PDF hosted at the Radboud Repository of the Radboud University Nijmegen The following full text is a publisher's version. For additional information about this publication click this link. http://hdl.handle.net/2066/26856 Please be advised that this information was generated on 2015-01-23 and may be subject to change. Physics Letters B 315 ( 1993 ) 494-502 North-Holland PHYSICS LETTERS B An S matrix analysis of the Z resonance L3 Collaboration 0 . A d ria n i0, M . Aguilar-Benitezx, S. A hlen1, J. A lcarazp, A. A loisioaa, G . Alversonj , M .G . A lvig giaa, G . Am brosiaf, Q. A n q, H. Anderhubat, A .L. Anderson“ , V .P. Andreev2-', T. Angelescuk, L. A ntonovan, D . Antreasyan8, P. A rcex, A. A refievz, A. Atamanchuk^, T. Azem oonc, T . A zizh, P .V .K .S . Bab aq, P. Bagnaia31, J.A . Bakkenah, R .C . B a ll0, S. Banerjee11, J. B a o e, R . B arillèrep, L. Barone31, A. Baschirotto y, R . Battistonaf, A. B a y r, F. Becattini0, J. Bechtluft3, R . Becker3, U . Becker“ > 3t, F. Behnerat, J. Behrens31, G y.L. Bencze*, J. Berdugo*, P. Berges“ , B. Bertu cciaf, B .L . B e te van,3t, M . B ia sin iaf, A. B ila n d at, G .M . B ile iaf, R . Bizzarri31, J.J. Blaisin g d, G .J. Bobbinkp-b, R . Bo ck3, A. Böhm 3, B . Borgia31, M . Bosettiy, D. Bo u rilko vac, M . Bourquinr, D . Boutignyp, B . Bouwensb, E. Bram b illa33, J.G . B ran so n ^ I.C . Bro ckag, M . Brooksv, A. Bujak iK), J.D . Burger", W .J. Burgerr, J. Busenitz3p, A. Buytenhuijsac, X .D . C a iq, M . C apell“ , M . Caria af, G . Carlino A .M . Cartacei0, R . Castello y, M . Cerrada*, F. Cesaron i al, Y .H . Chang", U .K . C haturvediq, M . Chem arinw, A. Chenav, C. Chenf, G . Chenf, G .M . C henf, H .F. Chens, H .S. C henf, M . C hen", W .Y . Chenav, G. C hiefari33, C .Y. C hiene, M .T. C h o iao, S. Chungn, C. C iv in in i0,1. C lare“ , R . C lare", T .E . Coanv, H .O . Cohn3d, G. Coignetd, N . Colino p, A. Contin s, F. Cotorobaik, X .T . C u iq, X .Y . C u iq, T.S. D a in, R. D ’Alessandro °, R . de Asm undisaa, A. Degré d, K . D eitersar, E. Dénes*, P. Denesah, F. DeNotaristefani31, M . D h in a3t, D . D iB ito n to ap, M . Diem ozai, H .R . D im itro van, C. D io n isiai, M . D ittm ar31, L. Djam bazov3*, M .T . D o va q, E . Drago33, D . Duchesneaur, P. D uinkerb, I. D uranaf, S. Easoaf, H . E l M am ouniw, A. Engler38, F .J. Eppling” , F.C . E rn é b, P. Exterm annr, R . Fabbrettiar, M . Fab re3r, S. Falcian o 31, S .J. F a n 31“ , O. Fackler“ , J. F a y w, M . F e lcin ip, T. Ferguson38, D . Fernandez*, G . Fernandez*, F. Ferro n i31, H . Fesefeldt3, E. Fian d rin i3f, J.H . F ie ld r, F. Filth au tac, G . Finocchiaro“ , P.H . Fish ere, G . Fo rco n ir, L. Fre.djr, K . Freudenreich31, W . Frieb el3S, M . Fukushim a” , M . G aillo u d 1, Y u . G alaktionovz,n, E. G allo 0, S.N. G angulip,h, P. Garcia-Abiax, D . G elew, S. G en tile“ , N . Gheordanescuk, S. G iaguai, S. Goldfarbj , Z .F. Gong5, E. Gonzalez*, A. Gougase, D. G oujonr, G . G rattaae, M . Gruenewaldp, C. G u q, M . G uanziroliq, J.K . G u o am, V .K . G upta311, A. G u rtu h, H .R . Gustafson0, L .J. G u tayaq, K . Hangarter3, B. H artm ann3, A. H asanq, D . H auschildtb, C.F. H e 3m, J.T . H e f, T. Hebbekerp, M . Hebert ^ A. H ervé p, K . H ilgers3, H . H o fer3*, H. H ooranir, G . H u q, G .Q . H u 3m, B. Ille w, M .M . IIya sq, V . Innocente11, H . Janssenp, S. Jezequeld, B.N . Jin f, L.W . Jo n es0, 1. Josa-M utuberriap, A. Kasser1, R .A . K h an q, Yu. Kam yshkovad, P. Kapinosaj,as, J.S . Kapustinskyv, Y . K aryotakisp, M . K a u rq, S. Khokharq, M .N . Kienzle-Focaccir, J.K . K im 30, S.C. K im ao, Y .G . K im 30, W .W . K innisonv, A. K irk b y3e, D . K irk b yae, S. K irsch as, W . K itte i30, A. K lim en to vn,z, R . Klöckner3, A.C. K ö n ig 30, E. Koffem anb, O. Kornadt3, V. Koutsenko“ > 2, A. KoulbardisaJ, R .W . Kraem er38, T. K ram er“ , V .R . K rastevan,af, W . K ren z3, A. Krivshich aj, H . K u ijte n 30, K .S. K u m arm, A. Kunin n-2, G . Lan d i0, D . Lanske3, S. Lanzano33, A. Lebedev” , P . Lebrun w, P. Lecom teat, P. Lecoqp, P. Le Coultre31, D .M . L e e v, J.S . Le e ao, K .Y . L e e 30, 1. Leedom J, C. L e g g e ttJ.M . Le G o ffp, R . Leiste3S, M . L e n ti0, E. Leonardiai, C. L i s>q, H .T . L i f, P .J. L i am, J.Y . L ia o 3"1, W .T . L in 3V, Z .Y . L in s, F.L. Lin d e b, B. Lindem ann3, L. L is ta 33, Y . L iu q, W . Lohm annas, E. Longoai, Y .S. L u f, J.M . Lubbersp, K . Lübelsm eyera, 494 \ Elsevier Science Publishers B.V. Volume 315, number 3,4 P H Y SIC S L E T T E R S B 7 October Í993 C. L u c i31, D. Luckeyg,n, L. Lu d o vicia‘, L. Lu m in ari31, W . Lusterm ann35, J.M . M a f, W .G . M a s, M . M acD erm ottat, R . M alik q, A. M alin in z, C. M aña*, M . M aolinbay3', P. M archesiniat, F. M arion d, A. M a rin 1, J.P . M artin w, L. Martinez-Laso *, F. M arzano31, G .G .G . Massaro b, K . M azum darr, P. M cB rid e 1", T. M cM ahonaq, D. M cN a llyat, M. M erkag, L. M erola33, M . M eschini0, W .J. M etzgerac, Y . M i\ A. M ih u lk, G .B. M ills v, Y . M irq, G. M irab elliai, J. M n ich 3, M . M ö lle r3, B. M onteleoni0, R. Morand d, S. M organti31, N .E. M o u laiq, R . M ountae, S. M ü lle r3, A. N adtochy3->,E. N ag y\ M . N apolitano33, F. Ncssi-Tedaldia\ H . Newm anae, C. N eyerat, M .A . N ia z q, A. N ip p e3, H . N ow ak3S, G . O rgantini31, D. Pandoulas3, S. Pao letti0, P. Paolucci33, G . Pascale31, G. Passaleva0,af, S. P a trice lli3a, T. P a u l6, M . Pauluzziaf, C. Pau s3, F. Paussa\ Y .J. P e i3, S. Pensottiy, D. Perret-Gallixd, J. Perrierr, A. Pevsnere, D. Piccoloaa, M . Pieri p , P.A . Piro u éah, F. P la s ilad, V. Plyaskinz, M. P o h lat, V. Pojidaevz-°, H. Postem a11, Z.D . Q i3m, J.M . Q ian c, K .N . Q ureshiq, R. Raghavanh, G. Rahal-Callot3t, P.G . Rancoitay, M . Rattaggiy, G . Raven b, P. R azisab, K . R ead ad, D. R e n 3t, Z. R e n q, M . Rescigno31, S. Reucroftj, A. R ick e r3, S. Riem ann35, B.C . Riem ers3q, K. R ile sc, O. R in d c, H .A. R iz v iq, S. R o 30, F .J. Rodriguez*, B .P . R o e c, M . Röhner3, L. Rom ero*, S. Rosier-Leesd, R . Rosm alenac, Ph. Rosselet \ W . van Rossum b, S. R o th 3, A. R ubbian, J.A . R u b io p, H. Rykaczewski3t, M . Sachw itz35, J. SalicioP, J.M . Salicio*, G .S. Sanders v, A. Santocchia af, M .S. Sarakinos", G. Sarto rellig,q, M . Sassowsky3, G. Sauvaged, V. Schegelskyaj, D. Schm itz3, P. Schm itz3, M . Schneegansd, H . Schopper3U, D J. Schotanusac, S. Shotkin", H J. Schreiberas, aa J. Shukla36, R . Schulte3, S. Schulte3, K . Schultze3, J. Schwenke3, G. Schwering3, C. Sciacca I. Sco ttm, R . Sehgalq, P .G . Seiler31-, J.C . SensP-b, L. Servo li3f, I. Sheer3k, D .Z. Shenam, S. Shevchenkoae, X .R . S h iae, E. Shum ilov2, V. Shoutkoz, D. Son30, A. Sopczakak, V. Soulim ov33, C. Spartiotise, T . Spickerm ann3, P. Sp illan tin i°, R . Starosta3, M. Steuer6,1*, D .P. Stickland3h, F. Sticozzi", H . Stoneah, K . Strauch“ , B.C . Stringfellowaq, K . Sudhakarh, G. Sultanovq, L .Z . Su n s,q, G .F. Susinnor, H . Suter31, J.D . Sw ainq, A.A. Syed3C, X .W . Tangf, L. Taylor J, G. T erz iy, Samuel C.C. T in g ", S.M . T in g D, M . T o n u tti3, S.C. Tonw arh, J. Tóth*, A. Tsaregorodtsev3-*, G . T sip o litis38, C. T u lly ab, K .L . Tungf, J. U lb rich t3*, L. Urbán U . U w e r3, E. V alente31, R .T . Van de W a lle 3C, I. V etlitskyz, G . V iertel31, P. V ikasq, U . V ik a sq, M . Vivargentd, H . Vogelag, H . Vogt35,1. V orobievz, A.A. Vorobyov«, L. Vuilleum ier1, M . W adhw ad, W . W a llra ff3, C. W ang", C .R . W ang5, X .L . W angs, Y .F . W ang", Z.M . W angq-S, C. W arn er3, A. W eb er3, J. W eb er31, R . W e ill \ T .J. W enaus“ , J. W enningerr, M . W h iten, C. W illm ott *, F. Wittgenstein p, D. W rig h t3h, S.X . W u q, S. W ynhoff3, B. Wyslouch ", Y .Y . X ie am, J.G . X u f, Z.Z. X u s, Z .L. X u e am, D .S. Y a n 31", B.Z. Yang5, C.G. Yangf, G. Yangq, C.H . Y e q, J.B . Y e s, Q. Y e q, S.C. Y e h 3V, Z .W . Y in 3m, J.M . Y o u q, N. Yunusq, M . Yzerm anb, C. Zaccardelli3e, N. Z aitsev33, P. Zem p3t, M . Zengq, Y . Zenga, D .H . Zhangb, Z.P. Zhangs,q, B. Zhou1, G .J. Zhouf, J.F . Zh o u 3, R .Y . Z h u ae, A. Zichichi g-P>q and B.C.C. van der Zw aanb â L Physikalisches Institut, R W T H , W-5100 Aachen, F R G 1 and III. Physikalisches Institut, RW TH , W-5100 Aachen, F R G 1 b National Institute for High Energy Physics, N IK H E F \ NL-1009 D B Amsterdam, The Netherlands c University of Michigan, Ann Arbor, M l 48109, USA d Laboratoire d’Annecy-le- Vieux de Physique des Particules, LAPP, IN2P3-CNRS, B P 110, F-74941 Annecy-le-Vieux CEDEX\ France e Johns Hopkins University; Baltimore, M D 21218, USA f Institute of High Energy Physics, IH E P , 100039 Beijing, China g IN F N - Sezione di Bologna, 1-40126 Bologna, Italy h Tata Institute of Fundamental Research, Bombay 400 005, India 1 Boston University, Boston, MA 02215, USA j Northeastern University, Boston, MA 02115, USA 495 Volume 315, number 3,4 P H Y SIC S L E T T E R S B 7 October 1993 k Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania 1 Central Research Institute fo r Physics of the Hungarian Academy of Sciences, H-Ì525 Budapest i 14, Hungary2 m Harvard University, Cambridge, MA 02139, USA n Massachusetts Institute of Technology, Cambridge, MA 02139, USA 0 IN FN Sezione di Firenze and University of Florence, 1-50125 Florence, Italy p European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland q World Laboratory, F B L JA Project, CH-1211 Geneva 23, Switzerland T University of Geneva, CH-1211 Geneva 4, Switzerland s Chinese University o f Science and Technology, USTC, Hefei, Anhui 230 029, China 1 University of Lausanne, CH-1015 Lausanne, Switzerland u Lawrence Livermore National Laboratory, Livermore, CA 94550, USA v Los Alamos National Laboratory, Los Alamos, N M 87544, USA w Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, F-69622 Villeurbanne Cedex, France x Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEM AT, E-28040 Madrid, Spain y IN F N - Sezione di M ilano , 1-20133 M ilan , Italy z Institute of Theoretical and Experimental Physics, IT EP, Moscow, Russia aa IN FN - Sezione di Napoli and University of Naples, 1-80125 Naples, Italy ab Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus ac University of Nymegen and N IK IIE F , NL-6525 ED Nymegen, The Netherlands ad Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA ae California Institute o f Technology, Pasadena, CA 91125, USA af IN F N - Sezione di Perugia and Università Degli Studi di Perugia, 1-06100 Perugia, Italy ag Carnegie Mellon University, Pittsburgh, PA 15213, USA ah Princeton University, Princeton, N J 08544, USA ai IN FN - Sezione di Roma and University of Rome, “La Sapienza ”, LOO 185 Rome, Italy aj Nuclear Physics Institute, St. Petersburg, Russia ak University of California, San Diego, CA 92093, USA Dept, de Fìsica de Partículas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain am Shanghai Institute of Ceramics, SIC , Shanghai, China an Bulgarian Academy of Sciences, Institute of Mechatronics, BU-1113 Sofia, Bulgaria ao Center for High Energy Physics, Korea Advanced Inst, o f Sciences and Technology, 305-701 Taejon, Republic of Korea ap University of Alabama, Tuscaloosa, A L 35486, USA aq Purdue University, West Lafayette>IN 47907, USA ar Paul Sc herrer Institut, PSI, CH-5232 Villigen, Switzerland as D ES Y - Institut für Hochenergiephysik, 0-1615 Zeuthen, FR G at Eidgenössische Technische Hochschule, E T H Zürich, CH-8093 Zurich, Switzerland au University of Hamburg, W-2000 Hamburg, FR G av High Energy Physics Group, Taiwan, China w ♦ Received 5 August 1993 Editor: K. Winter The 5* matrix ansatz is a rigorously model independent approach to describe the cross-sections and asymmetries in e+e“ annihilation. Using the cross-sections and asymmetries measured with the L3 detector during the 1990 and 1991 running period, we determine the mass and the width of the Z boson, the contributions of the Z exchange and of the yZ interference. Including the polarization of the t lepton in the analysis, the leptonic helicity amplitudes of the scattering process are determined assuming lepton universality. The results are compared with other model independent ansatzes as realized in Z F IT T E R . A systematic bias of the Z mass due to the yZ interference term is detected, which leads to an underestimation of the error on mz for model independent determinations. 1 Supported by the German Bundesministerium Forschung und Technologie. für 2 Supported by the Hungarian O TKA fund under contract number 2970. Volume 315, number 3,4 7 October 1993 PH Y SIC S L E T T E R S B 1. Introduction 2. The L3 detector The successful operation of LEP has allowed a precise measurement of the e+e_ annihilation crosssections and asymmetries near the Z resonance. The mass, total and partial widths of the Z boson have been determined with an excellent accuracy. The ex­ perimental results confirm the Standard Model with percent precision [1-3]. In this paper we investigate to what extent a sat­ isfactory description of the experimental data on the Z line shape can be reached with minimal assump­ tions. We base this study on an S matrix approach, the details of which are explained elsewhere [4]. The scattering process is described by the superposition of massless and massive boson exchange, without mak­ ing detailed assumptions about the dynamics of the process. For the total cross-section the S matrix approach is equivalent to the model independent approach derived earlier [5]. Other model independent ap­ proaches to the Z line shape have been described in the literature [6-8] and used by L3 in previous stud­ ies [ 1]. All of these studies have in common that the interference between the massless and the massive boson exchange for hadronic reactions is fixed to the value it assumes in the Standard Model. This treat­ ment was shown to be sufficient at the previous level of accuracy, since the interference term is suppressed in the vicinity of the Z resonance. The present ac­ curacy of lineshape measurements allows, however, to determine limits on the value of this interference term for total cross-sections as well as asymmetries, and for leptonic and hadronic final slates separately. We also study the influence of this term on the value of the Z mass, and the potential bias caused by fix­ ing it to its Standard Model value. A discussion of the theoretical predictions for the interference term in the Standard Model and its measurability can be found in ref. [9]. We use our experimental measurements of the total cross-sections, the forward-backward asymmetries for all leptonic and hadronic Z decay channels as well as the polarization of tau leptons from Z decay. The total luminosity used is 17.2 pb*” 1 (corresponding to about 40000 leptonic and 423 000 hadronic events) collected with the L3 detector in 1990 and 1991. The L3 detector at LEP covers 99% of the full solid angle. It is designed to measure energy and position of leptons, photons and jets with high precision. A de­ tailed description of the detector and its performance can be found elsewhere [10]. The detector consists of a time expansion cham­ ber (T EC ) for the tracking and vertex reconstruc­ tion of charged particles, a high resolution electromag­ netic calorimeter made of about 11 000 bismuth ger­ manium oxide (BG O ) crystals, a hadron calorimeter (H C A L) with uranium absorber and brass propor­ tional wire chambers and a high precision muon spec­ trometer, consisting of three layers of multi-wire drift chambers. A cylindrical array of 30 scintillation coun­ ters is installed in the barrel region between the BGO and the HCAL. The luminosity is measured by the luminosity monitors, two electromagnetic calorime­ ters, situated symmetrically on either side of the inter­ action point. Each calorimeter is a finely segmented and azimuthally symmetric array of 304 BGO crystals covering the polar range 24.93 < 0 < 69,94 mrad. All detectors are inside a 12 m inner diameter solenoidal magnet which provides a uniform magnetic field of 0.5 T along the beam direction. 3. Z lineshape measurements Operating the LEP storage ring in the vicinity of the Z mass with high luminosity permits a detailed study of the lineshape of the Z resonance. We have performed measurements of the reactions (1) e+e- -» hadrons, (2) e+e~ ß +ju~(y), (3 )e+e~ -► T+r~ (y ) , (4) e+e” —» e+e~ ( y ) . The analysis methods used for these reactions are de­ scribed in detail elsewhere [1,11]. The cross-sections and asymmetries determined with the data taken in the 1990 and 1991 runs of LEP have been published [1 ]. Additionally, we include the average r polariza497 ar PHYSICS LETTERS B Volume 315, number 3,4 tion [ 12 ] at x/? = 91.222 GeV, Vx = -0.132±0.026± 0 .021. The matrix element for the exchange of a photon and a Z boson in e+e" annihilation into massless fermions can be written as M u (s) + R -f CTq + CTj (1) m\ - imzr z. — ÍJ2 ” * 0*3• (4 cont’d) ^ + (j - m\ ) j {A ( s - m l)2 + m lT 2 z A = tot, fb, poi, fbpol, lÆyl2 if A = tot, 0 if A ^ tot. (5) The pole position for the Z-boson is given by sz, R y and Rz are the residuals for the photon and Z boson respectively. R r is defined by ( 2) Qf is the charge of the corresponding fermion and a (s) the running QED coupling constant. The coefficients R ¿ describe the four helicity am­ plitudes for the Z exchange: I* 9 fr fR+), (6 ) The Z exchange term, rA, and the yZ interference term, j Ai are given by rf 'A + R z {tL eg a 2 + Cr3 , ijy aA(s) = \na 1 ' A / n~ 1 with Rz crS, (¿ ) ,y / = 0,3, sz -j- (7q - where rl is the photon exchange term: OG fi Sz tf p o lO ) = The cross-sections can be parametrized as follows: 4. The S matrix formalism R 7 October 1993 R /=i ÎA f/ + 2 ^ l m C (A , mz 2 Re C\ , rA f (7) /=1 u where {±1} indicates that the sign of Rz * and of Rz corresponds to the sign of cr, in eq. (4). For the hadron channel one has to sum rA, rA and j A over all colours and open flavours. The asymmetries are defined by A a (s ) = <rA{s) A zfz tot. (8 ) Ö’tot (S ) ,fl Rz = ^z(eL eR ♦fR fL ) , The coefficients f)ll (s) of the power series in eq. ( 1) describe non-resonant contributions to the scattering process. As shown in refs. [4,5] these are numerically small around the Z resonance and are neglected for our analysis. The cross-sections, a¡, arising from the correspond­ ing M u can be combined to four linearly independent cross-sections, observable at LEP: Photonic corrections are included by convolution, for details see ref. [4], Eqs. (l)- (8 ) completely define the framework of an S matrix analysis of the Z lineshape. However, when comparing Z parameters to other approaches, the following clarification is necessary: First, it should be noted that in the S matrix ap­ proach the total width, r z, is constant in contrast to the parametrization of the Breit-Wigner resonance of the Z lineshape, where p¿ is a result of quantum cor­ rections, which are ^-dependent. This leads to a trans­ formation of the Z mass, mz, to mz and of the total Z width, 7z, to Fz [13]: ö-tot fa) = +a0 + ÖÏ + <r2 + <?3 rñz — [1 + (/z/^z)2] “ l/2mz ~ wz - 34 MeV, f2 Rz = -^z(eReL ß R'z = ^z(eReL fR" fL+) , * (3) , O fb (s ) = 498 + # 0 “ G I + Ö2 0*3 Í (4) r [1 + (r z/mz)2]- l,2r z * r z - l MeV. (9) Volume 315, number 3,4 PH Y SIC S L E T T E R S B Thus, the mass, Tñz, obtained from S matrix fits should be shifted by -34 MeV and the total width, F z, by -1 MeV, with respect to the results obtained from the standard procedure [ 1]. Second, with vector and axial vector couplings of the Z to the fermions, eqs. (3) can be expressed as R r o K(gv + ga)(gl + g l), ri R K (g ï + g l) (gl - g l), 1 2 R K(gv - g l) (gl - g l) , R Í3 K ('gv ~ ga) (gl + g l), with K \ V lln a ( 11) Interpreting the couplings, gv and ga, as effective pa­ rameters, the weak corrections are absorbed in the couplings. For leptonic channels, the cross-sections (eqs, (4 )), or respectively, the helicity amplitudes (eqs. (3) ), can all be measured separately, assuming lepton universal­ ity. However, for hadronic reactions the contributing flavours cannot all be separated. Therefore, one can only measure the sum of all contributions according to eq. (7), i.e. in terms of r^ad and ybad. In previous model independent studies [ 1], terms relating to jxSi were evaluated using the Standard Model relation gl = g l( l - 4|Qf| sin20W) , photon exponentiation. Interference between initial and final state is neglected for radiative corrections. The data listed in ref [ 1] have systematic uncer­ tainties in addition to their statistical errors. These are caused by selection bias, theoretical uncertainties, limited Monte Carlo statistics etc. We consider a par­ tial error correlation calculating a #2, X ( 10) ( 12 ) with sin 0w taken from the leptonic lineshape. 5. S matrix analysis We used the program SM ATASY [14] together with Z FIT T ER version 4,53 [7]. SM ATASY relies on the S matrix ansatz for the total cross-section and for the three asymmetries. It is a generalization of the existing Z FIT T ER branch ZUSM AT, which considers only the total cross-section. Initial and fi­ nal state QED corrections are taken into account by convolution in 0 (a 2), higher order corrections for initial state radiation are considered with common 7 October 1993 -l  l V ~ xÀ, (13) where A is a column vector with elements such as (<7th - crexp) and M th - ^ exp) and V is the N x N error correlation matrix between measurements. The diagonal elements of V are given by the quadratic sum of statistical and systematic errors, while the offdiagonal elements are given by the product of the com­ mon systematic errors. This can be generalized also to the common systematic error between different data sets. The procedure to implement the LEP energy un­ certainty is described in detail elsewhere [15]. 6. Results To study the influence of the yZ interference on the final results of mz and Fz the fits in the following sections are performed in two steps: (a) All parameters except the photon exchange, ry A, are left free. (b) In addition to r\, the contributions to the yZ interference, 7 th0atd, are fixed to the value expected by the Standard Model. In order to reduce the number of free parameters, lepton universality is assumed. The photon exchange term, rj0l (see eq. (2 )), is fixed using the running coupling constant value at LE P energies, | a -1 (5 ) 128,8, The quality of all fits is good. The x 2per degree of freedom varies between 0,75 and 0.78. The results of the S matrix approach are compared to those of the model independent ansatzes of ZFITTER. 6.1. A fit to the total cross-section and forward-backward asymmetry We perform a fit to the leptonic and hadronic cross-section data and the leptonic forward-backward asymmetries according to eq. (5), Assuming lepton universality, one gets for case (a) 8 and for (b) 6 free parameters: mz, Fz, and rth0atd, for hadrons and 499 Volume 315, number 3,4 PH Y SIC S L E T T E R S B Table 1 Results of the S matrix fit to total cross-sections and forward-backward asymmetries: (a) all parameters except the photon exchange are left free; (b) in addition the yZ interference terms are fixed to the Standard Model expec­ tation. Case (a) Case (b) Parameter mz (G eV) Pz (G eV) Jep 'tot •lep -'tot Jep 91.152 ± 0.015 2.494 ±0.012 91.160 ± 0.010 2.492 ±0.012 0.141 ±0.002 0.140 ± 0.002 0.032 ± 0.064 fixed to 0.0058 mz (G eV) Pz (G eV) lepQ R iepl R 0.004 ±0.001 0.004 ±0.001 0.674 ±0.087 2.859 ± 0.030 0.720 ±0.700 0.675 ± 0.087 2.855 ± 0.029 fixed to 0,219 Xd tot /had -'tot rton Jtou rfbP>^lbP f ° r lePtons- The results are shown in table 1 . Comparing both fits, one notices that mz increases by 8 MeV, when the yZ interference terms are fixed in fit (b ), whereas the error on mz decreases by 5 MeV. That means that fixing the yZ interference introduces a systematic bias in the determination of the Z mass. For all the other parameters the mean values and errors remain unchanged. If one compares the values for Tñz with the results for mz, determined with Z FIT T ER (see table 3), one finds the expected offset between mz and mz of -34 MeV, only when the yZ interference term for the hadron channel j th0atd is treated in the same way. (5.2. Determining the helicity amplitudes with the S matrix approach In addition to the data set used in section 6.1, the t polarization measured in 1991 is also taken into account. Assuming lepton universality and C P con­ servation three independent helicity amplitudes /?zp0, i?zPl and R f 1 can be determined corresponding to eqs. (3). It should be noted here, that in the r channel one has the possibility to determine all four ampli­ tudes, because one can measure the total cross-section and all three asymmetries. The amplitudes i?zpl an(^ i? 2 p3 are equal by time reversal symmetry. The avail­ able information is not sufficient to express rtoad and 7totd by helicity amplitudes. Therefore, they still re­ main independent parameters. The number of free pa­ rameters is 7 in case (a) and 6 in case (b). For the 500 Table 2 Results of the S matrix fit to total cross-sections, forwardbackward asymmetries and x polarization: (a) all parame­ ters except the photon exchange are left free; (b) in addi­ tion the hadronic yZ interference terms for the total crosssection are fixed to the Standard Model expectation. Parameter % 7 October 1993 Case (a) Case (b) 91.155 dh0.013 2,494 0 ,0 1 2 91.160 ± 0 .0 10 2.492 ± 0 .0 12 0.429 ± 0 .0 12 -0.370 ± 0.003 0.429 ± 0 .0 1 2 0.323 i 0.016 2.860 ± 0.030 0.620 ± 0.620 -0.370 ± 0.003 0.323 ± 0.016 2.856 ± 0.029 fixed to 0.219 mz (G eV) r z (G eV) 91.189 ± 0.013 2.495 ± 0 .0 1 2 91.194 ± 0 .0 10 2.493 ± 0 .0 12 &,lcp ÔlcP &a -0.037 ± 0 .0 10 -0.037 ± 0 .0 10 -0.4991± 0,0019 —0.4988± 0.0019 0.2317 ± 0.0037 0.2316 ± 0.0037 D¡ep2 AZ, rhad tot jhad Jtot sin¿ 0w fit we assume the helicity amplitudes to be real. The first part of table 2 shows the results. The sec­ ond part of table 2 shows quantities which are derived from the parameters in the upper part of the table, mz, Pz and mz, P z are related by eq. (9). Refering to eqs. ( 1 0 ) one can write the amplitudes R 1 ^ 1as func­ tion of the couplings gjep and galep. Here we use i? 2 P0 and R l pi to determine the couplings and sin2 #w, de­ fined by eq. ( 1 2 ). For the helicity fit one finds the same behaviour for mz as in the previous section. The error for mz increases when yth0ad is left free. The mean values and errors for all other parameters are almost unchanged. As a cross check we compare the results of the S matrix approach with the Z FIT T ER results using the same measurements as for the helicity fit. In Z F IT ­ T ER two alternative model independent ansatzes are applied: the first is based on the assumption of real vector and axial vector couplings of the Z boson to fermions; the second relies on the assumption that scattering through the Z boson may be considered as subsequent formation and decay of a resonance de­ scribed by the widths into the initial and final state fermions. The complications due to the handling of the yZ interference contribution for the hadronic final state, 7 th0atd, are solved by fixing it to the value expected in the Standard Model. In order to check this proce- P H Y SIC S L E T T E R S B Volume 315, number 3,4 Table 3 Results of a model independent fit to total cross-sections, forward-backward asymmetries and r polarization using Z F IT T E R : (a) all parameters except the photon exchange are left free; (b) in addition the hadronic yZ interference terms for the total cross-section are fixed to the Standard Model expectation. Parameter Case (a) Case (b) mz (G eV ) Tz (G eV) 91.187 ±0.013 2.492 ±0.012 91.194 ±0.009 2.490 ±0.012 ?,lep —0.040 ±0.006 -0.040 ±0.006 ? Jep -0.4989± 0.0016 1.751 ±0.011 1.0 0 ± 0.86 -0.4986± 0.0016 1.750 ±0.011 fixed to 0.219 0.2300± 0.0030 0.2300± 0.0029 ^had /had J tot sin¿ 0 \y dure a five parameter fit to the leptonic and hadronic cross-section data and the leptonic forward-backward asymmetry and the r polarization is performed. In case (a) the term yjjjt1 is left free, and in case (b) the standard Z FIT T ER code is used with the fixed yth0ad. The results are shown in table 3* The second part of table 3 shows sin2 0W derived from &jep and #Jep. If one modifies the standard Z FIT T ER program to allow for a fit to the hadronic interference term yth0ad, as it is done for the results (a) in table 3, one also finds that the mean value for mz decreases and that the error increases with respect to the standard Z FIT T ER results (b), by the same amount observed for the fits using the S matrix formalism, A comparison of the second part of table 2 with table 3 shows that one gets the same results for the S matrix approach as with Z FIT T ER . The 5 matrix approach can, however, reproduce the mean value and error for mz only if the treatment of yth0ad is identical to the standard ZFIT T ER . 7. Conclusions - The S matrix approach allows a general model inde­ pendent investigation of the cross-sections and asym­ metries measured in the vicinity of the Z resonance and a determination of the mass and the width of the Z boson. - The S matrix approach can reproduce, with addi­ tional assumptions, the results of other model inde­ 7 October 1993 pendent ansatzes realized in ZFITTER. - For model independent determinations, the fixing of the hadronic interference term for the total crosssection to the Standard Model expectation value leads to a systematic bias in the value of the Z mass and un­ derestimates the systematical error on mz. This effect is also observed for ZFITTER. All other parameter are independent of yth0ad. Although the yZ interference contribution to the hadronic final state, yth0ad, is sup­ pressed and its measurement is very poor, the influ­ ence ofythod on the value mz is not negligible. The pro­ cedure of fixing yth0ad by expressions predicted by the Standard Model should be checked when performing model independent fits to avoid misinterpretation of the results. An improved measurement of is ex­ pected by running with higher luminosity at energies off the resonance (see [9 ]). The results of the 5 matrix approach confirm the present values for mz and 7z within their errors. The good agreement of the 5 matrix approach with the Standard Model fit values means that there is no ev­ idence for new physics in the data. Acknowledgement We express our gratitude to the CERN accelerator divisions for the excellent performance of the LE P ma­ chine. We acknowledge the effort of all engineers and technicians who have participated in the construction and maintenance of this experiment. References [ 1] L3 Collab., 0. Adriani et al., Results from the L3 Experiment at L E P , CERN-PPE/93-31. [2] L E P Collaborations, Phys. Lett, B 276 (1992) 247. [3] S.L. Glashow, Nucl. Phys. 22 (1961) 579; S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264; A. Salam, Elementary Particle Theory, ed. N. Svartholm (Almquist and Wiksell, Stockholm, 1968) p. 367. [4] A. Leike, T. Riemann and J. Rose, Phys. Lett. B 273 (1991) 513; T. Riemann, Phys. Lett. B 293 (1992) 451, and references therein. [5] A. Borrelli et al., Nucl. Phys. B 333 (1990) 357. [ 6 ] F.A. Berends et al., in: Z Physics at L E P 1, C ER N Report C ER N 89-08, eds. G. Altarelli, R. Kleiss and C. Verzegnassi (C ER N , Geneva, 1989) Vol. Í, p. 89. 501 Volume 315, number 3,4 P H Y SIC S L E T T E R S B [7] D. Bardin et al., FO R T R A N program Z F IT T E R , and C ERN -TH . 6443/92; Z. Phys. C 44 ( 1989) 493; Nucl. Phys. B 351 (1991) 1; Phys. Lett B 255 (1991) 290. [ 8 ] M. Martinez et al., Z. Phys. C 49 ( I 99Í ) 645. [9] G. Isidori, IN F N preprint 945 (1993). [10] L3 Colîab., B. Adeva et al., Nucl. Inst. Meth. A 289 (1990) 35. [ 11 ] L3 Coilab., B. Adeva et al., Z. Phys. C 51 (1991) 179. 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