- Email: [email protected]
Search for CP violation in ZmF ττ
PhysicsLettersB297 (1992) 459-468 North-Holland
Search for C P violation in
PHYSICS LETTERS B
zz
ALEPH Collaboration
D. Buskulic, D. Decamp, C. Goy, J.-P. Lees, M.-N. Minard, B. Mours Laboratoire de Physique des Particules (LAPP), IN2P3-CNRS, F-74019 Annecy-le-Vieux Cedex, France
R. Alemany, F. Ariztizabal, P. Comas, J.M. Crespo, M. Delfino, E. Fernandez, V. Gaitan, L1. Garrido, T. Mattison, A. Pacheco, A. Pascual Institut de Fisica d'Altes Energies, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain t
D. Creanza, M. de Palma, A. Fariila, G. Iaselli, G. Maggi, M. Maggi, S. Natali, S. Nuzzo, M. Quattromini, A. Ranieri, G. Raso, F. Romano, F. Ruggieri, G. Selvaggi, L. Silvestris, P. Tempesta, G. Zito INFN, Sezione di Bari and Dipartimento di Fisica dell'Universit& 1-70126 Bari, Italy
H. Hu2, D. Huang, X. Huang, J. Lin, J. Lou, C. Qia02, T. Wang, Y. Xie, D. Xu, R. Xu, J. Zhang, W. Zhao Institute of High-Energy Physics, Academia Sinica, Beijing, China 3
L.A.T. Bauerdick 4, E. Blucher, G. Bonvicini, F. Bossi, J. Boudreau, D. Casper, H. Drevermann, R.W. Forty, G. Ganis, C. Gay, R. Hagelberg, J. Harvey, S. Haywood, J. Hilgart, R. Jacobsen, B. Jost, J. Knobloch, E. Langon, I. Lehraus, T. Lohse 5, A. Lusiani, M. Martinez, P. Mato, H. Meinhard, A. Minten, R. Miquel, H.-G. Moser, P. Palazzi, J.A. Perlas, J.-F. Pusztaszeri 6, F. Ranjard, G. Redlinger 7, L. Rolandi, J. Rothberg 8, T. Ruan 2,9, M. Saich, D. Schlatter, M. Schmelling, F. Sefkow, W. Tejessy, H. Wachsmuth, W. Wiedenmann, T. Wildish, W. Witzeling, J. Wotschack European Laboratory for Particle Physics (CERN), CH-1211 Geneva 23. Switzerland
Z. Ajaltouni, F. Badaud, M. Bardadin-Otwinowska, A.M. Bencheikh, R. E1 Fellous, A. Falvard, P. Gay, C. Guicheney, P. Henrard, J. Jousset, B. Michel, J.-C. Montret, D. Pallin, P. Perret, B. Pietrzyk, J. Proriol, F. Prulhibre, G. Stimpfl Laboratoire de Physique Corpusculaire, Universitk Blaise Pascal, 1N2P3-CNRS, Clermont-Ferrand, 1;'-63177 Aubikre, France
T. Fearnley, J.D. Hansen, J.R. Hansen ~0, P.H. Hansen, R. Mollerud, B.S. Nilsson Niels Bohr Institute, DKo2100 Copenhagen, Denmark I I
I. Efthymiopoulos, A. Kyriakis, E. Simopoulou, A. Vayaki, K. Zachariadou Nuclear Research Center Demokritos (NRCD), GR-15310 Athens, Greece
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J. Badier, A. Blondel, G. Bonneaud. J.C. Brient, G. Fouque, S. Orteu, A. Rosowsky, A. Roug6, M. Rumpf, R. Tanaka, M. Verderi, H. Videau Laboratoire de Physique Nuclbaire et des Hautes Energies, Ecole Polytechmque, IN2P3-CNRS. F-91128 Palaiseau Cedex, France
D.J. Candlin, M.I. Parsons, E. Veitch Department of Physics. Universtty of Edinburgh. Edinburgh Ett9 3JZ. UK 12
L. Moneta, G. Parrini Dipartimento di Fisica, Universita di Firenze, INFN Seztone di Firenze, 1-50125 Florence, Italy
M. Corden, C. Georgiopoulos, M. Ikeda, J. Lannulti, D. Levinthal is, M. Mermikides 14 L. Sawyer, S. Wasserbaech Supercomputer Computations Research Institute and Department of Physics. Florida State University. Tallahassee. FL 32306. USA 15.16.17
A. Antonelli, R. Baldini, G. Bencivenni, G. Bologna 18, p. Campana, G. Capon, F. Cerutti, V. Chiarella, B. D'Ettorre-Piazzoli 19 G. Felici, P. Laurelli, G. Mannocchi 20 F. Murtas, G.P. Murtas, L. Passalacqua, M. Pepe-Altarelli, P. Picchi ~8 Laboratori Nazionali dell'lNFN (LNF-INt'N). 1-00044 Frascat~. Ita(v
B. Altoon, O. Boyle, P. Colrain, I. ten Have, J.G. Lynch, W. Maitland, W.T. Morton, C. Raine, J.M. Scarr, K. Smith, A.S. Thompson, R.M. Turnbull Department of Physics and Astronomy, Universtty of Glasgow, Glasgow (;12 8QQ, UK 12
B. Brandl, O. Braun, T. Fischer, C. Geweniger, P. Hanke, V. Hepp, E.E. Kluge, Y. Maumary, A. Putzer, B. Rensch, A. Stahi, K. Tittei, M. Wunsch Institut far llochenergiephysik, Universitdt Heidelberg, W-6900 tteidelberg. FRG 21
A.T. Belk, R. Beuselinck, D.M. Binnie, W. Cameron, M. Cattaneo, D.J. Coiling, P.J. Dornan, S. Dugeay, A.M. Greene, J.F. Hassard, N.M. Lieske, J. Nash, S.J. Patton, D.G. Payne, M.J. Phillips, J.K. Sedgbeer, I.R. Tomalin, A.G. Wright Department of Physics, Imperial College. London SW7 2BZ. ('K 12
E. Kneringer, D. Kuhn, G. Rudolph Instttut j~r Experimentalphystk. Universiffit lnnsbruck, ,4-6020 Innsbruck, Austria 22
C.K. Bowdery, T.J. Brodbeck, A.J. Finch, F. Foster, G. Hughes. D. Jackson, N.R. Keemer, M. Nuttail, A. Patel, T. Sloan, S.W. Snow, E.P. Whelan Department of Phystcs. University of Lancaster. Lancaster L.41 4 YB, L'K 12
K. Kleinknecht, J. Raab, B. Renk, H.-G. Sander, H. Schmidt, F. Steeg, S.M. Walther, B. Wolf lnstitut )°ar Physik. Universitdt Mainz. W-6500 Mainz. t:'RG21
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J.-J. Aubert, C. Benchouk, A. Bonissent, J. Carr, P. Coyle, J. Drinkard, F. Etienne, S. Papalexiou, P. Payre, Z. Qian, L. Roos, D. Rousseau, P. Schwemling, M. Talby Centre de Physique des Particules. Facult~ des Sciences de Luminy, IN2P3-CNRS, F-13288 Marseille, France
S. Adlung, C. Bauer, W. Blum 10, D. Brown, P. Cattaneo 23, G. Cowan, B. Dehning, H. Dietl, F. Dydak 24, M. Fernandez-Bosman, M. Frank, A.W. Halley, J. Lauber, G. LiJtjens, G. Lutz, W. Mfinner, R. Richter, H. Rotscheidt, J. Schr6der, A.S. Schwarz, R. Settles, H. Seywerd, U. Stierlin, U. Stiegler, R. St. Denis, M. Takashima 25, j. Thomas 25, G. Wolf Max-Planck-lnstitut Fur Physik, Werner-tleisenberg-lnstitut, W-8000 Munich, FRG 21
J. Boucrot, O. Callot, A. Cordier, M. Davier, J.-F. Grivaz, Ph. Heusse, D.E. Jaffe. P. Janot, D.W. Kim 26, F. Le Diberder, J. Lefranqois, A.-M. Lutz, M.-H. Schune, J.-J. Veillet, I. Videau, Z. Zhang Laboratoire de I'Accbl&ateur Linbaire, Universitk de Paris-Sud, IN2P3-CNRS, F-91405 Orsay Cedex, France
D. Abbaneo, S.R. Amendolia, G. Bagliesi, G. Batignani, L. Bosisio, U. Bottigli, C. Bozzi, C. Bradaschia, M. Carpinelli, M.A. Ciocci, R. Dell'Orso, I. Ferrante, F. Fidecaro, L. Fo/l, E. Focardi, F. Forti, A. Giassi, M.A. Giorgi, F. Ligabue, E.B. Mannelli, P.S. Marrocchesi, A. Messineo, F. Palla, G. Rizzo, G. Sanguinetti, P. Spagnolo, J. Steinberger, R. Tenchini, G. Tonelli, G. Triggiani, C. Vannini, A. Venturi, P.G. Verdini, J. Walsh Dipartimento di Fisica dell"Universita, INFN Sezione di Pisa. e Scuola Normale Superiore. 1-56010 Pisa, Italy
J.M. Carter, M.G. Green, P.V. March, Ll.M. Mir, T. Medcalf, I.S. Quazi, J.A. Strong, L.R. West Department o.f Physics, Royal Holloway & Bedford New College, University of London. Surrey TW20 OEX, UK 12
D.R. Botterill, R.W. Clifft, T.R. Edgecock, M. Edwards, S.M. Fisher, T.J. Jones, P.R. Norton, D.P. Salmon, J.C. Thompson Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OXI I OQX, UK 12
B. Bloch-Devaux, P. Colas, H. Duarte, W. Kozanecki, M.C. Lemaire, E. Locci, S. Loucatos,
E. Monnier, P. Perez, F. Perrier, J. Rander, J.-F. Renardy, A. Roussarie, J.-P. Schuller, J. Schwindling, D. Si Mohand, B. Vallage Service de Physique des Particules. DAPNIA, CE-Saclay, F-91191 Gif sur- Yvette Cedex. France 27
R.P. Johnson, A.M. Litke, G. Taylor, J. Wear Institute for Particle Physics, University of California at Santa Cruz. Santa Cruz. CA 95064. USA 28
J.G. Ashman, W. Babbage, C.N. Booth, C. Buttar, R.E. Carney, S. Cartwright, F. Combley, F. Hatfield, P. Reeves, L.F. Thompson 10 Department of Physics. University of Sheffield, Sheffield $3 7Rfl, UK 12
E. Barberio, A. B6hrer, S. Brandt, C. Grupen, L. Mirabito 29, F. Rivera, U. Schiifer Fachbereich Physik. Universitiit Siegen, 14-5900 Siegen, FRG 2t
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31 December 1992
G. G i a n n i n i , B. G o b b o , F. R a g u s a 30
Dipartimento di Fisica, Universita di Trieste and 1NFN Sezione di Trieste, 1-34127 Trieste, Italy L. B e l l a n t o n i , W. C h e n , D. C i n a b r o 31, J.S. C o n w a y , D . F . C o w e n 32, Z. F e n g , D . P . S . F e r g u s o n , Y.S. G a o , J. G r a h l , J.L. H a r t o n , R.C. J a r e d 33 B.W. L e C l a i r e , C. L i s h k a , Y.B. P a n , J . R . P a t e r , Y. S a a d i , V. S h a r m a , M. S c h m i t t , Z . H . S h i , A . M . W a l s h , F.V. W e b e r , M . H . W h i t n e y , Sau L a n W u , X. W u a n d G. Z o b e r n i g
Department of Physics, University of Wisconsin, Madison, 14:153706, USA 34 Received 19 October 1992
Using the 18.8 pb -t of data accumulated at LEP in 1990 and 1991 with the ALEPH detector, a direct test of neutral current CP-invariance is performed by a search for CP-odd correlations in Z decays to r pairs where both r decay modes are identified. No evidence for CP-violation is observed. The weak dipole moment of the r has been measured to be dr (mz) = (1.3 -t- 1.4 :i: 0.1 ) × 10-17e • cm which results in an upper limit on the weak dipole moment of idr(mz)l ~< 3.7 × 10-17e .cm with 95% confidence level.
I. Introduction l Supported by CICYT, Spain. 2 Supported by the World Laboratory. 3 Supported by the National Science Foundation of China. 4 Present address: DESY, Hamburg, FRG. 5 Present address: Max-Planck-lnstitut f. Kernphysik, Heidelberg, FRG. 6 Visitor from University of Wisconsin, Madison, WI 53706, USA. Present address: TRIUMF, Vancouver, B.C., Canada. 8 Permanent address: University of Washington, Seattle, WA 98195, USA. 9 On leave of absence from IHEP, Beijing, China. to Present address: PPE Division, CERN, CH-1211 Geneva 23, Switzerland. t l Supported by the Danish Natural Science Research Council. 12 Supported by the UK Science and Engineering Research Council. 13 Supported by SLOAN fellowship, contract BR 2703. la Deceased. 15 Supported by the US Department of Energy, contract DE-FG05-87ER40319. 16 Supported by the NSF, contract PHY-8451274. 17 Supported by the US Department of Energy, contract DE-FCOS-85ER250000. 18 Also at Istituto di Fisica Generale, Universitfi di Torino, Torino, Italy. 19 Also at Universitfi di Napoli, Dipanimento di Scienze Fisiche, Naples, Italy. 20 Also at Istituto di Cosmo-Geofisica del CNR, Turin, Italy. 2J Supported by the Bundesministerium ffir Forschung und Technologie, FRG. 462
It has been pointed out that various decay modes of the Z boson can be used to search for CP-violating effects beyond the Kobayashi-Maskawa mechanism [1 ]. The measurements involve appropriate C P - o d d correlations which provide direct information about C P - o d d form factors [2]. C P - o d d quan-
22 Supported by Fonds zur F6rderung der wissenschaftlichen Forschung, Austria. 23 Present address: Universitfi di Pavia, Pavia, Italy. 24 Also at PPE Division, CERN, CH-1211 Geneva 23, Switzerland. 25 Present address: SSCL, Dallas, TX, USA. 26 Supported by the Korean Science and Engineering Foundation and Ministry of Education. 27 Supported by the Direction des Sciences de la Mati/:re, CEA. 28 Supported by the US Department of Energy, grant DEFG03-92ER40689. 29 Present address: Institut de Physique Nucl6aire de Lyon, F-69622 Villeurbanne, France. 30 Present address: Dipartimento di Fisica, Universita di Milano, Milan, Italy. 3t Present address: Harvard University, Cambridge, MA 02138, USA. 32 Present address: California Institute of Technology, Pasadena, CA 91125, USA. 33 Permanent address: LBL, Berkeley, CA 94720, USA. 34 Supported by the US Department of Energy, contract DE-AC02-76ER00881.
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tities for the leptonic Z boson decays, Z - , ~g, are accessible by measuring the correlation between the spins o f the leptons. Due to parity violation in z decays, the energy spectra and angular distributions of the decay products reflect the z polarization allowing m o m e n t u m correlations between the 3 + and r - decay products to be used to measure C P - o d d effects. With unpolarized beams, only two C P - o d d form factors contribute to C P - o d d correlation functions in e+e - -* r + r -. These are the electromagnetic and weak dipole moments, drem and d~', of the r and lead to non-vanishing values for the correlation functions. Observation o f a non-zero dipole m o m e n t would indicate physics beyond the standard model. The CP violating lagrangian for the zr production vertex is
[~ce = --ilZystr z[dt¢m (q 2 )Fur + d~'(q2)Zuv], (1) I
• -
av
where Fu~ and Zu, are the electromagnetic and weak field tensors. In the nonrelativistic limit, the corresponding interaction hamiltonian, H~, is given by Hi = - d o • E where d and E stand for the electric or weak dipole moments and the field strengths respectively. As this analysis is performed at q2 = m 2 the contribution of the weak dipole moment, written as dT ( m z ) , will be enhanced due to the Z resonance and it is assumed that any electric dipole m o m e n t contribution can be neglected. Visible CP violating correlations appear due to interference between the CP violating amplitude, Ace, from ( 1 ) and the CP conserving standard model amplitude resulting in a term approximately proportional to dT(s+ - s - ) where s+ ( s _ ) is the polarisation vector o f the r + ( r - ) . The C P - e v e n contribution, IAcel 2, to the cross section increases the partial width F ( Z - , zr) and therefore an indirect measurement o f the dipole moment can be obtained from the Z partial width. The width has a quadratic dependence on the dipole moment which gives a contribution of AFT ~ Id~(mz)f2m3z/24n [2]. Using the data accumulated at LEP the width has been measured to be F~ = ( 8 2 . 7 6 ± l . 0 2 ) MeV [3]. This can b e compared with the theoretical prediction F~SM= ( 8 3 . 7 + 0 . 4 ) M e V o f the standard model [4] or with the measured partial width Fe,u = ( 8 3 . 2 4 ± 0 . 4 2 ) MeV [3] and Z ~ ~t+~ - , assuming the weak dipole m o m e n t o f light lep-
31 December 1992
tons to be zero "1 . For F,TM the top and Higgs masses are varied in a correlated way in the intervals 90 < mt < 200 GeV and 50 < m n < 1000 GeV as is described in ref. [4]. Taking into account correlations between data one obtains AFtTM = ( - 0 . 9 4 + I. 10) MeV and A/re'u= ( - 0 . 4 8 ± 1.10) MeV respectively, which correspond, for both cases, to an indirect limit on the weak dipole moment o f Id~(mz)l < 0.7 × 10-17e • cm at 95% confidence level. However, the contribution of a non-zero dipole moment to the partial width could be compensated for by other unknown physical effects.
2. Analysis procedure The weak dipole moment is measured directly from a C P - o d d correlation between the m o m e n t a of the r + and r - decay products in a similar manner to the recent analysis of the O P A L Collaboration [5]. In this analysis the sensitivity is improved by exclusively identifying the specific r decay modes. Various correlation functions have been proposed [1] with one basic difference which is their behaviour under time reversal [6,71. Observables which are C P - o d d and CPT-even are required. For the decays r - ~ A - X , r + ~ B+Y the following quantity is chosen [6]
TAB ,,j
=
(kA - PB), (PA × PB)j + (i ~ j ) ,
(2)
IPa × PBI where PA(Pa) is the m o m e n t u m direction of the charged decay products of the negative (positive) r-lepton. The indices i and j refer to the cartesian coordinates where the third components are taken to be along the beam axis. The expectation value (TAB ij) changes sign under a CP transformation, but not under CPT. For unpolarized beams C P - o d d form factors at the eeZ vertex cannot contribute to TAB ,a, SO the mean value of TAB i,i is directly related to the dipole moment of the r [6]:
*~l In many models the magnitude of the lepton dipole moment increases with mass at least linearly [ 1]. 463
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½((TAB ,,j> +) = m z d , ( m z ) C a B d l• a g ( - g, i - g, i 3l ),.:. e
(3)
By the term diag is meant a diagonal matrix with diagonal elements as given above. The TaB i., (i = 1,2 ) have less analyzing power than TAB 3.3 due to the factor 2 and as they are also highly correlated to TAn 3,3, only this quantity is used in this analysis. The linear dependence of the expectation value (TaB ,.j) + (TnA ,.j) on dr (mz) is due to the interference between the CP-odd form factor and the standard model contribution. In addition there are terms quadratic in d, (mz), resulting from the normalization of (TAn ,,:), but these can be neglected for d , ( m z ) << e / m z . The proportionality constants CAB depend on the r decay mode and are listed in refs. [6,8] =2. As the interference term has the approximate form, d r ( s + - s _ ) , the proportionality constants can be written as CAn ~- CA + Cs where CA(Cn) are proportional to the analyzing power of the r + ( r - ) decay modes used as a polarimeter. Experimental cuts do not invalidate the choice of CP-odd correlation functions as long as they are C P blind which is the case in this analysis. However, they cause changes to the proportionality constants leading to effective constants C,]efto. The calculation of these effective constants using a Monte Carlo program written by the authors of refs. [6,8] is discussed in section 5. For the p decay mode there are in principle three different definitions of TaB ,j; one can use the momentum of the charged pion only, the neutral pion only, or the sum of both, resulting in differences in sensitivity up to a factor of 20 [8]. In the case of n p and p p modes the best sensitivity is achieved by calculating the correlation using the reconstructed p momenta. For the ep and/,tp correlation, however, the lowest error on the dipole moment is obtained if the n :~ m o m e n t u m is used. This is due to a cancelation of the sensitivities C~ and Co which are approximately equal but opposite in sign. Two methods can be used to select the events. It is possible to either exclusively identify all the r de=2 To obtain the above formula the V-A interaction was assumed in the r decays. It can be shown that to lowest order in the standard model couplings, (TAB ~,:) does not receive contributions from possible CP-violating effects in the r decay amplitudes [9].
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cay modes, or to only make the distinction between leptonic and hadronic decay modes as in refs. [5,10]. However, with the latter, inclusive, method the sum is over rather different CAt~ values leading to a lower analyzing power. In addition, the p decay modes cannot bc treated as described above. This analysis therefore uses the exclusive method resulting in a gain of around 1.6 in the statistical error on the dipole moment.
3. The detector The ALEPH detector is described in detail elsewhere [ 11 ]. The detector components from the beam pipe outwards are: - The Vertex Detector (VDET), two layers of silicon strip detectors with double-sided readout. The spatial resolution in r(,5 and z is 12pm for perpendicularly traversing particles. - The Inner Tracking Chamber (ITC), an 8-layer cylindrical drift chamber with sense and field wires parallel to the beam axis from 13 cm to 29 cm in radius. Particles with polar angles from 14° to 166 ° traverse all 8 layers. - The large cylindrical Time Projection Chamber (TPC), extending to an outer radius of 180 cm. Together with the ITC it provides an angular resolution of 0.3 mrad depending on the m o m e n t u m and the polar angle of the particle and a m o m e n t u m resolution of 6 p / p 2 = 0.0008 G e V - 1. - The highly granular Electromagnetic Calorimeter (ECAL), a lead/proportional wire chamber sandwich covering the polar angular range from 11 ° to 169 °. Cathode pads are arranged in towers of approximately 0.8 ° × 0.8 ° solid angle and read out in three storeys of 4, 9 and 9 radiation lengths. The signals from the 45 wire planes of each module are also read out, allowing an additional energy measurement. - The Hadron Calorimeter (HCAL), consisting of 23 layers of streamer tubes interleaved in the iron return yoke of the magnet system. The coverage in polar angle is from 6 ° to 174 °. Digital signals from each of the I × I cm 2 tubes are read out. In addition, analogue signals are recorded from pads, which are arranged in towers and cover solid angles of about 3.7 ° x 3.7 °. - The muon chambers, two double layers of streamer tubes with orthogonal strips surrounding the HCAL.
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The m o m e n t a of the particles are defined by the tracking chambers and the ECAL. Particle identification involves TPC, ECAL, HCAL and muon chambers.
4. Event selection This analysis uses the z decay modes with only one charged track r --* e u u , z ~ # u u , r ~ n ( K ) u and r ~ p ( K " ) u . The data were accumulated at LEP during 1990 and 1991. The integrated luminosity represents 18.8 pb-~ distributed in energy around the Z mass and corresponds to 21 600 r r events. In an event, two particles were required with opposite charge and each with a m o m e n t u m greater than 3GeV. The scattering angle was restricted to be within icos01 < 0.9 and the cosine o f the acollinearity to be less than - 0 . 9 5 . Particle identification techniques similar to those described in ref. [12] were applied. Electrons are identified using the transverse and longitudinal profile of the shower in ECAL and the difference between the observed and expected track ionisation. The estimator sensitive to the transverse profile also requires a balance between the ECAL energy and the TPC track m o m e n t u m measurement. Muons are identified from hits in the muon chambers and by their penetration and characteristic shower pattern in HCAL. Pions are positively identified on the basis o f the depth and width of showers in HCAL and the energy deposited in ECAL. To reject p, pion candidates must have no photon within 60 degrees o f the track direction; a photon is defined as a cluster o f energy o f more than 400 MeV in ECAL separated from the track impact position by more than 5 cm and having at least 70% of its energy in the first 13 radiation lengths. For p+ ~ n ± n ° candidates, a track is required which does not enter the electron or muon classes described above, and which is accompanied by one or two photons. If only one photon is found its energy must be larger than 4 GeV, whereas in the case of two photons, their invariant mass must be within 60 MeV o f the n o mass. Furthermore, the invariant mass of the charged track and the photons must be between 0.5 GeV and 1.2 GeV. The p m o m e n t u m is calculated by adding the charged pion m o m e n t u m and the reconstructed photon momenta using the ECAL storey
31 December 1992
information. If only one photon is reconstructed then its m o m e n t u m is taken to be the n ° m o m e n t u m [ 12 ]. With these selection criteria the efficiencies for particle identification are 75% for electrons, 92% for muons, 74% for pions and 56% for p candidates. Bhabha events and e+e - ~ /~+/~- events are rejected as follows. If both charged particles are identified as muons, it is required that the higher (lower) particle momentum be less than 85% (60%) o f the beam energy and that there is no photon with an energy above 1 GeV. F o r / z n events the muon momentum must be less than 90% of the beam energy. In the case of err (ep) pairs the total energy deposited in the electromagnetic calorimeter must be lower than 0.65 (0.8) v/'~. Bhabha background causes a non-zero expectation value of TAB 3.3 due to bremsstrahlung (cf. section 5), therefore electron pairs are not used in this analysis. Table I shows the number o f selected pairs, the detection efficiency and the background. The non-z background for all decay modes is less than 1%, except for the/~/t class, which has an e+e - ~ e + e - / ~ + ~ background of 10.5%. From the number of selected pairs the branching ratio for r + r - ~ X + Y - u ~ is calculated as shown in table 1. The branching ratios are in agreement with ref. [13], with a global X 2 of 13.4 with eight degrees of freedom.
5. Corrections and systematic errors Systematic errors are classified in two ways. Firstly there are errors on T,4B 3,3 coming from experimental biases faking a C P - o d d form factor. For instance, if one of the TPC end plates is rotated around the beam axis by a twist angle of ¢OvPc = I mrad, then there would be a contribution to (TAs 3.3) of 0.01. Secondly, errors on the effective proportionality constants C,]Un arise from background and experimental cuts; these are only significant for a non-zero dipole moment. 5. I. S y s t e m a t i c errors on T,~B 3,3
Radiation in the material of the detector causes a systematic shift in the acoplanarity measured in the plane perpendicular to the beam axis. This leads to a shift in T,4B 3.3, equal in magnitude but opposite in sign, for forward and backward scattering. Since 465
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31 December 1992
Table 1 The number of selected decay modes, their efficiencies, backgrounds, and the measured branching ratios. Mode
Events
e/~ en ep bt/z ,un /tp 7tn
np pp
601 414 486 481 417 663 128 365 290
sum
3845
Efficiency
Background
(51.4+ (37.4 + (28.0 + (63.9 + (45.44(35.5 + (36.2 + (26.2 + (21.7 ±
(2.6 (10.0 (3.0 (13.2 (10.1 (8.2 (11.0 (12.4 (11.4
1.4)% 1.7)% 1.2)% 2.0)% 1.7)% 1.2)% 2.8)% 1.5)% 1.6)%
the forward-backward asymmetry in r pair production is relatively small, this effect can be neglected. The Bhabha background causes a non-zero expectation value due to the large forward-backward asymmetry and the high degree of radiation in the detector material. Values of (T.4s 3.3) between 0.10 and 0.25 are obtained depending upon the cuts. Therefore the ee correlation was not used. The twist angle OgTPCwas measured to be less than 0.4 mrad using p pair events. This leads to a shift in (TAn 3.3) of 0.004 resulting in a fake dipole moment between -O.020e/mz and O.035e/mz, depending on the decay modes. The different sign of the various decay modes enables this source of systematic error to be eliminated. A constant shift, AT, for all decay modes can be measured by inspecting the dipole moments d+ and d_ derived from decay modes with positive or negative C]~ respectively. These two moments are functions of the shift, AT, and the dipole moment d, (mz): d± = d , ( m z ) ± 3ATIc±[,
(4)
where c+ is given by the weighted sums of 1/CAB.err The difference between these two moments depends only on the shift but not on the physical dipole moment. Conversely, an appropriately weighted sum of these moments depends on the physical dipole moment alone. The weighted mean value of the dipole moments d+ and d_ for positive and negative C]~ are measured, using the results of table 3, to e: d+ = 0 . 0 1 7 + 0 . 1 2 8
[e/mz],
d_ = 0 . 1 1 2 ± 0 . 0 7 4
[e/mz],
466
(5)
+ 0.4)% + 1.2)% + 0.6)% 4- 1.2)% + 1.1)% + 0.8)% ± 2.0)% ± 1.4)% + 1.6)%
Branching ratio 5.27 + 0.27)% 4.61 + 0.32)% 7.79 5: 0.50)% 3.02 + 0.18)% 3.82 + 0.25)% 7.93 + 0.43)% 1.46 + 0.18)% 5.65 + 0.46)% 5.48 + 0.54)%
leading to a shift AT of AT = - 0 . 0 1 6 z~ 0.019.
(6)
This is observed to be compatible with zero. For the np and pp correlation, the electromagnetic calorimeter is used to reconstruct the p momentum. Therefore a different twist of the TPC and ECAL end plates can still fake a non-zero dipole moment. The dependence of the dipole moment on the twist angles ogTpc and OJECALwas studied by adding rotations of the end plates into the Monte Carlo program. This yields -
Ad
-
[e/mz]
~
4
WT~C - OJrecAt. [ radl
(7)
The twist angles, W'rpc and OgECAL,measured using ~pair events are compatible with zero and results in an error on the dipole moment of O.O03e/mz. Several other sources of systematic errors, like a tilt or a displacement, were also studied and found to be one order of magnitude lower than the error due to a possible twist.
5.2. Corrections and systematic errors on the sensitivity The ratio between C]~ and C4s is a result of both the background and the kinematical cuts (cf. table 2). Systematic errors from the former arise from both experimental uncertainties and a lack of knowledge of CAs for some types of background. Errors resulting from the cuts are negligible. The error from the experimental uncertainty in the background is estimated by
Volume 297, number 3,4
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31 December 1992
Table 2 The contribution to the ratio between C] ff and CAB caused by background and cuts on the kinematics of the event. The last eft The first and second error on the background are due to experimental column shows the final proportionality constant CaB. and theoretical uncertainties, respectively. The errors arising from the cuts are negligible. The error on C]~ combines the errors due to background estimation and the statistics of the Monte Carlo sample. Mode
Background
ep en ep ,uu /~n /tp
0.984 0.876 0.956 0.865 0.868 0.962 0.942 0.900 0.886
nn np pp
4- 0.008 + 0.062 + 0.022 4- 0.054 4- 0.066 + 0.019 4- 0.029 + 0.050 4- 0.057
+ 0.005 + 0.058 + 0.107 4- 0.012 + 0.034 4- 0.061 4- 0.005 4- 0.050 + 0.134
varying the background by a relative a m o u n t o f 50%. In the second case, where CAB is u n k n o w n the error is e s t i m a t e d by varying CAB f r o m - 1 to 1. T h e separate errors are shown in table 2. T o e v a l u a t e the systematic error on C,]g induced by cuts on k i n e m a t i c a l variables like acollinearity, lowest allowed m o m e n t u m o f the track, and polar angle these cuts were varied o v e r a wide range c o m p a r e d to the errors on these variables. eft A c c o r d i n g This caused insignificant changes to C]B. to M o n t e Carlo studies, the m o m e n t u m and angular resolutions have a negligible influence on the proportionality constants. An error caused by a w r o n g definition o f the z-axis also belongs to the first group o f errors, because the m e a s u r e d TaB 3.3 is then a linear c o m b i n a t i o n o f the v a r i o u s TAB ~a. T h e error is negligibly small because the g e o m e t r y is k n o w n to 1 mrad.
6.
Results
Table 3 shows the m e a s u r e d dipole m o m e n t in units
o f e / m z . In the case o f the ep and p p correlation the highest analyzing p o w e r is given by the lepton and charged pion m o m e n t u m as discussed above, so this definition o f TAs 3,3 for the l e p t o n - p correlation was used. As p o i n t e d out in section 4, an a p p r o p r i a t e l y weighted sum o f d+ and d_ results in a weak dipole m o m e n t which is i n d e p e n d e n t o f a c o n s t a n t shift o f TAB 3.3. T h e m e a n value o f d, ( m z ) as well as the statistical error on d r ( m z ) receive an a d d i t i o n a l error elf due to the error on CAB. P r o p a g a t i o n o f the errors,
Kinematical cuts
C] ff
1.17 I. 13 1.04 1.15 I. I I 1.04 1.09 1.05 1.01
+0.7134-0.014 -0.614 4- 0.053 +0.338 + 0.038 + 0.615 4- 0.035 -0.597 4- 0.045 +0.340 + 0.024 - 1.869 + 0.056 -1.455 4- 0.103 -0.816+0.119
Table 3 The measured dipole moments and the statistical errors in units of e/mz for the various decay modes. Mode
dr (mz) [e/mz ]
e/~ en ep /z/~
0.378 0.262 -0.056 -0.251 0.375 -0.450 0.212 0.071 -0.289
ltrt /lp
nn np pp mean
4- 0.190 + 0.249 4- 0.414 = 0.222 4- 0.255 4- 0.362 4- 0.146 + 0.107 + 0.238
0.085 + 0.064
a s s u m i n g t h e m to be gaussian and non-correlated, resuits in a relative error on the m e a n value o f dr ( m z ) o f 5.6% and on the statistical error o f 2.9%. O n e obtains dr(mz) =0.062+0.064+0.005
[e/mz],
(8)
where the systematic error c o m i n g f r o m the measurem e n t o f TAB 3,3 is O.O03e/mz, the rest arising from uncertainties in the CAB. err C o m p a r i s o n with table 3 shows that the weighting p r o c e d u r e a d o p t e d to reduce the systematic error has m i n i m a l effect on the statistical error. In units o f e - cm the result reads d r ( r n z ) = ( 1 . 3 + 1 . 4 + 0 . 1 ) × 10-lYe • cm and yields a limit on the weak dipole m o m e n t o f 467
Volume 297, number 3,4
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31 December 1992
Id,(mz)[ < 3.7 × 10-17e • cm
References
at a confidence level of 95%.
[ 1] J. F. Donoghue and G. Valencia, Phys. Rev. Lett. 58 (1987) 451; F. Hoogeveen and LStodolsky, Phys. Lett. B 212 (1988) 505; J. Bernabeu and M. B. Gavela, CP violation, ed. C. Jarlskog (World Scientific, Singapore, 1989); J. Bernabeau and N. Rius, Phys. Lett. B 232 (1989) 127; W. Bernreuther and O. Nachtmann, Phys. Rev. Lett. 63 (1989) 2787; 64 (1990) 1072(E); M.B. Gavela et al., Phys. Rev. D 39 (1989) 1870; C.A. Nelson, Phys. Rev. D 41 (1090) 2805; D 43 (1991) 1465; J. Bernabeu, N. Rius and T. Pich, Phys. Lett. B 257 (1991) 219; S. Goozovat and C. A. Nelson, Phys. Lett. B 267 (1991) 128; B 271 (1991) 468(E); Phys. Rev. D44 (1991) 2818. [2] W. Bernreuther, U. Low, J. P. Ma and O. Nachtmann, Z. Phys. C 43 (1989) 117. [3] LEP Collabs., Phys. Left. B 276 (1992) 247. [4] W. Hollik, preprint MPI-Ph/92-9 (I 992). [5] OPAL Collab., P. D. Acton et al., Phys. Lett. B 281 (1992) 405. [61W. Bernreuther, G. W. Botz, O. Nachtmann and P. Overmann, Z. Phys. C 52 (1991) 567. [ 7 ] W. Bernreuther and O. Nachtmann, Phys. Lett. B 268 (1991) 424. [8] P. Overmann, PhD thesis, University of Heidelberg (1992). [9] W. Bernreuther, private communication. [10] T. Fischer, Diplomarbeit, HD-IHEP 92-03 (1992). [11] ALEPH Collab., D. Decamp et al., Nucl. Instrum. Methods A 286 (1990) 121. [12] ALEPH Collab., D. Decamp et al., Phys. Lett. B 265 (1991) 430. [13] Particle Data Group, K. Hikasa et al., Review of particle properties, Phys. Rev. D 45 (1992).
7. Conclusion The limit on the weak dipole moment of the z lepton has been determined to be Id~(mz)l < 3.7 × 10-17e • cm. The results here benefit from treating the r decay channels exclusively because the proportionality constants, CAB, between the measured quantities TAB 3,3 and the weak dipole moment differ in magnitude and sign for the various decay modes. The increased sensitivity results in a reduction of the statistical errors by a factor of around 1.6 compared to the inclusive method and an appropriately weighted sum of the dipole moments with positive and negative proportionality constants leads to a cancellation of systematic errors.
Acknowledgement It is a pleasure to thank our colleagues from the SL division for the operation of LEP. We are indebted to the engineers and technicians at CERN and our home institutions for their contributions to ALEPH's success. Those of us from non-member countries thank CERN for its hospitality. We acknowledge the helpful comments and support from W. Bernreuther and P. Overmann.
468
Search for C P violation in
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zz
ALEPH Collaboration
D. Buskulic, D. Decamp, C. Goy, J.-P. Lees, M.-N. Minard, B. Mours Laboratoire de Physique des Particules (LAPP), IN2P3-CNRS, F-74019 Annecy-le-Vieux Cedex, France
R. Alemany, F. Ariztizabal, P. Comas, J.M. Crespo, M. Delfino, E. Fernandez, V. Gaitan, L1. Garrido, T. Mattison, A. Pacheco, A. Pascual Institut de Fisica d'Altes Energies, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain t
D. Creanza, M. de Palma, A. Fariila, G. Iaselli, G. Maggi, M. Maggi, S. Natali, S. Nuzzo, M. Quattromini, A. Ranieri, G. Raso, F. Romano, F. Ruggieri, G. Selvaggi, L. Silvestris, P. Tempesta, G. Zito INFN, Sezione di Bari and Dipartimento di Fisica dell'Universit& 1-70126 Bari, Italy
H. Hu2, D. Huang, X. Huang, J. Lin, J. Lou, C. Qia02, T. Wang, Y. Xie, D. Xu, R. Xu, J. Zhang, W. Zhao Institute of High-Energy Physics, Academia Sinica, Beijing, China 3
L.A.T. Bauerdick 4, E. Blucher, G. Bonvicini, F. Bossi, J. Boudreau, D. Casper, H. Drevermann, R.W. Forty, G. Ganis, C. Gay, R. Hagelberg, J. Harvey, S. Haywood, J. Hilgart, R. Jacobsen, B. Jost, J. Knobloch, E. Langon, I. Lehraus, T. Lohse 5, A. Lusiani, M. Martinez, P. Mato, H. Meinhard, A. Minten, R. Miquel, H.-G. Moser, P. Palazzi, J.A. Perlas, J.-F. Pusztaszeri 6, F. Ranjard, G. Redlinger 7, L. Rolandi, J. Rothberg 8, T. Ruan 2,9, M. Saich, D. Schlatter, M. Schmelling, F. Sefkow, W. Tejessy, H. Wachsmuth, W. Wiedenmann, T. Wildish, W. Witzeling, J. Wotschack European Laboratory for Particle Physics (CERN), CH-1211 Geneva 23. Switzerland
Z. Ajaltouni, F. Badaud, M. Bardadin-Otwinowska, A.M. Bencheikh, R. E1 Fellous, A. Falvard, P. Gay, C. Guicheney, P. Henrard, J. Jousset, B. Michel, J.-C. Montret, D. Pallin, P. Perret, B. Pietrzyk, J. Proriol, F. Prulhibre, G. Stimpfl Laboratoire de Physique Corpusculaire, Universitk Blaise Pascal, 1N2P3-CNRS, Clermont-Ferrand, 1;'-63177 Aubikre, France
T. Fearnley, J.D. Hansen, J.R. Hansen ~0, P.H. Hansen, R. Mollerud, B.S. Nilsson Niels Bohr Institute, DKo2100 Copenhagen, Denmark I I
I. Efthymiopoulos, A. Kyriakis, E. Simopoulou, A. Vayaki, K. Zachariadou Nuclear Research Center Demokritos (NRCD), GR-15310 Athens, Greece
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J. Badier, A. Blondel, G. Bonneaud. J.C. Brient, G. Fouque, S. Orteu, A. Rosowsky, A. Roug6, M. Rumpf, R. Tanaka, M. Verderi, H. Videau Laboratoire de Physique Nuclbaire et des Hautes Energies, Ecole Polytechmque, IN2P3-CNRS. F-91128 Palaiseau Cedex, France
D.J. Candlin, M.I. Parsons, E. Veitch Department of Physics. Universtty of Edinburgh. Edinburgh Ett9 3JZ. UK 12
L. Moneta, G. Parrini Dipartimento di Fisica, Universita di Firenze, INFN Seztone di Firenze, 1-50125 Florence, Italy
M. Corden, C. Georgiopoulos, M. Ikeda, J. Lannulti, D. Levinthal is, M. Mermikides 14 L. Sawyer, S. Wasserbaech Supercomputer Computations Research Institute and Department of Physics. Florida State University. Tallahassee. FL 32306. USA 15.16.17
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S. Adlung, C. Bauer, W. Blum 10, D. Brown, P. Cattaneo 23, G. Cowan, B. Dehning, H. Dietl, F. Dydak 24, M. Fernandez-Bosman, M. Frank, A.W. Halley, J. Lauber, G. LiJtjens, G. Lutz, W. Mfinner, R. Richter, H. Rotscheidt, J. Schr6der, A.S. Schwarz, R. Settles, H. Seywerd, U. Stierlin, U. Stiegler, R. St. Denis, M. Takashima 25, j. Thomas 25, G. Wolf Max-Planck-lnstitut Fur Physik, Werner-tleisenberg-lnstitut, W-8000 Munich, FRG 21
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J.M. Carter, M.G. Green, P.V. March, Ll.M. Mir, T. Medcalf, I.S. Quazi, J.A. Strong, L.R. West Department o.f Physics, Royal Holloway & Bedford New College, University of London. Surrey TW20 OEX, UK 12
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E. Barberio, A. B6hrer, S. Brandt, C. Grupen, L. Mirabito 29, F. Rivera, U. Schiifer Fachbereich Physik. Universitiit Siegen, 14-5900 Siegen, FRG 2t
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G. G i a n n i n i , B. G o b b o , F. R a g u s a 30
Dipartimento di Fisica, Universita di Trieste and 1NFN Sezione di Trieste, 1-34127 Trieste, Italy L. B e l l a n t o n i , W. C h e n , D. C i n a b r o 31, J.S. C o n w a y , D . F . C o w e n 32, Z. F e n g , D . P . S . F e r g u s o n , Y.S. G a o , J. G r a h l , J.L. H a r t o n , R.C. J a r e d 33 B.W. L e C l a i r e , C. L i s h k a , Y.B. P a n , J . R . P a t e r , Y. S a a d i , V. S h a r m a , M. S c h m i t t , Z . H . S h i , A . M . W a l s h , F.V. W e b e r , M . H . W h i t n e y , Sau L a n W u , X. W u a n d G. Z o b e r n i g
Department of Physics, University of Wisconsin, Madison, 14:153706, USA 34 Received 19 October 1992
Using the 18.8 pb -t of data accumulated at LEP in 1990 and 1991 with the ALEPH detector, a direct test of neutral current CP-invariance is performed by a search for CP-odd correlations in Z decays to r pairs where both r decay modes are identified. No evidence for CP-violation is observed. The weak dipole moment of the r has been measured to be dr (mz) = (1.3 -t- 1.4 :i: 0.1 ) × 10-17e • cm which results in an upper limit on the weak dipole moment of idr(mz)l ~< 3.7 × 10-17e .cm with 95% confidence level.
I. Introduction l Supported by CICYT, Spain. 2 Supported by the World Laboratory. 3 Supported by the National Science Foundation of China. 4 Present address: DESY, Hamburg, FRG. 5 Present address: Max-Planck-lnstitut f. Kernphysik, Heidelberg, FRG. 6 Visitor from University of Wisconsin, Madison, WI 53706, USA. Present address: TRIUMF, Vancouver, B.C., Canada. 8 Permanent address: University of Washington, Seattle, WA 98195, USA. 9 On leave of absence from IHEP, Beijing, China. to Present address: PPE Division, CERN, CH-1211 Geneva 23, Switzerland. t l Supported by the Danish Natural Science Research Council. 12 Supported by the UK Science and Engineering Research Council. 13 Supported by SLOAN fellowship, contract BR 2703. la Deceased. 15 Supported by the US Department of Energy, contract DE-FG05-87ER40319. 16 Supported by the NSF, contract PHY-8451274. 17 Supported by the US Department of Energy, contract DE-FCOS-85ER250000. 18 Also at Istituto di Fisica Generale, Universitfi di Torino, Torino, Italy. 19 Also at Universitfi di Napoli, Dipanimento di Scienze Fisiche, Naples, Italy. 20 Also at Istituto di Cosmo-Geofisica del CNR, Turin, Italy. 2J Supported by the Bundesministerium ffir Forschung und Technologie, FRG. 462
It has been pointed out that various decay modes of the Z boson can be used to search for CP-violating effects beyond the Kobayashi-Maskawa mechanism [1 ]. The measurements involve appropriate C P - o d d correlations which provide direct information about C P - o d d form factors [2]. C P - o d d quan-
22 Supported by Fonds zur F6rderung der wissenschaftlichen Forschung, Austria. 23 Present address: Universitfi di Pavia, Pavia, Italy. 24 Also at PPE Division, CERN, CH-1211 Geneva 23, Switzerland. 25 Present address: SSCL, Dallas, TX, USA. 26 Supported by the Korean Science and Engineering Foundation and Ministry of Education. 27 Supported by the Direction des Sciences de la Mati/:re, CEA. 28 Supported by the US Department of Energy, grant DEFG03-92ER40689. 29 Present address: Institut de Physique Nucl6aire de Lyon, F-69622 Villeurbanne, France. 30 Present address: Dipartimento di Fisica, Universita di Milano, Milan, Italy. 3t Present address: Harvard University, Cambridge, MA 02138, USA. 32 Present address: California Institute of Technology, Pasadena, CA 91125, USA. 33 Permanent address: LBL, Berkeley, CA 94720, USA. 34 Supported by the US Department of Energy, contract DE-AC02-76ER00881.
Volume 297, number 3,4
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tities for the leptonic Z boson decays, Z - , ~g, are accessible by measuring the correlation between the spins o f the leptons. Due to parity violation in z decays, the energy spectra and angular distributions of the decay products reflect the z polarization allowing m o m e n t u m correlations between the 3 + and r - decay products to be used to measure C P - o d d effects. With unpolarized beams, only two C P - o d d form factors contribute to C P - o d d correlation functions in e+e - -* r + r -. These are the electromagnetic and weak dipole moments, drem and d~', of the r and lead to non-vanishing values for the correlation functions. Observation o f a non-zero dipole m o m e n t would indicate physics beyond the standard model. The CP violating lagrangian for the zr production vertex is
[~ce = --ilZystr z[dt¢m (q 2 )Fur + d~'(q2)Zuv], (1) I
• -
av
where Fu~ and Zu, are the electromagnetic and weak field tensors. In the nonrelativistic limit, the corresponding interaction hamiltonian, H~, is given by Hi = - d o • E where d and E stand for the electric or weak dipole moments and the field strengths respectively. As this analysis is performed at q2 = m 2 the contribution of the weak dipole moment, written as dT ( m z ) , will be enhanced due to the Z resonance and it is assumed that any electric dipole m o m e n t contribution can be neglected. Visible CP violating correlations appear due to interference between the CP violating amplitude, Ace, from ( 1 ) and the CP conserving standard model amplitude resulting in a term approximately proportional to dT(s+ - s - ) where s+ ( s _ ) is the polarisation vector o f the r + ( r - ) . The C P - e v e n contribution, IAcel 2, to the cross section increases the partial width F ( Z - , zr) and therefore an indirect measurement o f the dipole moment can be obtained from the Z partial width. The width has a quadratic dependence on the dipole moment which gives a contribution of AFT ~ Id~(mz)f2m3z/24n [2]. Using the data accumulated at LEP the width has been measured to be F~ = ( 8 2 . 7 6 ± l . 0 2 ) MeV [3]. This can b e compared with the theoretical prediction F~SM= ( 8 3 . 7 + 0 . 4 ) M e V o f the standard model [4] or with the measured partial width Fe,u = ( 8 3 . 2 4 ± 0 . 4 2 ) MeV [3] and Z ~ ~t+~ - , assuming the weak dipole m o m e n t o f light lep-
31 December 1992
tons to be zero "1 . For F,TM the top and Higgs masses are varied in a correlated way in the intervals 90 < mt < 200 GeV and 50 < m n < 1000 GeV as is described in ref. [4]. Taking into account correlations between data one obtains AFtTM = ( - 0 . 9 4 + I. 10) MeV and A/re'u= ( - 0 . 4 8 ± 1.10) MeV respectively, which correspond, for both cases, to an indirect limit on the weak dipole moment o f Id~(mz)l < 0.7 × 10-17e • cm at 95% confidence level. However, the contribution of a non-zero dipole moment to the partial width could be compensated for by other unknown physical effects.
2. Analysis procedure The weak dipole moment is measured directly from a C P - o d d correlation between the m o m e n t a of the r + and r - decay products in a similar manner to the recent analysis of the O P A L Collaboration [5]. In this analysis the sensitivity is improved by exclusively identifying the specific r decay modes. Various correlation functions have been proposed [1] with one basic difference which is their behaviour under time reversal [6,71. Observables which are C P - o d d and CPT-even are required. For the decays r - ~ A - X , r + ~ B+Y the following quantity is chosen [6]
TAB ,,j
=
(kA - PB), (PA × PB)j + (i ~ j ) ,
(2)
IPa × PBI where PA(Pa) is the m o m e n t u m direction of the charged decay products of the negative (positive) r-lepton. The indices i and j refer to the cartesian coordinates where the third components are taken to be along the beam axis. The expectation value (TAB ij) changes sign under a CP transformation, but not under CPT. For unpolarized beams C P - o d d form factors at the eeZ vertex cannot contribute to TAB ,a, SO the mean value of TAB i,i is directly related to the dipole moment of the r [6]:
*~l In many models the magnitude of the lepton dipole moment increases with mass at least linearly [ 1]. 463
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½((TAB ,,j> +
(3)
By the term diag is meant a diagonal matrix with diagonal elements as given above. The TaB i., (i = 1,2 ) have less analyzing power than TAB 3.3 due to the factor 2 and as they are also highly correlated to TAn 3,3, only this quantity is used in this analysis. The linear dependence of the expectation value (TaB ,.j) + (TnA ,.j) on dr (mz) is due to the interference between the CP-odd form factor and the standard model contribution. In addition there are terms quadratic in d, (mz), resulting from the normalization of (TAn ,,:), but these can be neglected for d , ( m z ) << e / m z . The proportionality constants CAB depend on the r decay mode and are listed in refs. [6,8] =2. As the interference term has the approximate form, d r ( s + - s _ ) , the proportionality constants can be written as CAn ~- CA + Cs where CA(Cn) are proportional to the analyzing power of the r + ( r - ) decay modes used as a polarimeter. Experimental cuts do not invalidate the choice of CP-odd correlation functions as long as they are C P blind which is the case in this analysis. However, they cause changes to the proportionality constants leading to effective constants C,]efto. The calculation of these effective constants using a Monte Carlo program written by the authors of refs. [6,8] is discussed in section 5. For the p decay mode there are in principle three different definitions of TaB ,j; one can use the momentum of the charged pion only, the neutral pion only, or the sum of both, resulting in differences in sensitivity up to a factor of 20 [8]. In the case of n p and p p modes the best sensitivity is achieved by calculating the correlation using the reconstructed p momenta. For the ep and/,tp correlation, however, the lowest error on the dipole moment is obtained if the n :~ m o m e n t u m is used. This is due to a cancelation of the sensitivities C~ and Co which are approximately equal but opposite in sign. Two methods can be used to select the events. It is possible to either exclusively identify all the r de=2 To obtain the above formula the V-A interaction was assumed in the r decays. It can be shown that to lowest order in the standard model couplings, (TAB ~,:) does not receive contributions from possible CP-violating effects in the r decay amplitudes [9].
464
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cay modes, or to only make the distinction between leptonic and hadronic decay modes as in refs. [5,10]. However, with the latter, inclusive, method the sum is over rather different CAt~ values leading to a lower analyzing power. In addition, the p decay modes cannot bc treated as described above. This analysis therefore uses the exclusive method resulting in a gain of around 1.6 in the statistical error on the dipole moment.
3. The detector The ALEPH detector is described in detail elsewhere [ 11 ]. The detector components from the beam pipe outwards are: - The Vertex Detector (VDET), two layers of silicon strip detectors with double-sided readout. The spatial resolution in r(,5 and z is 12pm for perpendicularly traversing particles. - The Inner Tracking Chamber (ITC), an 8-layer cylindrical drift chamber with sense and field wires parallel to the beam axis from 13 cm to 29 cm in radius. Particles with polar angles from 14° to 166 ° traverse all 8 layers. - The large cylindrical Time Projection Chamber (TPC), extending to an outer radius of 180 cm. Together with the ITC it provides an angular resolution of 0.3 mrad depending on the m o m e n t u m and the polar angle of the particle and a m o m e n t u m resolution of 6 p / p 2 = 0.0008 G e V - 1. - The highly granular Electromagnetic Calorimeter (ECAL), a lead/proportional wire chamber sandwich covering the polar angular range from 11 ° to 169 °. Cathode pads are arranged in towers of approximately 0.8 ° × 0.8 ° solid angle and read out in three storeys of 4, 9 and 9 radiation lengths. The signals from the 45 wire planes of each module are also read out, allowing an additional energy measurement. - The Hadron Calorimeter (HCAL), consisting of 23 layers of streamer tubes interleaved in the iron return yoke of the magnet system. The coverage in polar angle is from 6 ° to 174 °. Digital signals from each of the I × I cm 2 tubes are read out. In addition, analogue signals are recorded from pads, which are arranged in towers and cover solid angles of about 3.7 ° x 3.7 °. - The muon chambers, two double layers of streamer tubes with orthogonal strips surrounding the HCAL.
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The m o m e n t a of the particles are defined by the tracking chambers and the ECAL. Particle identification involves TPC, ECAL, HCAL and muon chambers.
4. Event selection This analysis uses the z decay modes with only one charged track r --* e u u , z ~ # u u , r ~ n ( K ) u and r ~ p ( K " ) u . The data were accumulated at LEP during 1990 and 1991. The integrated luminosity represents 18.8 pb-~ distributed in energy around the Z mass and corresponds to 21 600 r r events. In an event, two particles were required with opposite charge and each with a m o m e n t u m greater than 3GeV. The scattering angle was restricted to be within icos01 < 0.9 and the cosine o f the acollinearity to be less than - 0 . 9 5 . Particle identification techniques similar to those described in ref. [12] were applied. Electrons are identified using the transverse and longitudinal profile of the shower in ECAL and the difference between the observed and expected track ionisation. The estimator sensitive to the transverse profile also requires a balance between the ECAL energy and the TPC track m o m e n t u m measurement. Muons are identified from hits in the muon chambers and by their penetration and characteristic shower pattern in HCAL. Pions are positively identified on the basis o f the depth and width of showers in HCAL and the energy deposited in ECAL. To reject p, pion candidates must have no photon within 60 degrees o f the track direction; a photon is defined as a cluster o f energy o f more than 400 MeV in ECAL separated from the track impact position by more than 5 cm and having at least 70% of its energy in the first 13 radiation lengths. For p+ ~ n ± n ° candidates, a track is required which does not enter the electron or muon classes described above, and which is accompanied by one or two photons. If only one photon is found its energy must be larger than 4 GeV, whereas in the case of two photons, their invariant mass must be within 60 MeV o f the n o mass. Furthermore, the invariant mass of the charged track and the photons must be between 0.5 GeV and 1.2 GeV. The p m o m e n t u m is calculated by adding the charged pion m o m e n t u m and the reconstructed photon momenta using the ECAL storey
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information. If only one photon is reconstructed then its m o m e n t u m is taken to be the n ° m o m e n t u m [ 12 ]. With these selection criteria the efficiencies for particle identification are 75% for electrons, 92% for muons, 74% for pions and 56% for p candidates. Bhabha events and e+e - ~ /~+/~- events are rejected as follows. If both charged particles are identified as muons, it is required that the higher (lower) particle momentum be less than 85% (60%) o f the beam energy and that there is no photon with an energy above 1 GeV. F o r / z n events the muon momentum must be less than 90% of the beam energy. In the case of err (ep) pairs the total energy deposited in the electromagnetic calorimeter must be lower than 0.65 (0.8) v/'~. Bhabha background causes a non-zero expectation value of TAB 3.3 due to bremsstrahlung (cf. section 5), therefore electron pairs are not used in this analysis. Table I shows the number o f selected pairs, the detection efficiency and the background. The non-z background for all decay modes is less than 1%, except for the/~/t class, which has an e+e - ~ e + e - / ~ + ~ background of 10.5%. From the number of selected pairs the branching ratio for r + r - ~ X + Y - u ~ is calculated as shown in table 1. The branching ratios are in agreement with ref. [13], with a global X 2 of 13.4 with eight degrees of freedom.
5. Corrections and systematic errors Systematic errors are classified in two ways. Firstly there are errors on T,4B 3,3 coming from experimental biases faking a C P - o d d form factor. For instance, if one of the TPC end plates is rotated around the beam axis by a twist angle of ¢OvPc = I mrad, then there would be a contribution to (TAs 3.3) of 0.01. Secondly, errors on the effective proportionality constants C,]Un arise from background and experimental cuts; these are only significant for a non-zero dipole moment. 5. I. S y s t e m a t i c errors on T,~B 3,3
Radiation in the material of the detector causes a systematic shift in the acoplanarity measured in the plane perpendicular to the beam axis. This leads to a shift in T,4B 3.3, equal in magnitude but opposite in sign, for forward and backward scattering. Since 465
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Table 1 The number of selected decay modes, their efficiencies, backgrounds, and the measured branching ratios. Mode
Events
e/~ en ep bt/z ,un /tp 7tn
np pp
601 414 486 481 417 663 128 365 290
sum
3845
Efficiency
Background
(51.4+ (37.4 + (28.0 + (63.9 + (45.44(35.5 + (36.2 + (26.2 + (21.7 ±
(2.6 (10.0 (3.0 (13.2 (10.1 (8.2 (11.0 (12.4 (11.4
1.4)% 1.7)% 1.2)% 2.0)% 1.7)% 1.2)% 2.8)% 1.5)% 1.6)%
the forward-backward asymmetry in r pair production is relatively small, this effect can be neglected. The Bhabha background causes a non-zero expectation value due to the large forward-backward asymmetry and the high degree of radiation in the detector material. Values of (T.4s 3.3) between 0.10 and 0.25 are obtained depending upon the cuts. Therefore the ee correlation was not used. The twist angle OgTPCwas measured to be less than 0.4 mrad using p pair events. This leads to a shift in (TAn 3.3) of 0.004 resulting in a fake dipole moment between -O.020e/mz and O.035e/mz, depending on the decay modes. The different sign of the various decay modes enables this source of systematic error to be eliminated. A constant shift, AT, for all decay modes can be measured by inspecting the dipole moments d+ and d_ derived from decay modes with positive or negative C]~ respectively. These two moments are functions of the shift, AT, and the dipole moment d, (mz): d± = d , ( m z ) ± 3ATIc±[,
(4)
where c+ is given by the weighted sums of 1/CAB.err The difference between these two moments depends only on the shift but not on the physical dipole moment. Conversely, an appropriately weighted sum of these moments depends on the physical dipole moment alone. The weighted mean value of the dipole moments d+ and d_ for positive and negative C]~ are measured, using the results of table 3, to e: d+ = 0 . 0 1 7 + 0 . 1 2 8
[e/mz],
d_ = 0 . 1 1 2 ± 0 . 0 7 4
[e/mz],
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(5)
+ 0.4)% + 1.2)% + 0.6)% 4- 1.2)% + 1.1)% + 0.8)% ± 2.0)% ± 1.4)% + 1.6)%
Branching ratio 5.27 + 0.27)% 4.61 + 0.32)% 7.79 5: 0.50)% 3.02 + 0.18)% 3.82 + 0.25)% 7.93 + 0.43)% 1.46 + 0.18)% 5.65 + 0.46)% 5.48 + 0.54)%
leading to a shift AT of AT = - 0 . 0 1 6 z~ 0.019.
(6)
This is observed to be compatible with zero. For the np and pp correlation, the electromagnetic calorimeter is used to reconstruct the p momentum. Therefore a different twist of the TPC and ECAL end plates can still fake a non-zero dipole moment. The dependence of the dipole moment on the twist angles ogTpc and OJECALwas studied by adding rotations of the end plates into the Monte Carlo program. This yields -
Ad
-
[e/mz]
~
4
WT~C - OJrecAt. [ radl
(7)
The twist angles, W'rpc and OgECAL,measured using ~pair events are compatible with zero and results in an error on the dipole moment of O.O03e/mz. Several other sources of systematic errors, like a tilt or a displacement, were also studied and found to be one order of magnitude lower than the error due to a possible twist.
5.2. Corrections and systematic errors on the sensitivity The ratio between C]~ and C4s is a result of both the background and the kinematical cuts (cf. table 2). Systematic errors from the former arise from both experimental uncertainties and a lack of knowledge of CAs for some types of background. Errors resulting from the cuts are negligible. The error from the experimental uncertainty in the background is estimated by
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Table 2 The contribution to the ratio between C] ff and CAB caused by background and cuts on the kinematics of the event. The last eft The first and second error on the background are due to experimental column shows the final proportionality constant CaB. and theoretical uncertainties, respectively. The errors arising from the cuts are negligible. The error on C]~ combines the errors due to background estimation and the statistics of the Monte Carlo sample. Mode
Background
ep en ep ,uu /~n /tp
0.984 0.876 0.956 0.865 0.868 0.962 0.942 0.900 0.886
nn np pp
4- 0.008 + 0.062 + 0.022 4- 0.054 4- 0.066 + 0.019 4- 0.029 + 0.050 4- 0.057
+ 0.005 + 0.058 + 0.107 4- 0.012 + 0.034 4- 0.061 4- 0.005 4- 0.050 + 0.134
varying the background by a relative a m o u n t o f 50%. In the second case, where CAB is u n k n o w n the error is e s t i m a t e d by varying CAB f r o m - 1 to 1. T h e separate errors are shown in table 2. T o e v a l u a t e the systematic error on C,]g induced by cuts on k i n e m a t i c a l variables like acollinearity, lowest allowed m o m e n t u m o f the track, and polar angle these cuts were varied o v e r a wide range c o m p a r e d to the errors on these variables. eft A c c o r d i n g This caused insignificant changes to C]B. to M o n t e Carlo studies, the m o m e n t u m and angular resolutions have a negligible influence on the proportionality constants. An error caused by a w r o n g definition o f the z-axis also belongs to the first group o f errors, because the m e a s u r e d TaB 3.3 is then a linear c o m b i n a t i o n o f the v a r i o u s TAB ~a. T h e error is negligibly small because the g e o m e t r y is k n o w n to 1 mrad.
6.
Results
Table 3 shows the m e a s u r e d dipole m o m e n t in units
o f e / m z . In the case o f the ep and p p correlation the highest analyzing p o w e r is given by the lepton and charged pion m o m e n t u m as discussed above, so this definition o f TAs 3,3 for the l e p t o n - p correlation was used. As p o i n t e d out in section 4, an a p p r o p r i a t e l y weighted sum o f d+ and d_ results in a weak dipole m o m e n t which is i n d e p e n d e n t o f a c o n s t a n t shift o f TAB 3.3. T h e m e a n value o f d, ( m z ) as well as the statistical error on d r ( m z ) receive an a d d i t i o n a l error elf due to the error on CAB. P r o p a g a t i o n o f the errors,
Kinematical cuts
C] ff
1.17 I. 13 1.04 1.15 I. I I 1.04 1.09 1.05 1.01
+0.7134-0.014 -0.614 4- 0.053 +0.338 + 0.038 + 0.615 4- 0.035 -0.597 4- 0.045 +0.340 + 0.024 - 1.869 + 0.056 -1.455 4- 0.103 -0.816+0.119
Table 3 The measured dipole moments and the statistical errors in units of e/mz for the various decay modes. Mode
dr (mz) [e/mz ]
e/~ en ep /z/~
0.378 0.262 -0.056 -0.251 0.375 -0.450 0.212 0.071 -0.289
ltrt /lp
nn np pp mean
4- 0.190 + 0.249 4- 0.414 = 0.222 4- 0.255 4- 0.362 4- 0.146 + 0.107 + 0.238
0.085 + 0.064
a s s u m i n g t h e m to be gaussian and non-correlated, resuits in a relative error on the m e a n value o f dr ( m z ) o f 5.6% and on the statistical error o f 2.9%. O n e obtains dr(mz) =0.062+0.064+0.005
[e/mz],
(8)
where the systematic error c o m i n g f r o m the measurem e n t o f TAB 3,3 is O.O03e/mz, the rest arising from uncertainties in the CAB. err C o m p a r i s o n with table 3 shows that the weighting p r o c e d u r e a d o p t e d to reduce the systematic error has m i n i m a l effect on the statistical error. In units o f e - cm the result reads d r ( r n z ) = ( 1 . 3 + 1 . 4 + 0 . 1 ) × 10-lYe • cm and yields a limit on the weak dipole m o m e n t o f 467
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Id,(mz)[ < 3.7 × 10-17e • cm
References
at a confidence level of 95%.
[ 1] J. F. Donoghue and G. Valencia, Phys. Rev. Lett. 58 (1987) 451; F. Hoogeveen and LStodolsky, Phys. Lett. B 212 (1988) 505; J. Bernabeu and M. B. Gavela, CP violation, ed. C. Jarlskog (World Scientific, Singapore, 1989); J. Bernabeau and N. Rius, Phys. Lett. B 232 (1989) 127; W. Bernreuther and O. Nachtmann, Phys. Rev. Lett. 63 (1989) 2787; 64 (1990) 1072(E); M.B. Gavela et al., Phys. Rev. D 39 (1989) 1870; C.A. Nelson, Phys. Rev. D 41 (1090) 2805; D 43 (1991) 1465; J. Bernabeu, N. Rius and T. Pich, Phys. Lett. B 257 (1991) 219; S. Goozovat and C. A. Nelson, Phys. Lett. B 267 (1991) 128; B 271 (1991) 468(E); Phys. Rev. D44 (1991) 2818. [2] W. Bernreuther, U. Low, J. P. Ma and O. Nachtmann, Z. Phys. C 43 (1989) 117. [3] LEP Collabs., Phys. Left. B 276 (1992) 247. [4] W. Hollik, preprint MPI-Ph/92-9 (I 992). [5] OPAL Collab., P. D. Acton et al., Phys. Lett. B 281 (1992) 405. [61W. Bernreuther, G. W. Botz, O. Nachtmann and P. Overmann, Z. Phys. C 52 (1991) 567. [ 7 ] W. Bernreuther and O. Nachtmann, Phys. Lett. B 268 (1991) 424. [8] P. Overmann, PhD thesis, University of Heidelberg (1992). [9] W. Bernreuther, private communication. [10] T. Fischer, Diplomarbeit, HD-IHEP 92-03 (1992). [11] ALEPH Collab., D. Decamp et al., Nucl. Instrum. Methods A 286 (1990) 121. [12] ALEPH Collab., D. Decamp et al., Phys. Lett. B 265 (1991) 430. [13] Particle Data Group, K. Hikasa et al., Review of particle properties, Phys. Rev. D 45 (1992).
7. Conclusion The limit on the weak dipole moment of the z lepton has been determined to be Id~(mz)l < 3.7 × 10-17e • cm. The results here benefit from treating the r decay channels exclusively because the proportionality constants, CAB, between the measured quantities TAB 3,3 and the weak dipole moment differ in magnitude and sign for the various decay modes. The increased sensitivity results in a reduction of the statistical errors by a factor of around 1.6 compared to the inclusive method and an appropriately weighted sum of the dipole moments with positive and negative proportionality constants leads to a cancellation of systematic errors.
Acknowledgement It is a pleasure to thank our colleagues from the SL division for the operation of LEP. We are indebted to the engineers and technicians at CERN and our home institutions for their contributions to ALEPH's success. Those of us from non-member countries thank CERN for its hospitality. We acknowledge the helpful comments and support from W. Bernreuther and P. Overmann.
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