17 October 19%

PHYSICS LETTERS I3

ELSEWIE% Physics Letters B 387 (1996) 432-442

Test of the four-fermion contact interaction in e+e- collisions at 130-140 GeV

OPAL Collaboration

G. Alexander w, J. Allison P, N. Altekamp e, K. Ametewee Y, K.J. Anderson i, S. Anderson e, S. Arcelli b, S. Asai ‘, D. Axen ac, G. Azuelos’p’, A.H. Ballq, E. Barberio h, R.J. Barlowp,

R. BartoldusC, J.R. Batleye, J. Bechtluft “, C. Beestonr, T. Behnke h, A.N. Bell a, K.W. Bell t, G. Bella”, S. Bentvelsen h, P. Berlichj, S. Bethke “, 0. Biebel n, V. Blobel h,

I.J. Bloodwortha, J.E. Bloomera, M. Bobinskij, P. Bockk, H.M. Boschk, M. Boutemeurah, B.T. Bouwens ‘, S. Braibantl, R.M. Brown’, H.J. Burckhart h, C. Burgard h, R. Btirginj,

P Capiluppi b, R.K. Carnegie f, A.A. Carter m, J.R. Carter e, C.Y. Chang 9, C. Charlesworth f, D G Charlton a,2, D. Chrisman d, S.L. Chu d, P.E.L. Clarke O, I. Cohen w, J.E. Conboy O, . .

O.C. Cooker, M. Cuffiani b, S. Dado “, C. Dallapiccola 9, G.M. Dallavalle b, S. De Jong e, L.A. de1 Pozo h, K. Desch c, M.S. Dixit s, E. do Couto e Silvae, M. Doucet r, E. Duchovni z,

G. Duckeck&, 1.P Duerdothp, J.E.G. Edwards P, PG. Estabrooks f, H.G. Evans i, M. Evans m, F. Fabbri b, P Fath k, F. Fiedlere, M. Fierro b, H.M. Fischer ‘, R. Folman ‘,

D.G. Fongq, M. Foucherq, A. Ftirtjes h, P. Gagnon s, A. Gaidot “, J.W. Gary d, J. Gascon r, S.M. Gascon-Shotkinq, N.I. Geddes t, C. Geich-GimbelC, F.X. Gentit “, T. Geralis t,

G. Giacomelli b, P. Giacomelli d, R. Giacomelli b, V. Gibson”, W.R. Gibsonm, D.M. Gingrichadyl, D. Glenzinski’, J. Goldberg”, M.J. Goodricke, W. Gornd, C. Grandi b,

E. Gross z, M. GruwC h, C. Hajduaf, G.G. Hansone, M. Hansroul h, M. Hapke m, C.K. Hargrove s, PA. Hart i, C. HartmannC, M. Hauschild h, C.M. Hawkes”, R. Hawkings h,

R.J. Hemingway f, G. Hertenj, R.D. Heuer h, M.D. Hildrethh, J.C. Hille, S.J. Hilliera, T. Hilse j, P.R. Hobson Y, R.J. Homer ‘, A.K. Honmaab*‘, D. Horvath af*3, R. Howard ac, R.E. Hughes-Jones P, D.E. Hutchcrofte, P Igo-Kemenesk, D.C. Imriey, M.R. Ingramp,

K. IshiiX, A. Jawahery 9, P.W. Jeffreys t, H. Jeremie’, M. Jimack a, A. Joly r, C.R. Jones e, G. Jones P, M. Jones f, R.W.L. Jones h, U. Jost k, P Jovanovic a, T.R. Junk h, D. Karlen f,

K. KawagoeX, T. Kawamoto”, R.K. Keeler ab, R.G. Kellogg q, B.W. Kennedy t, B.J. King h, J. Kirk ac, S. Kluth h, T. Kobayashi ‘, M. Kobelj, D.S. Koetke f, T.P. Kokott ‘,

S. KomamiyaX, R. Kowalewski h, T. Kress k, P. Krieger f, J. von Krogh k, P Kyberd m, G.D. Lafferty P, H. Lafoux”, R. Lahmann q, W.P. Lai ‘, D. Lanske n, J. Lauber O,

S.R. Lautenschlager =, J.G. Layter d, D. Lazic “, A.M. Lee =, E. Lefebvre’, D. Lellouch ‘,

0370-2693/96/$12.00 Copyright 0 1996 Published by Elsevier Science B.V. All rights resewed.

PII S0370-2693(96fOl 156-2

OPAL Collaboration/ Physics Letters B 387 (1996) 432-442 433

J. Letts b, L. Levinson ‘, C. Lewis O, S.L. Lloyd m, F.K. Loebinger P, G.D. Long q, M.J. Losty a, J. Ludwigj, A. Luigj, A. Malik”, M. Mannelli h, S. Marcellini b, C. Markus ‘,

A.J. Martinm, J.P. Martin’, G. Martinezq, T. Mashimo ‘, W. Matthews Y, P. MattigC, W.J. McDonald ad, J. McKennaac, E.A. Mckigney O, T.J. McMahon a, AI. McNab m,

R.A. McPhersonh, F. Meijers h, S. Menke”, ES. Merritt’, H. Mesa, J. Meyeraa, A. Michelini b, G. Mikenberg ‘, D.J. Miller O, R. Mir ‘, W. Mohr j, A. Montanari b, T. Mori ‘,

M. Morii x, U. Mtiller ‘, K. Nagai ‘, I. Nakamura”, H.A. Nealh, B. NellenC, B. Nijjharr, R. Nisius h, S.W. O’Neale a, F.G. Oakhamg, F. Odorici b, H.O. Ogren ‘, T. Omori ‘,

M.J. Oreglia’, S. OritoX, J. P51inkasas,4, G. P6sztor af, J.R. Paterp, G.N. Patrickt, J. Pattj, M.J. Pearce a, S. Petzold =, P. Pfeifenschneider “, J.E. P&her i, J. Pinfold ad, D.E. Plane h,

P. Poffenberger , ab B. Poli b, A. Posthaus ‘, H. Przysiezniakad, D.L. Rees a, D. Rigby a, S.A. Robins m, N. Rodning ad, J.M. Roney ab, A. Rooke O, E. Ros h, A.M. Rossi b,

M. Rosvick ab, P. Routenburg ad, Y. Rozen “, K. Rungej, 0. Runolfsson h, U. Ruppel n, D.R. Rust’, R. Rylkoy, K. Sachsj, E.K.G. Sarkisyan”, M. Sasaki”, C. Sbarrab,

A.D. Schaile&, 0. Schaile ah, F. Scharfc, P. Scharff-Hansenh, P. Schenkd, B. Schmitt h, S. Schmittk, M. Schr6derh, H.C. Schultz-Coulonj, M. Schulz h, M. SchumacherC,

P. SchtitzC, W.G. Scott’, T.G. Shearsp, B.C. Shend, C.H. Shepherd-Themistocleous”, P. Sherwood’, G.P. Sirolib, A. Sittler”, A. Skillman’, A. Skujaq, A.M. Smithh, T.J. Smithab, G.A. Snowq, R. Sobieab, S. Siildner-Remboldj, R.W. Springerad, M. Sprostont, A. Stahl ‘, M. Starks[, M. Steiertk, K. Stephensr, J. Steuereraa,

B. Stockhausenc, D. Strom”, F. Strumiah, P Szymanski’, R. Tafirout’, S.D. Talbota, S. Tam&ax, P. Taras r, S. Tarem”, M. Tecchio h, M. Thiergenj, M.A. Thomson h,

E. von Tome ‘, S. Towers f, T. Tsukamoto ‘, E. Tsur w, AS. Turcot i, M.F. Turner-Watson h, P. Utzat k, R. Van Kooten’, G. Vasseur “, M. Verzocchi j, P Vikas’, M. Vincter ab, E.H. Vokurkap, F. Wackerle j, A. Wagner =, C.P. Ward e, D.R. Ward e, J.J. Ward O,

PM. Watkins a, A.T. Watson a, N.K. Watson a, P. Weber f, P.S. Wells h, N. Wermes c, J.S. White ab, B. Wilkens j, G.W. Wilson aa, J.A. Wilson a, G. Wolf ‘, S. Wotton e,

T.R. Wyattp, S. Yamashita”, G. Yekutieli ‘, V. Zacek r, a School of Physics and Space Research, University of Birmingham, Birmingham Bi5 217: UK

b Dipartimento di Fisica dell’ Universita di Bologna and INFN, I-40126 Bologna, Italy ’ Physikalisches Institut, Universitiit Bonn, D-53115 Bonn, Germany

e Department of Physics, University of Cal@nia, Riverside CA 92521, USA e Cavendish Laboratory, Cambridge CB3 OHE, UK

f Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario KIS 586, Canada g Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario KlS 586, Canada

h CERN, European Organisation for Particle Physics, CH-1211 Geneva 23, Switzerland i Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 66637, USA

j Fakultiit fiir Physik, Albert Ludwigs Universitat, D-79164 Freiburg, Germany k Physikalisches Institut, Universitiit Heidelberg, D-69120 Heidelberg, Germany

’ Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405, USA

m Queen Mary and Wesrfield College, University of London, London El 4N.X UK ’ Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany

O University College London, London WCIE 6BT, UK v Department of Physics, Schuster Laboratory, The University, Manchester Ml3 9PL. UK

a Department of Physics, University of Maryland, College Park, MD 20742, USA

434 OPAL Collaboration/ Physics Letters B 387 (1996) 432-442

’ Luboratoire de Physique Nucliaire, Universite’ de Montrial, Montrt!al, Quebec H3C 3J7, Canada

’ University of Oregon, Department of Physics, Eugene OR 97403, USA ’ Rutheqord Appleton Laboratory. Chilton, Didcot, Oxfordshire OX1 I OQX, UK

’ CEA, DAPNlMSPF1 CE-Saclay. F-91 I91 Gif-sur- Yvette, France ’ Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel w Department of Physics and Astronomy, Tel Aviv Universify, Tel Aviv 69978, Israel

’ International Cenfre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113. Japan and Kobe University, Kobe 657, Japan

Y Brunel University Uxbridge, Middlesex UB8 3PH, UK ’ Particle Physics Department, Weivnann Institute of Science, Rehovot 76100, Israel

aa Universitiit Hamburg/DES): II Institutfiir Experimental Physik, Notkestrasse 85, D-22607 Hamburg. Germany ab University of Wctoria. Department of Physics, PO. Box 3055, Victoria BC V8W 3P6, Canada

ac University of British Columbia, Department of Physics, Vancouver BC V6T lZ1, Canada ad University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada

ae Duke University, Department of Physics, Durham, NC 27708-0305, USA ac Research Institute for Particle and Nuclear Physics, H-1525 Budapest, PO Box 49, Hungary

ag Institute of Nuclear Research, H-4001 Debrecen, PO Box 51, Hungary ah Ludwigs-Maximilians-Universitiit Miinchen, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

Received 17 July 1996 Editor: K. Winter

Abstract

The differential cross-sections for e+e- + e’e-, e+e- + ptp- and efe- --f r+r-, and the total cross-section for e’e- --+ q4 at centre-of-mass energies of 130-140 GeV were studied using about 5 pb-’ of data collected with the OPAL detector at LEP in October and November 1995. The results are in agreement with the Standard Model predictions. Four-fermion contact interaction models were fitted to the data and lower limits were obtained on the energy scale A at the 95% confidence level.

1. Introduction

The measurements at LEP at 130-140 GeV have

provided the first e+e- collision data at energies

well above the Z” resonance. T’he cross-sections and

angular distributions for e+e- -+ qCj and efe- --+

Fe- (e = e, p, T) have been observed by OPAL to be in good agreement with Standard Model expecta- tions [ 11. It is interesting to see what constraints are

set by these data on possible contributions from new

physics. Here we study the four-fermion contact interac-

tion [ 21. The basic idea is that the Standard Model is a part of a more general theory characterised by an

I And at TRIUMF, Vancouver, Canada V6T 2A3.

2 And Royal Society University Research Fellow.

3 And Institute of Nuclear Research, Jlebrecen, Hungary.

4 And Department of Experimental Physics, Lajos Kossuth Uni-

versity, Debrecen, Hungary.

energy scale A and the consequences of the theory are

observed at energies well below A as a deviation from the Standard Model which can be described by an ef-

fective contact interaction. In the context of composite models of leptons and quarks, the contact interaction

is regarded as a remnant of the binding force between

the substructure of fermions. If electrons are compos- ite such an effect would appear in Bhabha scatter- ing (e+e- + e+e- ). If the other leptons and quarks share the same type of substructure, the contact in- teraction would exist also in the processes efe- +

p+p-, r+r- and e+e- --+ q4. More generally, the

contact interaction is considered to be a convenient parametrisation to describe a possible deviation from the Standard Model, which may be caused by some

new physics. Analyses of such contact interactions have been per-

formed at lower energy experiments for the processes efe- + F- [3-lo] and e+e- + qq [5,11]. It

OPAL Collaboration/Physics Letters B 387 (19961432-442 435

is expected that the sensitivity of the measurements to the contact interaction will increase with centre-of- mass energy ( 4) due to the decrease of the Standard Model cross-section as 1 /s, while some contributions of the contact interaction stay constant or even increase in proportion to s [ 121. Here we present a contact interaction analysis of the e+e- -+ e+e-, e+e- --)

+ - + - + r+r- and e+e- -+ qq channels us- h,“o<& iata at centre-of-mass energies of 130- 140 GeV. The cross-sections are compared with expecta- tions of contact interaction models in order to set lower limits on the energy scale A.

2. Four-femion contact interaction

In the contact interaction approach, the Standard Model contribution remains unchanged, but an effec- tive new interaction is added to it. Following the no- tation in [ 131, the effective Lagrangian for the four- fermion contact interaction in the process e+e- + fJ1 is defined by :

2

L contact =

(1 +%A2 ij=LR c rlij[ziVeil [_fjTjrpfjl 3 .

11)

with

S= 1 f=e Of+e*

Here eL and eR (f~ and fR) are chirality projections of electron (fermion) spinors. The unknown coeffi- cients vii determine the type of chiral coupling of the four fermions, and A is the energy scale of the con- tact interaction. The indices L and R denote left- and right-handed currents, respectively. By convention, the unknown coupling constant g is set to g2/47r = 1 and ]qij] 5 1. For the process eie- -+ e+e-, the size of the contact interaction differs from the other chan- nels by a statistical factor of l/2. A number of differ- ent models (choice of vij parameters) are customarily considered. They are summarised in Table 1. The W and AA denote the vector and axial vector couplings, respectively. The signs (zk) of the qij indicate posi- tive or negative interference with the Standard Model amplitude.

Table I Different models of the four-fermion contact interaction.

Model llLL ~)RR ?1LR 7)RL

LLf il 0 0 0 RRf 0 fl 0 0 Wf fl fl *1 fl AA* fl fl FI 71 LR* 0 0 i1 0

RL* 0 0 0 51

In the presence of the contact interaction the differ- ential cross-section for e+e- --t ff, as a function of the polar angle 6 of the outgoing fermion with respect to the e- beam direction, can be written to lowest or- der as

1 4s da --- Fc m2 d cos 0

= [la~(tv+ IA:L,‘,(t)12] (;)2s

+ [/A:{(s)12+ IA;{(s)12] (i)2

+ [iA;{Wj2 + ~A;{(s)/~] (;)2

with t = +(l - cos0) and u = +(l +cos0). The overall colour factor FC is 1 for C+e- and 3 for qq. The helicity amplitudes are

+(1 +S)7)iji$ (i= j).

Here LY is the electromagnetic coupling constant. The left- and right-handed couplings, & and gi, of the fermion f to the Z? are given by

A=. s,new:osew ( 13 - Qf sjn2hd 9

A= sinew~osew ( -Qf sin%d 1

where e is the electron charge, Qr is the electric charge in units of (e] of the fermion f, Z3 is the third component

436 OPAL Collaboration/Physics Letters B 387 (1996) 432-442

of the weak isospin and 8~ is the electroweak mixing angle. The s- and t-channel p propagators are

x(s) = s/(s - Mi+ isTz/Md,

/y(t) = t/(t - M;).

It should be noted that the LR and RL models give identical results for lepton pair channels while for the qq final state the results of the LR and RL models are different.

The cross-section formula (2) can be decomposed into three parts

(6)

The first term denotes the Standard Model cross- section. The second and third terms come from the contact interaction and represent deviations from the Standard Model expectation. The Cg term comes from the interference of the contact interaction with the Standard Model amplitude and the Ci term from the square of the contact interaction amplitude. The coefficients C,“(s, t) and C,“(s, t) have different de- pendencies on s and f depending on the final state fermion and the choice of the contact interaction model.

3. Data sample

A feature of e+e- collision data at centre-of-mass energies well above the p resonance is a tendency for radiative return to the p by emitting initial-state radiation photons which reduces the effective centre- of-mass energy, fi, of the subsequent e+e- collision to the region of the Z” resonance. Here we consider the cross-sections for e+e- ---t e+e-, e+e- + $,z”-, e+e- + ran- and e+e- ---) q4 at large fl so ex- cluding the events from radiative return to the p. The selection of such an event sample and the luminosity measurement are described in [ 11. For the e+e- 3 J.L+,u-, r+r- and e+e- * qq channels s//s > 0.8 was required. An almost equivalent cut was applied to the e+e- * efe- sample using a cut on the max- imum acollinearity angle at 10”. The integrated lumi- nosity of the data sample is about 5.2 pb-’ divided among three centre-of-mass energies of 130.26 GeV

(2.7 pb-‘), 136.23 GeV (2.5 pb-‘) and 140 GeV (0.05 pb-’ ). The numbers of events used in this anal- ysis were 967 e+e- --f e+e-, 53 e+e- -_, ,u+F-, 19 e+e- 4 r+r- and 334 efe- --P q4 events 5 . The backgrounds in the P+,u-, rfr- and qq samples are of the order of lo%, as discussed in [ 11, and mainly arise from events at lower s’fs; the background in the e+e- sample is mainly from 7 pair and is much smaller (less than 1 S) . The systematic errors of the event se- lection are 2.4% (e+e- 4 e+e- ), 2.0% (e+e- ---) ,u+,u-), 2.8% (e+e- --+ rfr-> and 4.0% (e+e- 3 qq) . The luminosity error was estimated to be 1%.

The angular distributions of the leptonic channels are expressed in 9 bins over -0.9 < cos 8 < 0.9 for e+e- --) e+e-, and 10 bins over - 1 .O < cos 0 < 1 .O for the e+e- --t pip- and @r- channels. The re- sults are summarised in Tables 2-4 together with the corresponding values of the differential cross-sections. For the eie- j qq channel only the total cross- sections given in [ l] were used in this analysis.

4. Calculation of predicted cross-sections

In order to compare the model with the data, the lowest order cross-section (6) must be corrected for electroweak and QED radiative effects and the ex- pected cross-section calculated taking into account the experimental cuts. The e+e- -+ qq channel must be corrected also for QCD effects. Different approaches were used for the Standard Model part and for the contact interaction terms.

The Standard Model cross-sections were calcu- lated for each cos 8 bin and centre-of-mass energy using ALIEW3A [ 141 for ete- ---) ete-, and ZFJIT- TER [ 151 for e+e- --t pL+p-, r+r- and qq with the cut on the acollinearity angle (e+e- ) or s’ (P+,u-, T+T- and q4) at the same value as in the data sam- ple. The systematic uncertainty of these predictions is estimated to be 2.5%, 1.0% and 2.0% for the e+e- + e+e-, e+e- ---) ,u+,u-/~+T- and e+e- --)

5The same numbers of pfpCL- and &F events were used in [ 1 ] for the measurement of forward-backward asymmetry; these are slightly different from those used for the cross-section measurement because of additional requirements to ensure good charge determination.

OPAL Collaboration/Physics Letters B 387 (1996) 432-442 437

Table 2 Numbers of selected events and differential cross-sections of e+e-.

cos t3

130.26 GeV (2.7 pb-‘)

N ee du/d cos 0 (pb)

136.23 GeV (2.5 pb-‘)

N,, da/d cos 0 ( pb)

-0.9 -0.7 2 4f 3

-0.7 -0.5 3 6f 3

-0.5 -0.3 2 4f 3

-0.3 -0.1 3 6f 3

-0.1 0.1 7 13f 5

0.1 0.3 10 195 6

0.3 0.5 27 52flO

0.5 0.7 59 113fl5

0.7 0.9 408 817f41

3 6% 4 3 6f 4 3 6f 4 3 6f 4 5 10f 5 8 16f 6

12 24f 7 61 123fl6

348 735f39

Table 3 Numbers of selected events and differential cross-sections of /L+/A-.

cos B

130.26 GeV (2.7 pb-‘)

NW du/d cos 0 ( pb)

136.23 GeV (2.5 pb-‘)

NW dufd cos 0 (pb)

-1.0 -0.8 0 0 0 0 -0.8 -0.6 2 4f3 0 0

-0.6 -0.4 1 2f2 0 0

-0.4 -0.2 4 7f4 3 6f4

-0.2 0.0 0 0 1 2f2 0.0 0.2 2 3f3 3 6f3 0.2 0.4 5 9f4 2 4f3 0.4 0.6 2 343 7 1456 0.6 0.8 3 5f4 5 lOf5 0.8 1.0 6 15f7 7 20f8

Table 4 Numbers of selected events and differential cross-sections of T+T-.

cos e

130.26 GeV (2.7 pb-‘)

N77 duldcos8 (pb)

136.23 GeV (2.5 pb-I)

N77 du/d cos B (pb)

-1.0 : -0.8 0 0 0 0 -0.8 : -0.6 0 0 0 0 -0.6 : -0.4 0 0 0 0 -0.4 : -0.2 0 0 0 0 -0.2 : 0.0 0 0 0 0

0.0 : 0.2 1 3f3 1 3f3 0.2 : 0.4 2 6f4 2 6f4 0.4 : 0.6 3 9f5 5 16f7 0.6 : 0.8 1 3f3 2 7f5 0.8 : 1.0 2 llf8 0 0

438 OPAL Collaboration/ Physics Letters B 387 (1996) 432-442

qq channels, respectively. 6 The Standard Model pa- rameters were fixed at MZ = 91.188 GeV, Mtop = 180 GeV and Mt-nggs = 100 GeV. The dependencies of the cross-section on these parameters within their uncer- tainties are negligible compared to the sensitivity of the present fit.

The contact interaction terms Ci and Ci were eval- uated using the improved Born approximation. The value of the effective weak mixing angle sin*& was calculated by ZFIITER. The running QED coupling constant a(s) was used for the s-channel part. The Cg, Ci coefficients were then corrected for the effect of photon radiation according to [ 171. Initial-state ra- diation was calculated up to order my2 in the leading log approximation with soft photon exponentiation, and the order a leading log final state QED correction was applied.

The cross-section for e+e- --+ e+.!- at the centre- of-mass energy point k and cos 8 bin i is then expressed as a function of E = l/A2 by

(+j,k(&) =SMi,k + Cz(i,k) e+C~(i,k) a2

(e+e- --+ e+l-) , (7)

where SMi,k is the Standard Model cross-section. The values of the radiatively corrected contact interaction coefficients, C2 (i, k) and C4 (i, k), were calculated by integrating over each cos 0 bin i at each centre-of- mass energy point k for each of the contact interaction models and final state fermions considered. Similarly the total cross-section for e+e- + qq is defined by

gk(c) = SMk + c [G(k) e+ Cd(k) c*] . &CD

u,d,c,s,b

(e+e- + q4) , (8)

where the additional QCD correction factor RQCD =

1+ as /IT + 1.409( a,/~)~ has been shown separately for the contact interaction terms. The contact interac- tion is assumed to be independent of the quark flavour.

6~hese are estimates based on our comparisons of the results

using different programs. Similar comparisons in [ 161 indicate that ZFTJTER agrees with other programs better than 1% at the

LEP 2 energy region.

5. Fit results

The predictions of the contact interaction models were fitted to the data using a binned maximum likeli- hood method. The likelihood function L is defined by

Ns Nbin

C=g(r;Ar)II,P(,,,,N~d(~,r)), k=I i=l

(9)

where the index k runs over the Ns centre-of-mass energy points and i runs over the Nbin cos 0 points. P is the Poisson probability of finding NtiU events

of data when N$“(c, r) events are predicted. The parameter r is a correction to the overall normalisation and 6( r; Ar) is the Gaussian probability distribution for r with mean 0 and standard deviation Ar. The number of events predicted is given by

N$d(e, r) = (1 f r) [gi,k(&)Ei,k + Bi,k] Lk, ( 10)

where (+i,k ( E) is the cross-section defined above (Eqs. (7), (8)), Ei,k is the correction factor for the ex- perimental efficiency, Bi,k is the expected background cross-section and Lk is the integrated luminosity. The value of Ar was set to the value of the sum in quadra- ture of the luminosity error, the systematic error of the event selection and the theoretical uncertainty on the cross-section calculation.

The contact interaction models were fitted to the data with r and E s l/A* as fitting parameters. Note that both positive and negative values of c are phys- ically meaningful. As seen from Eqs. (2)-( 5), the term C2 * E is linear in vij and C4 . E* contains only terms proportional to r$. The results of positive and negative interference with the Standard Model ampli- tude (sign of vii parameters) are equivalent under the transformation E H --E. It is therefore sufficient to fit only for the case of positive interference, but to allow E to be both positive and negative.

The results of the fits are tabulated in Table 5 for the four individual channels. Fits are also made for all the leptonic channels combined (e+e- + C+!- ) and the lepton and qq channels combined (all combined). As described before, for the lepton pair channels the results of the LR and RL models are identical and only the LR results are quoted. The fitted values and their one standard deviation errors on E are listed in the second column. Fig. 1 shows the fitted E values from

OPAL Collaboration/ Physics Letters B 387 (1996) 432-442 439

Table 5 Results of the contact interaction fits.

Model E (TeV-*) h (TeV) A- (TeV) A+ (TeV)

e+e- + e+e- W

AA

LL

RR

LR

e+e- -+ p+p- W 0.1 10+0.0s3 -0.053 3.4 4.1 2.2

AA 0.1 60+“.070 -0.077

2.9 3.5 1.9

LL 0.258fo.“7 -0.119 2.3 2.7 1.5

RR 0 282+0.‘24 . -0.128

2.2 2.5 1.4

LR o.200+o.‘56 -0.216 1.9 1.2 1.5

e+e- -+ 7+7- W -0.084+“.m3 -0.073 2.9 2.2 3.2

AA o.010+“m7 -0.fJ77 2.8 2.6 2.5

LL -O.l14+O.‘74 -0.199 1.8 1.2 2.0

RR -0. 132+“.200 -0.264 1.7 I.0 1.9

LR -0 147+0.184 . -0.184 1.8 1.5 1.9

e+e- 4 efe- W

AA

LL

RR

LR

e+e- -+ qCj

all combined

W

AA

LL

RR

LR

RL

W

AA

LL

RR

LR

RL

0 0()1+0.03’ . -0.031

4.4 3.6

0.057fo.” -0.056

3.4 2.6

() .250+0.198 . -0.175

1.8 2.0

0.243+“.201 -0.173

1.8 2.0

-0 052+0.1m . -0.085

2.6 2.2

0.020M.m6 -0.026 4.9

0,)69+0.037 -0.038 4.0

o.147+O.o84 -0.084 2.7

0. 160+“.wo -0.090 2.6

-o.055+“~w -0.084 2.7

4.6 3.7

4.6 2.8

3.0 1.8

2.9 1.8

2.2 2.2

0.025+“~m2 -0.072 _0.~7+O.cJ79

-0.073 -0 134M.158

. -0.144

o.o50+“‘43 -0.145 0.00yg+o.143

-0.143 0 178+0.‘49

. -0.169

0.020”.025 -0.uz4

0.038+“.029 -0.031

0.066”.060 -0.065

0.129+O~07* -0.077

-0.038”.081 -0073

o.009+“.~ -0.068

2.8 3.1 2.7

2.6 2.4 3.4

1.9 1.7 2.4

1.9 2.2 1.9

2.0 2.0 2.0

1.8 2.5 1.6

5.0 4.9 3.8

4.5 4.5 3.4

3.1 2.9 2.4

2.9 3.1 2.0

2.8 2.4 2.5

2.9 2.7 2.2

3.5

2.7

1.3

1.3

1.6

440 OPAL Collaboration/Physics Letters B 387 (1996) 432-442

OPAL

99 ~_S_ qi +.

all, y-- a) VV all iiLcl La_-. ,b’_A,A -0.25

E !TeV-') 0.25 -0.25

E TTeV-2)

0.25

w -*.j

all L. .,-_., c) LL

-0.8

E FTeV")

0.8

99

all LI_-. -0.8

E &ev-2)

0.8

-0.6

& YTeV-2)

0.6 -0.6

& &ev-2)

0.6

Fig. 1. Values of E (TeV-*) shown with one standard deviation errors for the six contact interaction models. The results for the leptonic channels are identical for the LR and RL.

the efe-, p+p-, r+r-, &’ and CI + qq channels. The error bars in the plots show the positive and negative one standard deviation errors. No significant deviation of the fitted E from 0 (Standard Model) was observed. The largest deviations are for the p+p- channel by about 2 standard deviations.

Now we check the sensitivity of the present data to the energy scale A of the contact interaction. For this purpose the sensitivity estimate A is defined in terms of the one sided 95% confidence level upper limit on e:

A= l/JixG&,

where a, is the one standard deviation parabolic error on E. This corresponds to the upper limit on E allowed for the fluctuation of the data at the 95% confidence level. The values of h are listed in the third column of Table 5. They are in the range of 1.7 to 5.0 TeV depending on the model and the final state fermion.

The 95% confidence level lower limit on the energy scale A is defined by

A* = l/&Z, (11)

where E+ and E- are the 95% confidence level limits on E for positive (+) and negative ( -) interference, respectively. The limits .c* are derived by integrating the probability in the range F > 0 for the ‘+’ case

jfL&=09S?L&

0 0

and E < 0 for the ‘--’ case

0 0

! L d& = 0.95

s Cd&.

-co

Here L is the likelihood function given by Hq. (9). In the integration the overall scale error r was adjusted at each value of E to maxim&e the likelihood. It shouId be noted that the limits on A defined in this way tend to be conservative if the true value of E is close to zero [ 181. In previous analyses [3-l 1,131 the limits were calculated from the positive and negative one standard deviation errors (~5) and the fitted value (co) of E

by A * = l/ 1.64a* f ea. However, in that case a problem occurs when ~0 deviates substantially from 0, where A cannot be defined (unphysical region) and the positive and negative limits tend to be quite asymmetric. In order to avoid this problem, A was used in [lo] when A > A.

The results are summarised in the fourth and fifth columns of Table 5. The limits on A obtained using ( 11) are generally quite close to the sensitivity es- timate A, indicating that these limits are reasonable. It is seen that the present data are particularly sensi- tive for the VV and AA models. When all channels are combined the limits on A are in the range of 3.4-4.9 TeV for the W and AA models, and 2.0-3.1 TeV for the other models. Note that, as described in Section 2, the coupling constant of the contact interaction is set by convention to g2/4n- = 1. What is actually con- strained by the data is A/g. In Fig. 2 the measured cross-sections are compared with the Standard Model predictions and with contact interaction models W and AA for A& at the corresponding 95% confidence level lower limits.

OPAL CoHaboration/ Physics Letters B 387 (1996) 432-442 441

0.5

0

OPAL

Fig. 2. Differential cross-sections normahsed to the expectations of the Standard Model for the e+e- (a), ,u+p- (b), T+T- (c) and qij (d) channels. The points with error bars are the pnzsent measurements and the curves indicate maximum deviations allowed at 95% confidence level for the W and AA models.

The measured total cross-sections for e+e- * qq are lower by up to two standard deviations than the predictions. Note that the contact interaction cannot produce a large negative contribution to the total cross- section for e+e- 4 qq in this energy region and above. This is a consequence of the assumption that the contact interaction is universal for all five quark flavours. The cross-section for an individual quark flavour can deviate either positively or negatively due to interference of the contact interaction with the Stan- dard Model amplitude. The signs of the interferences are opposite for up and down type quarks, and so largely cancel each other. Due to the positive contribu- tion from the l/A4 term the net result turns out to be insufficient to accommodate the data. Under other as- sumptions, for example that contact interactions apply only to down (or up) type quarks, both positive and negative deviations may be produced for the e+e- ---f qij cross-section.

6. Conclusion

The differential cross-sections for e+e- ---) e+e-, e+e- ---t pip-, e+e- ---) r+r- and the total cross- section for e+e- --) qq at centre-of-mass energies of 130-140 GeV are compared with predictions of the Standard Model and of the contact interaction models. The measured cross-sections are in agreement with the Standard Model expectations. The limits obtained by OPAL on the energy scale A are competitive with, or in some cases stronger than, those using existing measurements at lower energies [ 3- 11,131.

Acknowledgements

We particularly wish to thank the SL Division for the efficient operation of the LEP accelerator and for their continuing close cooperation with our experi- mental group. In addition to the support staff at our own institutions we are pleased to acknowledge the Department of Energy, USA, National Science Foundation, USA, Particle Physics and Astronomy Research Council, UK Natural Sciences and Engineering Research Council, Canada, Israel Ministry of Science, Israel Science Foundation, administered by the Israel Academy of Science and Humanities, Minerva Gesellschaft, Japanese Ministry of Education, Science and Culture (the Monbusho) and a grant under the Monbusho International Science Research Program, German Israeli Bi-national Science Foundation (GIFl, Direction des Sciences de la Mat&e du Commissariat a 1’Energie Atomique, France, Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie, Germany, National Research Council of Canada, Hungarian Foundation for Scientific Research, GTKA T-016660, and GTKA F-015089.

442 OPAL Collaborarion/Physics Letters B 387 (1996) 432-442

References [lOI [Ill

[ I] OPAL Collaboration, G. Alexander et al., Phys. Lett. B 376 (1996) 232.

[2] E. Eichten, K. Lane and M. Peskin, Phys. Rev. Lett. 50 (1983) 811.

[31 HRS Collaboration, M. Derrick et al., Phys. Rev. D 34 (1986) 3286.

[4] MAC Collaboration, E. Femandez et al., Phys. Rev. D 35 (1987) 10. CELLO Collaboration, H.J. Behrend et al., Z. Phys. C 51 (1991) 149, 143; Phys. LA%. B 191 (1987) 209; B 222 (1989) 163.

[I21

El31 1141

[51

1151

[I61

[61

171

[81

[91

[17 ‘I JADE Collaboration, W. Bartel et al., Z. Phys. C 30 ( 1986) 371. PLUTO Collaboration, Ch. Berger et al., Z. Phys. C 27 (1985) 341. TASS0 Collaboration, W. Braunschweig et al., Z. Phys. C 37 (1988) 171; C 40 (1988) 163; C 43 (1989) 549. VENUS Collaboration, K. Abe et al., Z. Phys. C 48 (1990) 13.

[18

ALEPH Collaboration, Z. Phys. C 59 (1993) 215. VENUS Collaboration, K. Abe et al., Phys. Lett. B 232 ( 1989) 425; TOPAZ Collaboration, I. Adachi et al., Phys. Lett. B 255 (1991) 613. B. Schrempp, E Schrcmpp, N. Wermes and D. Zeppenfeld, Nucl. Phys. B 296 ( 1988) 1. H. Kroha, Phys. Rev. D 46 ( 1992) 58. W. Beenakker et al., Nucl. Phys. B 349 ( 1991) 323. D. Bardin et al., CERN-TH 6443/92 (May 1992); Phys. Lett. B 255 (1991) 290; Nucl. Phys. B 351 (1991) 1; Z. Phys. C 44 (1090) 493. Physics at LEP2, Editors G. Altarelli, T. Sjijstrand and E Zwimer, CERN 96-01 (February 1996). Model independent e+e- + e+e- lineshape program MIBA, M. Martinez and R. Miquel, Z. Phys. C 53 ( 1992) 115. Particle Data Group, L. Montanet et al., ‘Statistics’ in: Review of Particle Properties, Phys. Rev. B 50 (1994) 1280.