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Measurement of the Muon Decay Parameter  RAPID COMMUNICATIONS PHYSICAL REVIEW D 71, 071101(R) (2005) Measurement of the muon decay parameter A. Gaponenko,1 R. Bayes,7,* Yu. I. Davydov,7,† P. Depommier,4 J. Doornbos,7 W. Faszer,7 M. C. Fujiwara,7 C. A. Gagliardi,6 D. R. Gill,7 P. Green,1 P. Gumplinger,7 M. D. Hasinoff,2 R. S. Henderson,7 J. Hu,7 B. Jamieson,2 P. Kitching,1 D. D. Koetke,8 A. A. Krushinsky,3 Yu. Yu. Lachin,3 J. A. Macdonald,7,‡ R. P. MacDonald,1 G. M. Marshall,7 E. L. Mathie,5 L. V. Miasoedov,3 R. E. Mischke,7 J. R. Musser,6 P.M. Nord,8 M. Nozar,7 K. Olchanski,7 A. Olin,7,* R. Openshaw,7 T. A. Porcelli,7,x J.-M. Poutissou,7 R. Poutissou,7 M. A. Quraan,1 N. L. Rodning,1,‡ V. Selivanov,3 G. Sheffer,7 B. Shin,7,k F. Sobratee,1 T. D. S. Stanislaus,8 R. Tacik,5 V.D. Torokhov,3 R. E. Tribble,6 M. A. Vasiliev,6 and D. H. Wright7,{ 1University of Alberta, Edmonton, AB, T6G 2J1, Canada 2University of British Columbia, Vancouver, BC, V6T 1Z1, Canada 3Kurchatov Institute, Moscow, 123182, Russia 4University of Montreal, Montreal, QC, H3C 3J7, Canada 5University of Regina, Regina, SK, S4S 0A2, Canada 6Texas A&M University, College Station, Texas 77843, USA 7TRIUMF, Vancouver, BC, V6T 2A3, Canada 8Valparaiso University, Valparaiso, Indiana 46383, USA (Received 17 October 2004; published 4 April 2005) The muon decay parameter has been measured by the TWIST collaboration. We find 0:74964 0:00066 stat:0:00112 syst:, consistent with the standard model value of 3=4. This result implies that the product P of the muon polarization in pion decay, P, and the muon decay parameter falls within the 90% confidence interval 0:9960 <P <1:0040. It also has implications for left-right- symmetric and other extensions of the standard model. DOI: 10.1103/PhysRevD.71.071101 PACS numbers: 13.35.Bv, 12.60.Cn, 14.60.Ef The TWIST spectrometer [1] was designed to measure a d2ÿ 2 / 3 1 ÿ x 4x ÿ 3 broad range of the normal muon decay spectrum, ! x2dxd cos 3 e e, allowing the simultaneous extraction of the spec- 2 trum shape parameters. Assuming the weak interaction is P cos 1 ÿ x 4x ÿ 3 ; (2) 3 local and invariant under the Lorentz group, the effective four fermion muon decay matrix element can be written in where is the angle between the muon polarization and the terms of helicity-preserving amplitudes: outgoing electron direction, x Ee=Emax, and P is the muon polarization. The fourth parameter, , appears in the G X 4 F isotropic term when the electron mass is included in the M p ghejÿ jihjÿ ji; (1) 2 S;V;T;;R;L analysis. In the standard model, the Michel parameters take on precise values. where the g specify the scalar, vector, and tensor cou- The parameter expresses the level of parity violation in plings between -handed muons and -handed electrons muon decay, while parametrizes its momentum depen- V dence. Recently, TWIST reported a new measurement of [2]. In this form, the standard model implies gLL = 1 and all other coupling constants are zero. [4]. In this paper we report a new measurement of . The The differential decay spectrum [3] of the e emitted in currently accepted value of 0:7486 0:0026 the decay of polarized is provided in terms of four 0:0028 [5] agrees with the standard model expectation of parameters, , , , and , commonly referred to as the 3=4. Some standard model extensions require deviations Michel parameters, which are bilinear combinations of the from pure V ÿ A coupling that can alter . Some of these coupling constants. In the limit where the electron and models involve right-handed interactions. The positive neutrino masses as well as radiative corrections are ne- definite quantity, glected, this spectrum is given by 1 S 2 1 S 2 V 2 V 2 T 2 QR jgLRj jgRRj jgLRj jgRRj 3jgLRj 4 4 *Affiliated with: University of Victoria, Victoria, BC. 1 1 16 †Affiliated with: Kurchatov Institute, Moscow, Russia. 1 ÿ ; (3) ‡Deceased. 2 3 9 xPresent address: University of Manitoba, Winnipeg, MB. kAffiliated with: University of Saskatchewan, Saskatoon, SK. can serve to set a model independent limit on any muon {Present address: Stanford Linear Accelerator Center, right-handed couplings [2,6]. A recent review of muon Stanford, CA. decay is presented in [7]. 1550-7998=2005=71(7)=071101(5)$23.00 071101-1 2005 The American Physical Society RAPID COMMUNICATIONS A. GAPONENKO ET AL. PHYSICAL REVIEW D 71, 071101 (2005) Highly polarized surface muons [8] are delivered to the contains virtually all the components of the spectrometer TWIST spectrometer [1] from the M13 channel at with which a muon or a decay positron could interact. The TRIUMF. The spectrometer consists of a detector made output exactly mimics the binary files generated by the data up of 56 very thin high precision chamber planes, all acquisition system. mounted perpendicularly to a solenoidal 2 T magnetic Factors that influence the momentum and angle deter- field. The muons enter this array of chambers through a mination must be well simulated in the MC, so special runs 195m scintillator that acts as the event trigger. More than were taken specifically to address the accuracy of the 80% of the muons come to rest in the central stopping simulation of energy loss and multiple scattering. Muons target, which also acts as the cathode plane for the multi were stopped in the extreme upstream wire chambers in wire proportional chambers (MWPC) on either side. The both the experiment and in the MC simulation. The decay decay positrons spiral through the chambers producing hits positrons were tracked through the upstream half and on the wires that are recorded by time to digital converters. separately through the downstream half of the spectrome- These helical tracks are later analyzed to determine pre- ter. Differences in momentum and angle were histo- cisely the positron energy and angle. The observed mo- grammed on a track by track basis. Figure 1 presents, for mentum resolution is 100 keV/c [4]. The cos resolution both data and MC, the changes in momentum and angle derived from Monte Carlo (MC) is about 0.005. The re- that occur primarily at the central stopping target. The construction is similar to [4], except for some details widths of the peaks in this figure do not represent the discussed below. experimental resolution for a number of reasons. First, TWIST determines the Michel parameters by fitting because the same track is being reconstructed twice with two-dimensional histograms of reconstructed experimental finite resolution the differences in the measured values can decay positron momenta and angles with histograms of be either positive or negative. Second, the particle sees reconstructed Monte Carlo data. This approach has several approximately twice the thickness of materials. As well, advantages. First, spectrum distortions introduced by the the tracking in the upstream region is in the opposite event reconstruction largely cancel because MC and ex- perimental data are analyzed identically. Second, because 400 the MC simulates the detector response well, no explicit ∆ Data corrections of the result are required. Third, a blind analy- p sis of the result is straightforward. It is implemented by Counts 300 MC utilizing hidden Michel parameters H;H, and H to generate the theoretical decays. The decay rate can be 200 written as X 2 d2ÿ @ d ÿ 100 dxd cos H;H;H ;; @ dxd cos 0 since the decay spectrum is linear in the shape parameters. -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 The sum of MC spectra is fit to the data spectrum by Change in Momentum (MeV/c) adjusting the . is extracted as HH = H . Since the hidden parameters were 200 ∆ θ Data allowed to only deviate from their standard model values by no more than 0.03 it was sufficient for the extraction of Counts 150 MC systematic uncertainties to assume that they had their standard model values during the blind stage of the analy- sis. The MC spectra were generated including full O 100 radiative corrections with exact electron mass dependence, leading and next-to-leading logarithmic terms of O 2, 50 leading logarithmic terms of O 3, corrections for soft pairs, virtual pairs, and an ad hoc exponentiation [9]. -0.04 -0.02 0 0.02 0.04 Because TWIST at the present stage could not provide an Change in Angle (radians) improved measurement of eta, we set it, for MC spectra production, to its current highest precision value of ÿ0:007 FIG. 1 (color online). The difference between downstream and [6] in order to constrain other parameters better. The upstream tracks, for both data and MC, resulting in: top, the uncertainty of 0:013 on the accepted value of gives a positron momentum change in the central stopping target, bot- negligible uncertainty on the final value of . tom, for a positron that passed through the central stopping The TWIST simulation model is based on GEANT 3.21 target. The MC results were normalized to those of the data for [10] with the chamber response based on GARFIELD [11]. It the purposes of this figure. 071101-2 RAPID COMMUNICATIONS MEASUREMENT OF THE MUON DECAY PARAMETER PHYSICAL REVIEW D 71, 071101 (2005) direction for which the code is optimized and in this region ibrations. Finally, the track-selection algorithm was im- the track does not see as many planes due to the distribu- proved by merging those used for the analysis.
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