CLEO Results on Tau Michel Parameters Alan J

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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 decays 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 extensions [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 momentum 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 electron 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 electron 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 constraint. 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. π π ντ , but the kinematically-identiﬁed low-momentum muons are not used. We analyze the τ + + 0 →+ π π ν¯τ decay to extract information on the τ spin orientation; the QED-predicted spin corre- + + lations in e e− τ τ − thus give information → on the recoil τ − spin direction. We then analyze the momentum of the charged lepton in the τ − `−ν`ν τ decay in order to extract ξ and δ, separately→ − for electronic and muonic decays. At the same time, we measure the magnitude of

the tau neutrino helicity hντ , and re-measure the ρ parameter. We assume the value of η as measured from the ﬁrst analysis. We also select 11177 0 + 0 Figure 1. The electron scaled pseudo rest frame events of the type π−π ντ vs. π π ντ ,toex- energy spectra (solid points are data, histogram tract hν with greater precision. | τ | is the ﬁt function). Open circles give the MC The ρ+ π+π0 decay is used to analyze the → predicted spectrum for V +A. Events with X>1 parent tau spin orientation. The energy of the result from the imperfect reconstruction of the τ π+π0 system, and the angle of the pion mo- direction. mentum in the π+π0 rest frame relative to the π+π0 momentum in the lab frame can be combined to give a “polarimeter” variable [10] ω = ~ p~τ Hτ = ω(Eρ, cos θ(ρ ππ)). Clear cor- · φντ → D E 4

all the observed particles. Evaluation of the likelihood per event re- quires integration over the unobserved neutrinos and radiated photons: a 22 dimensional in- tegral. This is performed using a unique “re- verse Monte Carlo” technique. All major “backgrounds” (π, Kπ, π2π0 ππ0, π µ) are modeled, with full Michel parameter→ dependence.→ The detector efficiency and resolution is fully modeled. The fit procedure was tested with many ensem- bles of Monte Carlo events with all three topolo- gies (e vs.ρ, µ vs.ρ, ρ vs. ρ), including backgrounds;− no bias− was observed.− − A measurement of the spin-dependent Michel parameters allows one to distinguish the Standard Figure 3. Results from the lepton spectrum anal- Model V A interaction (left-handed ν ) from − τ ysis. The shaded band denotes the electron mode V + A (right-handed ντ ). The probability that a result, the large dotted contour indicates the right-handed (massless) tau neutrino participates muon mode 1σ error ellipse obtained in the η ρ in the decay can be expressed as plane, and the small dark ellipse indicates the cor-− responding 1σ result obtained from the simulta- P τ =1/2[1+1/9(3ξ 16ξδ)] , R − neous fit to both modes. The Standard Model τ expectation is indicated by the cross. and PR = 0 for the SM V A interaction. The results of the fits to− the e vs.ρ sample are: − relations between the value of ω from the τ + de- ρe =0.747 0.012 0.004 (SM =3/4) ± ± cay and the charged lepton momentum from the ξ =0.979 0.048 0.016 (SM =1) e ± ± τ − decay are observed, consistent with Standard ξ δ =0.720 0.032 0.010 (SM =3/4). Model expectations. e e ± ± To make full use of all the available kinemati- All measures of goodness-of-fit yield satisfactory cal information, we do a multi-dimensional like- results. From the distribution of the likelihoods lihood fit to all of the observed three-momenta for each event as compared to Monte Carlo ex- in the lab, using the full production and decay pectations, the confidence level (CL) for the fit is matrix element, including the effects of radiation 73%. Comparisons of various kinematical quanti- (ISR/FSR, decay, and external bremsstrahlung). ties between the data and the results of the fit are Schematically, for the µ vs.ρ sample, shown in Fig. 4. We extract the limit P R < 0.065 − τ 2 at 90% CL. The last three plots in this figure = H1 P [L1 + ρL2 + ηL3] clearly demonstrate the spin correlations and the |M| × × αβ +h H0 C [ξL0 + ξδL0 ]. effectiveness of the fit in modeling them. ντ 1α × × 1β 2β For the µ vs.ρ sample, the results (using ηµ = Here, H1 describes the spin-independent part of 0.010 from the− first analysis) are: the τ ππ0ν decay rate, L through L de- → 1 3 scribe the spin-independent part of the τ `νν ρµ =0.750 0.017 0.045 decay rate (with explicit Michel parameter→ de- ± ± ξµ =1.054 0.069 0.047 pendence), and P describes the spin-independent ± ± + ξµδµ =0.786 0.041 0.032, part of the τ τ − production. H10α, L10 β and L20 β, ± ± and Cαβ describe the analogous spin-dependent with a confidence level for the fit of 21%. We R quantities. All are functions of the momenta of extract the limit Pτ < 0.067 at 90% CL. 5 ] 2000 and ξδ. We then obtain:

1000 N/0.25 ρeµ =0.747 0.010 0.006 0.1 GeV/c [ ± ±

N/ ξ =1.007 0.040 0.015 eµ ± ± 0 0 -5 0 5 10 15 024 (ξδ) =0.745 0.026 0.009. [ ] eµ -2ln(L) per event pe GeV/c ± ± R 0.05≤ We extract the limit P < 0.044 at 90% CL. 2000 hz-0.3τ

N/0.04 These results are consistent with the Standard Model Prediction, and are, in most cases, more precise than the world average values [11]. These

0 0 results supersede those on ρ , ρ , ρ from the -1 -0.5024 0 0.5 1e µ eµ h p [GeV/c] z e first analysis. 0.05< < 0.05≥ -0.3 hz 0.3 hz0.3 + 5. SPIN CORRELATIONS IN π vs. π− In the third analysis [12], we again exploit the + + 0 0 fact that in e e− γ∗ τ τ − at 10 GeV, 024[ ] 024[ ] → → pe GeV/c pe GeV/c the τ spins are 95% anti-correlated. If both taus decay semi-hadronically, then in the lab frame, the differential distribution of the energies of the two hadronic systems scaled to the beam energy, Figure 4. Comparison of the e vs.ρ data (points) x E /Eb is given by: with the fit results (histograms)− for the following ± ≡ ± 2 quantities: the 2ln (log-likelihood) per event; d σ 2 − L = F1(x+,x )+ hντ F2(x+,x ) the electron momentum in the lab; the polarime- dx+dx − | | − ter variable ω h for the ρ decay, and the − ≡ Z electron momentum for three ranges of polarime- where the functions F1 and F2 are well known + ter variable of the recoiling ρ decay: ω 0.3, and are particularly simple for π vs. π− events. 0.3 <ω<0.3, and ω 0.3. ≤− We select events of the type (τ − π−ντ ) vs. + + → − ≥ (τ π ντ ), with no extra photons. In order to suppress→ µ π backgrounds, we require the pions to shower→ in the calorimeter. We use our For the ρ vs.ρ sample, the results are: − limited dE/dx separation to suppress τ K±ν. → h2 =0.995 0.010 0.003 (SM =1) Kinematical cuts suppress two-photon events and ντ ± ± other backgrounds. From 1.5 106 produced tau with a confidence level for the fit of 9%. + × pairs, we obtain 2041 π vs. π− candidates. The The following sources of systematic errors were distribution of scaled energies x+ vs. x is given considered: Monte Carlo statistics; lepton identi- in Fig. 5. − fication efficiency; spin analyzer efficiency; mod- From a fit to this distribution (and related eled backgrounds; remaining unmodeled back- ones), we obtain h =1.03 0.06 0.04, con- 0 ντ grounds; contribution of ρ0 to the ππ dynam- sistent with the SM| expectation| ± of 1.± ics; the value of the Michel parameter η; detector energy, momentum, and angular resolution; 6. DISCUSSION OF RESULTS and modeled and unmodeled radiation effects. There is no sign of significant systematic bias, and From these results, limits can be obtained on Monte Carlo statistics remains the largest source the complex couplings in the generalized four- of systematic error in most cases. fermion interaction model [1,4]; these are shown Under the assumption of lepton universality, we in Fig. 6. the couplings are shown normalized can constrain ρ = ρ ρ , and similarly for ξ to their maximum value (hence the prime0), and e µ ≡ eµ 6

1601296-007 / / / / +i g S +i g S +i g S +i g S RR LR RL LL

-1 -1 -1 -1 80 +1 +1 +1 +1

-i -i -i -i 60 / / / / +i g V+i g V+i g VV+i g RLRRRL LL 40 -1 +1 -1 +1 -1 +1 -1 +1

20 -i -i -i -i

/ / +i g TT+i g 0 LR RL 1.00 -1 +1 -1 +1

x + 0.60 1.00 -i -i 0.60 x 0.20 I

Figure 6. 90% confidence limits on the reduced coupling constants gγ0 = gγ /max(gγ ), in the Figure 5. The raw correlation between the scaled µ µ µ complex plane. The circles with unit radii in- energies x E /Eb of the two pions in (τ − ± ≡+ ± + → dicate the maximum possible values, the other π−ν ) vs. (τ π ν )events. τ → τ solid circles indicate the constraints obtained using present world average results, and the hatched regions indicate the new constraints obtained af- V gLL0 is fixed to be real. The new results improve ter including the results presented here. the limits on couplings to right-handed tau neutrinos, but are unable to distinguish amongst the couplings to left-handed neutrinos without independent information such as a measurement of the cross-section σ(ντ e τνe). In the V A 6.2. W in Left-right symmetric models → − R Standard Model, all of the couplings are zero ex- In left-right symmetric models [3], there are cept gV = 1. The results are clearly consistent LL0 two sets of weak charged bosons W1± and W2±, with the Standard Model, but are still at the level which mix to form the observed “light” left- of precision achieved for muon decays. handed WL± and a heavier (so far, unobserved) right-handed W . The parameters in these mod- 6.1. Limits on Charged Higgs R± els are α = M(W )/M (W ) (= 0 in the SM), In the minimal supersymmetric extension to 1 2 and ζ = mixing angle, = 0 in the SM. The heavy the Standard Model (MSSM), a charged Higgs right-handed W will contribute to the decay of boson will contribute to the decay of the tau, in- R± the tau, interfering with the left-handed W di- terfering with the left-handed W diagram, and − − agram, and producing deviations from the Stan- producing a non-zero value for η.Forτ µνν, → dard Model values for the Michel parameters ρ m m tan2β and ξ. η = τ µ , 2m2 By using the results of these analyses assum- − H τ ing lepton universality, especially the limit on PR and similar formulas exist for ξ and ξδ. With (the probability that a right-handed tau neutrino the measurements reported here of η, ξ,and participates in the decay), we can obtain limits ξδ combined, we can extract the limit mH > on α and β in these models, shown in Fig. 7. For 2 ± 2 1.02 tan β GeV/c at 90% CL. This limit is sig- mixing angle ζ =0,weobtainmR >304 GeV/c nificant in comparison with direct search limits, at 90 % CL, and for free mixing angle ζ,weobtain in the region tan β >200 [13]. m >260 GeV/c2 at 90 % CL. ∼ 2 7

3100497-005 2 M (GeV / c ) 8. ACKNOWLEDGEMENTS 2 800 400 200 0.2 We gratefully acknowledge the eﬀort of the 3 0.1 2 CESR staﬀ in providing us with excellent lumi- 1 nosity and running conditions. This work was 0 min supported by the U.S. NSF and DoE. I thank the tan conference organizers for a thoroughly stimulat- I 0.1 ing and pleasant conference.

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