM), mediated by the charged Higgs of the Minimal the Michel Parameters have the values ρ =3/4, + Supersymmetric extensions [2] to the Standard η =0,ξ=1andδ=3/4. Since τ τ − events are + Model, MSSM), or small deviations from maxi- produced with no net polarization at e e− center- 0 mal parity violation (such as those mediated by of-mass energies below the Z mass, the lepton momentum spectrum alone is not sensitive to the the right-handed WR of left-right symmetric ex- tensions [3] to the Standard Model). spin-dependent parameters ξ and δ.Theselat- In the decays of the τ to `νν, information on ter parameters are measurable by analyzing the the decay can be extracted from the shape of the decays of both taus in an event. In addition, semi- momentum distribution of the lepton `, and from hadronic tau decays permit the measurement of the parameter h ξ = g g /(g2 +g2), some- its angular distribution relative to the parent τ ντ h v a v a times referred to as≡ the “tau− neutrino helicity”, 2 which takes the value +1 in the V A SM. 3. LEPTON SPECTRUM ANALYSIS − 0 In the first analysis [6], the ρ∓ π∓π decay → 2. CLEO DATA SAMPLE AND ANALY- is used to estimate the τ ∓ flight direction. The SIS angle between the ρ∓ momentum and the tau mo- mentum in the lab can be calculated (in the ab- Here we report on measurements of these sence of radiative effects). In approximately 60% Michel parameters in three separate analyses per- of the events, this angle is less than 11◦ and is formed on data from the CLEO II experiment used to estimate the τ ∓ direction, and thus the [5] at Cornell’s CESR collider, from the reaction recoiling τ ± direction in the lab. This permits + + e e− τ τ − at center of mass energy near 10.58 us to boost the daughter charged lepton `± mo- GeV. → mentum into the tau rest frame so estimated (the In the first analysis, events of the type `−νντ “pseudo-rest frame” [7]). For events in which the + 0 1 0 vs. π π ντ are selected The π±π system is above angle is greater than 11◦,the`± momen- used as a tag (to identify a tau pair event), and to tum is analyzed in the lab frame. estimate the tau direction in the lab. The lepton Muons with lab frame momentum pµ < 1.5 energy spectrum is measured and the parameters GeV/c are not well identified in the CLEO muon ρ and η are extracted for τ eνν and τ µνν. detectors. We can select decays with one charged → → In the second analysis, the same `−νντ vs. track which is inconsistent with being an electron, + 0 0 π π ντ sample used in the first analysis is again and which has no extra photons from π decays. used. Here, the π π0 system is used to analyze Such decays are most likely either τ µνν or ± → the spin of the decaying τ ±. The spin correlations τ πν. If the energy of the charged track in the 0 → produce a correlation between the π±π system pseudo-rest frame Eµ < 0.6mτ then the event is from one tau and the momentum of the charged kinematically inconsistent with being a τ πν lepton from the other tau. A fitter which ex- decay. We thus obtain a sample of τ →µνν tracts all the available information from the full decays with low momentum muons (particularly→ measured kinematics of these events is used to sensitive to the η parameter), with an estimated measure the parameters ρ, ξ, δ,and hντ . purity of 96%. The value of ρ obtained in this analysis super-| | The final τ eνν decay sample consists of sedes that of the first, and no attempt is made to 18587 events analyzed→ in the pseudo-rest frame re-measure η. and 12981 analyzed in the lab frame. The final In the third analysis, events of the type π−ντ τ µνν decay sample consists of 12580 events + → vs. π ντ are selected. The tau spin correlations with muons identified in the CLEO muon detec- produce correlations in the momenta of the two tor and 2931 events with muons identified kine- 2 pions, which are used to extract hντ . matically and analyzed in the pseudo-rest frame, The first and second analyses| use| 3.0 106 and 9186 events with muons identified in the produced tau pairs, while the third uses× only CLEO muon detector and analyzed in the lab 1.5 106. frame. Backgrounds from pions misidentified as For× the first two analyses, we select events hadrons are measured from the data and sub- where one τ decays leptonically (e∓ or µ∓), and tracted. All other backgrounds are estimated by 0 0 the other decays to π±π ντ .Theπ±πντ mode the Monte Carlo to be negligible. is used because it has a large branching fraction, The resulting momentum spectra were fitted to + + + negligible background from e e− e e−, µ µ−, Monte Carlo [8] distributions, including all radia- → or qq, and a high, well-understood trigger effi- tive effects, ρ∓ dynamics, spin correlations, and ciency. detector efficiency and resolution. The two elec- tron spectra were fitted with one parameter, ρe, with the result ρe =0.732 0.015. The three 1 Throughout this paper, charge conjugate processes are muon spectra were fitted with± two parameters, implied. 3 ρ and η , with the results ρ =0.747 0.055 µ µ µ ± and ηµ =0.010 0.174; these values are strongly correlated (see± Fig. 3). All five spectra were fitted simultaneously, with the constraint that ρ = ρ ρ , with the two parameters ρ e µ ≡ eµ eµ and ηeµ. Note, here, that ηeµ is the value of η appropriate for the muon decays, since the elec- tron decays are largely insensitive to the value of η. The subscripted ηeµ is simply a reminder that the result is obtained with the ρe = ρµ con- straint. The results are: ρ =0.735 0.014 and eµ ± ηeµ = 0.015 0.066. The− spectra± in the pseudo-rest frame, and the fit results, are shown in Figs. 1 and 2. the results Figure 2. The muon scaled pseudo rest frame are summarized in Fig. 3. Many systematic stud- energy spectra (solid points are data, histogram ies and fit variations were performed, all consis- is the fit function). Open circles give the MC tent with each other. The results quoted above predicted spectrum for η = 1. The addition of the include systematic errors. All these results are low momentum muons results in the discontinuity consistent with the Standard Model expectation observed at Xµ =0.6. that ρe = ρµ =3/4andηµ =0. 4. SPIN-DEPENDENT ANALYSIS The second analysis [9] uses the same event + 0 sample as in the first, `−νντ vs.
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