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Measurement of the Michel Parameters and the Average $\Tau EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN-PPE/96{46 March 26, 1996 Measurement of the Michel parameters and the average + + neutrino helicity from decays in e e ! The L3 Collab oration Abstract The Michel parameters , , and , the chirality parameter and the h p olarization P are measured using 32012 pair decays. Their values are extracted from the energy sp ectra of leptons and hadrons in ! l and ! l decays, the energy and decay angular distributions in ! decays, and the correlations in the energy sp ectra and angular distributions of the decay pro ducts. Assuming universality in leptonic and semileptonic decays, the results are =0:794 0:039 0:031, =0:25 0:17 0:11, =0:94 0:21 0:07, = 0:81 0:14 0:06, =0:970 0:053 0:011, and P = 0:154 0:018 0:012. h The measurement is in agreement with the VAhyp othesis for the weak charged current. Submitted to Phys. Lett. B Intro duction The sub ject of this pap er is an investigation of the Lorentz structure of the charged currentin leptonic and semileptonic decays. The undetected neutrinos and the unmeasured p olarization of the outgoing lepton allow the measurement of only four Michel parameters [1] in the leptonic 1) decays, ! l (l =e,). Of these four parameters, and describ e the isotropic part l of the lepton energy sp ectrum, while and describ e the angular distribution asymmetry of the sp ectrum with resp ect to the spin direction. In semileptonic decays, ! h 2) (h = ; K or ) the chirality parameter is interpreted as twice the average neutrino h helicity. In muon decays the Lorentz structure was studied with high precision supp orting the Stan- dard Mo del VAchoice of the charged current structure and placing stringent b ounds on charged currentinteractions other than VA [2, 3]. The purely leptonic decays of the lepton allow an indep endent study of the structure of the charged current. The larger mass of the expands the range of momentum transfers from that examined in muon decay, allowing more sensitive prob es for new physics whose couplings are prop ortional to the lepton mass. Measurements of Michel parameters in lepton decays have b een p erformed at low energy machines [4, 5] and at LEP [6]. The advantage at LEP is the non-vanishing p olarization which facilitates the measurementof and . In this analysis data collected with the L3 detector in 1991, 1992 and 1993 are used. The Michel parameters , , and , the chirality parameter and the average p olarization h P are determined from a combined t to the energy sp ectra of leptons and hadrons from ! l and ! decays, energy and decay angular distributions in ! l decays, and the correlations in the joint distributions of the decay pro ducts of b oth 's. Metho d of the Measurement Purely leptonic decays ! l can b e describ ed by the most general four-fermion contact l interaction Hamiltonian [1]. The matrix element in the helicity pro jection form can b e written as [7, 8]: X 4G F p M = l j j( ) >< ( ) j j >: (1) g < l n m 2 =S; V ; T ; =R; L Here G is the Fermi constant, lab els the scalar, vector and tensor interactions and , the F chiral pro jections of the charged leptons. The neutrino helicities, n and m, are xed when , and are given. The 10 complex coupling constants g can b e expressed in terms of Michel parameters [8]. Four of them, , , and , app ear together with the average p olarization P in the charged lepton decay sp ectrum of the [9]: d( ! l ) 1 l l l l l l (x )] (2) (x )+h (x ) P [h (x )+h (x )+h = h l l l l l 0 dx l l l = H (x ) P H (x ); l l 0 1 1) Formulae are given for the decay of the . In the analysis the charge conjugate decays are also used. 2) No distinction b etween charged pions and kaons is made in ! h decay. 2 where x = E =E E =E is the normalized lepton energy in the lab oratory system. The l l l beam l h (x ) are kinematical functions. In a similar way the semileptonic decays can b e describ ed l i with a matrix element ansatz leading to the relation [9]: 1 d( ! h ) h h h h = h (x ) P h (x ) = H (x )P H (x ); (3) h h h h h 0 1 0 1 dx h where is the chirality parameter for a particular decay. For ! , x = E =E h E =E is the normalized pion energy. In the case of ! , a quantity ! [10] is beam 0 intro duced and h and h are functions of ! . The quantity ! dep ends on the and 0 1 0 energies and op ening angle in the decay ! and conserves their sensitivitytothe p olarization . Qualitatively, negativevalues of ! are enriched by left handed and p ositive + by right handed . In the neutral current decayZ ! , the helicities of the 's are nearly + + 100% anti-correlated. The joint decay distribution for e e ! ! A B n (n =2;3;4), where A and B are e, , or , is [9]: 2 1 d (A) (B ) (A) (B ) = H (x )H (x )+H (x )H (x ) (4) A B A B 0 0 1 1 dx dx A B h i (A) (B ) (A) (B ) P H (x )H (x )+H (x )H (x ) : A B A B 1 0 0 1 From this distribution, we can disentangle the Michel parameters, the chirality parameter and the average p olarization up to a sign ambiguity. The latter is resolved taking into account the left-right asymmetry measurement from the SLD exp eriment [11] or the direct measurementof in the ! a decay [12]. h 1 The L3 Detector The L3 detector is describ ed in detail in Ref. [13]. The central tracker consists of a time expan- sion chamb er (TEC) surrounded bytwo thin prop ortional (Z-)chamb ers. The TEC delivers a precise track measurement in the b ending plane p erp endicular to the b eam direction and the Z-chamb ers provide a co ordinate along the b eam direction. The central tracker is surrounded by a ne grained and high resolution electromagnetic calorimeter (BGO) comp osed of Bis- muth Germanium Oxide crystals, a ring of scintillation counters, a uranium and brass hadron calorimeter with prop ortional wire chamb ers readout (HCAL) and a precise muon sp ectrometer consisting of three layers of multiwire drift chamb ers. These sub detectors are installed in a 12 m diameter solenoidal magnet which provides a uniform eld of 0.5 T along the b eam direction. In the following analysis only the barrel part of the detector with j cos j < 0:7 is used, where is the p olar angle with resp ect to the electron b eam direction. The TEC transverse momentum resolution is parametrized as =p =0:018p (GeV/c), p T T T the BGO resolution is less than 2% ab ove 1 GeV, the HCAL energy resolution for is p determined to b e E=E = 55%= E (GeV)+8% and the transverse momentum resolution of the muon sp ectrometer is 2.8% for charged particles with p = 45 GeV. T Data Analysis 1 A data sample corresp onding to a total integrated luminosity of69pb collected by the L3 exp eriment during the 1991, 1992 and 1993 data taking p erio ds is used in this analysis. A clean 3 sample of lepton pairs pro duced in Z decays is obtained by following the preselection describ ed in Ref. [14]. Only lowmultiplicityevents with a `back{to{back' top ology are accepted. Each event is divided into two hemispheres by a plane p erp endicular to the thrust axis. Particles are identi ed indep endently in each hemisphere. Lepton identi cation Electron candidates consist of an energy dep osition in the BGO which is electromagnetic in shap e and consistent in p osition and energy with a track in the central tracker. The energy dep osition in the HCAL must b e consistent with the tail of an electromagnetic shower and b e less than 3 GeV. Muon candidates consist of tracks in the muon sp ectrometer originating from the interaction p oint with a minimum ionizing particle resp onse in BGO and HCAL. Only muons with track segments in three planes of the muon sp ectrometer are accepted. Muons with energies b elow 2.5 GeV are stopp ed in the calorimeter. The electron and muon identi cation eciency is estimated from Monte Carlo. The average values are 84% and 65%, resp ectively. Hadron identi cation The selection of ! and ! uses the central tracker and the calorimeters. An algorithm [14] is applied to disentangle overlapping neutral electromagnetic clusters in the vicinity of the impact p oint of the charged hadron in the BGO. Around the impact p oint, which is precisely predicted by the central tracker, a hadronic shower whose shap e is assumed energy indep endent is subtracted from the energy dep osition. Remaining lo cal maxima of energy dep osition are sub ject to electromagnetic neutral cluster criteria. For accepted electromagnetic 0 neutral clusters, the energies and angles are determined. Two distinct neutral clusters form a 0 candidate if their invariant mass is within 40 MeV of the mass. A single neutral cluster forms 0 a candidate if its energy exceeds 1 GeV. Its transverse energy pro le has to b e consistent with either a single electromagnetic shower or a two photon hyp othesis for which the invariant 0 mass is within 50 MeV of the mass.
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