A study of Ks0 production in Z0 decays

Volume 264, number 3,4 PHYSICS LETTERS B 1 August 1991

A study of production in Z ° decays

OPAL Collaboration

G. Alexander a, J. Allison b, P.P. Allport c, K.J. Anderson d, S. Arcelli e, J.C. Armitage f, P. Ashton b, A. Astbury 1, D. Axen 2, G. Azuelos g'3, G.A. Bahan b, J.T.M. Baines b, A.H. Ball h, J. Banks b, G.J. Barker i, R.J. Barlow b, J.R. Batley c, G. Beaudoin g, A. Beck a, J. BeckerJ, T. Behnke k, K.W. Bell e, G. Bella a, S. Bethke m, O. Biebel n, U. Binder j, I.J. Bloodworth °, P. Bock m, H.M. Bosch m, S. Bougerolle 2, B.B. Brabson P, H. Breuker k, R.M. Brown e, R. Brun k, A. Buijs k, H.J. Burckhart k, P. Capiluppi e, R.K. Carnegie f, A.A. Carter i, J.R. Carter c, C.Y. Chang h, D.G. Charlton k, J.T.M. Chrin b, P.E.L. Clarke q, I. Cohen a, W.J. Collins c, J.E. Conboy r, M. Cooper s, M. Couch °, M. Coupland t, M. Cuffiani e, S. Dado s, G.M. Dallavalle e, S. De Jong k, P. Debu u, M.M. Deninno e, A. Dieckmann m, M. Di t tmar v, M.S. Dixit w, E. Duchovni x, G. Duckeck m, I.P. Duerdoth b, D.J.P. Dumas f, G. Eckerlin m, P.A. Elcombe c, P.G. Estabrooks f, E. Etzion a F. Fabbri e, M. Fincke-Keeler l, H.M. Fischer n, D.G. Fong h, C. Fukunaga Y, A. Gaidot u, O. Ganel x, J.W. Gary m, J. Gascon g, R.F. McGowan b, N.I. Geddes ~, C. Geich-Gimbel n, S.W. Gensler d, F.X. Genti t u, G. Giacomelli e, V. Gibson c, W.R. Gibson i, J.D. Gillies e, J. Goldberg s, M.J. Goodrick c, W. Gorn v, C. Grandi e, E. Gross x, J. Hagemann k, G.G. Hanson P, M. Hansroul k, C.K. Hargrove w, P.F. Harrison i, j . Hart c, P.M. Hattersley °, M. Hauschild k, C.M. Hawkes k, E. Heflin v, R.J. Hemingway f, R.D. Heuer k, J.C. Hill c, S.J. Hillier °, D.A. Hinshawg, C. Ho v, J.D. Hobbs d, P.R. Hobson q, D. Hochman x, B. Holl k, R.J. Homer °, S.R. Hou h, C.P. Howarth r, R.E. Hughes-Jones b, R. Humber t J, P. Igo-Kemenes m, H. Ihssen m, D.C. Imrie q, L. Janissen f, A. Jawahery h, P.W. Jeffreys e, H. Jeremie g, M. Jimack e, M. Jobes °, R.W.L. Jones i, P. Jovanovic °, D. Karlen f, K. Kawagoe Y, T. Kawamoto Y, R.K. Keeler 1, R.G. Kellogg h, B.W. Kennedy r, C. Kleinwort k, D.E. Klem z, T. Kobayashi Y, T.P. Kokott n, S. Komamiya Y, L. K6pke k, R. Kowalewski f, H. Kreu tzmann n, J. von Krogh m, j. Kroll d, M. Kuwano Y, P. Kyberd i, G.D. Lafferty b, F. Lamarche g, W.J. Larson v, J.G. Layter v, P. Le Du u, P. Leblanc g, A.M. Lee h, M.H. Lehto r, D. Lellouch k, P. Lennert m, C. Leroy g, L. Lessard g, S. Levegriin n, L. Levinson x, S.L. Lloyd i, F.K. Loebinger b, J.M. Lorah h, B. Lorazo g, M.J. Losty w, X.C. Lou p, J. Ludwig j, M. Mannell i k, S. Marcellini e, G. Maringer n, A.J. Martin i, J.P. Martin g, T. Mashimo Y, P. Mfittig n, U. Maur n, T.J. McMahon °, J.R. McNut t q, F. Meijers k, D. Menszner m, F.S. Merritt d, H. Mes w, A. Michelini k, R.P. Middleton ~, G. Mikenberg x, j. Mildenberger f, D.J. Miller r, C. Milstene a, R. Mir p, W. Mohr j, C. Moisan g, A. Montanari e, T. Mori y, M.W. Moss b, T. Mouthuy p, P.G. Murphy b, B. Nellen n, H.H. Nguyen d, M. Nozaki Y, S.W. O'Neale k,4, B.P. O'Neill v, F.G. Oakham w, F. Odorici e, M. Ogg f, H.O. Ogren p, H. Oh v, C.J. Oram 5, M.J. Oreglia d, S. Orito Y, J.P. Pansart ~, B. Panzer-Steindel k, p. Paschievici x, G.N. Patrick e, S.J. Pawley b, P. PfisterJ, J.E. Pilcher d, J.L. Pinfold x, D.E. Plane k, p. poffenberger l, B. Poli e, A. Pouladdej f, E. Prebys k, T.W. Pri tchard i, H. Przysiezniak g, G. Quast k, M.W. Redmond d, D.L. Rees o, K. Riles v, S.A. Robins i, D. Robinson k, A. Rollnik n, J.M. Roney d, S. Rossberg j, A.M. Rossi e,6, P. Routenburg f, K. Runge j, O. Runolfsson k, D.R. Rust p, S. Sanghera f, M. Sasaki Y, A.D. SchaileJ, O. SchaileJ, W. Schappert f, P. Scharff-Hansen k, p. Schenk l, H. von der Schmitt m, S. Schreiber n, j. SchwarzJ, J. Schwiening n, W.G. Scott e, M. Settles P, B.C. Shen v, P. Sherwood r, R. Shypit 2, A. Simon n, P. Singh i, G.P. Siroli e, A. Skuja h, A.M. Smith k, T.J. Smith k, G.A. Snow h, R. Sobie 7, R.W. Springer h, M. Sproston e,

0370-2693/91/$ 03.50 ~) 1991-Elsevier Science Publishers B.V. (North-Holland) 467


K. S t ephens b, H.E. StierJ, D. S t r o m d, H. T a k e d a Y, T. T a k e s h i t a Y, P. T a r a s g, S. T a r e m x, P. T e i x e i r a - D i a s rn, N.J . T h a c k r a y o, T. T s u k a m o t o Y, M.F . T u r n e r c, G. T y s a r c z y k - N i e m e y e r m, D. V a n den plasg, R. V a n K o o t e n k, G.J . V a n D a l e n v, G. Vasseu r u, C.J. Vi r tue z, A. W a g n e r m, C. W a h l J, J .P. W a l k e r °, C.P. W a r d c, D .R . W a r d c, P .M. W a t k i n s °, A.T. W a t s o n °, N .K . W a t s o n k, M. W e b e r m, S. Wei sz k, P.S. Wel ls k, N. W e r m e s m, M. W e y m a n n k, M.A. Wha l l ey °, G . W . Wi l son u, J.A. Wi l son °, I. W i n g e r t e r k, V. -H. Win te re r J , N .C. W o o d b, S. W o t t o n k, T .R . W y a t t b, R. Y a a r i x, y . Y a n g v,8, G. Yekut ie l i x, I. Z a c h a r o v k, W. Z e u n e r k a n d G .T . Z o r n h

a Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel b Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UK c Cavendish Laboratory, Cambridge CB30HE, UK d Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA e Dipartimento di Fisica dell' Universiti~ di Bologna and INFN, L40126 Bologna, Italy f Department of Physics, Carleton University, Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6 g Laboratoire de Physique Nuclkaire, Universitk de Montrkal, Montreal, Quebec, Canada H3C 3J7 h Department of Physics and Astronomy, University of Maryland, College Park, MD 20742, USA i Queen Mary and Westfield College, University of London, London E1 4NS, UK J Fakultdt J~r Physik, Albert Ludwigs Universitdt, W- 7800 Freiburg, FRG k CERN, European Organisationfor Particle Physics, CH-1211 Geneva 23, Switzerland

Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OXl l OQX, UK m Physikalisches lnstitut, Universitiit Heidelberg, W-6900 Heidelberg, FRG n Physikalisches Institut, Universit~it Bonn, W-5300 Bonn 1, FRG o School of Physics and Space Research, University of Birmingham, Birmingham B15 2TT, UK P Department of Physics, Indiana University, Swain Hall West 117, Bloomington, IN 47405, USA q Brunel University, Uxbridge, Middlesex UB8 3PH, UK r University College London, London WC1E 6BT, UK s Department of Physics, Technion - Israel Institute of Technology, Haifa 32000, Israel t Birkbeck College, London WCIE 7HV, UK u DPhPE, CEN-Saclay, F-91191 Gif-sur-Yvette, France v Department of Physics, University of California, Riverside, CA 92521, USA w Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario, Canada K1S 5B6 x Nuclear Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel Y International Center for Elementary Particle Physics and Department of Physics,

University of Tokyo, Tokyo 113, Japan and Kobe University, Kobe 657, Japan

z National Research Council of Canada, Herzberg Institute of Astrophysics, Ottawa, Ontario, Canada K1A OR6

Received 30 May 1991

The production of K ° mesons in e + e - interactions at center of mass energies in the region of the Z ° mass has been investigated with the OPAL detector at LEP. The rate is found to be 2.10+0.02+0.14 K °, Z ° per hadronic event. The predictions from the JETSET and HERWIG generators agree very well with both the rate and the scale invariant cross section (1/O'hadfl)(do'/dXE) for K ° production. Comparisons of the inclusive momentum spectrum with predictions of an analytical QCD formula and with data from lower center of mass energies are presented.

468


I. Introduction

In this paper, the first measurement of the process e+e - ~ K°X at x/s ~- Mz0 is presented. The results have been obtained with the OPAL detector at the CERN LEP collider. K ° mesons were identified in the decay channel K ° ~ n + n - by reconstruction of the decay vertex and the invariant mass of the decay

system. Hadron product ion in e+e - interactions involves

the fragmentat ion process, the transit ion of coloured partons into colourless hadrons. No exact theoretical prescription exists for this process yet. Rather, a variety of phenomenological models has been de- veloped. At present, the most commonly used ones are the string fragmentat ion model [ 1 ] and the cluster fragmentat ion model [2 ]. Strange particle production in e+e - annihilat ions [3-5] has been an important tool in studying the fragmentat ion process, since K ° mesons can be cleanly identif ied over a large momentum range. We compare the measured K ° momentum spectrum with predict ions of the JETSET [6] and H E R W I G [7] models and find that the total K ° rate and the differential cross section are in good agreement with both models.

Another approach to describe the hadron momentum spectra combines the modif ied leading log approximat ion (MLLA) [ 8 ] of QCD with the picture of local parton hadron duali ty (LPHD) [8]. The MLLA approximat ion consists of a summation of double and

1 University of Victoria, Department of Physics, P.O. Box 3055, Victoria, Canada BC V8W 3P6.

2 University of British Columbia, Department of Physics, 6224 Agriculture Road, Vancouver, Canada BC V6T IZI.

3 Also at: TRIUMF, Vancouver, Canada V6T 2A3. 4 On leave from Birmingham University, Birmingham

B 15 2TT, UK. 5 University of Victoria, Department of Physics, P.O. Box

1700, Victoria, Canada BC V8W 2Y2 and TRIUMF, Vancouver, Canada V6T 2A3.

6 Present address: Dipartimento di Fisica, Universith della Calabria and INFN, 1-87036 Rende, Italy.

7 University of British Columbia, Department of Physics, 6224 Agriculture Road, Vancouver, Canada BC V6T 2A6 and IPP, McGill University, High Energy Physics Department, 3600 University Street, Montreal, Quebec, Canada H3A 2T8.

8 On leave from Research Institute for Computer Periph- erals, Hangzhou, China.

single leading-log contributions. It predicts the momentum spectrum of partons. The LPHD hypothesis assumes that the measured hadron spectra can be directly compared to the calculated parton spectra. Our measurement is compared with an analytical formula derived within the MLLA and LPHD framework.

Finally, a comparison of our data with experimental results from lower energies is presented, showing the evolution of the K ° multiplici ty as well as the behaviour of the differential cross section as a function of the center of mass energy.

2. The OPAL detector and hadronic event selection

The OPAL detector, a mult i-purpose detector de- signed to reconstruct the decay products of the Z ° boson, has been described in detail elsewhere [9]. The present analysis is based mainly on the information from the central tracking chambers, consisting of a large jet chamber, a precision vertex detector and addit ional z-chambers surrounding the je t chamber. The main detector, the jet chamber, has a length of 4 m and a diameter of 3.7 m. It is d iv ided into 24 sectors, each equipped with 159 sense wires ensuring a large number of measured points even for particles emerging from a secondary vertex. The vertex detector, a 1 m long cylindrical drift chamber of 470 mm diameter, surrounds the beam pipe and consists of an inner layer of 36 cells each with 12 sense wires and an outer layer of 36 small angle (4 ° ) stereo cells each with 6 sense wires. The z-chambers consist of 24 drift chambers, 4 m long, 50 cm wide and 59 m m thick. They are subdivided in 8 cells each with 6 sense wires perpendicular to those of the jet chamber. They cover a polar angle from 44 ° to 136 ° and 94% of the azimuthal angle. All the chambers are contained in a solenoid providing an axial magnetic field of 0.435 T.

The present analysis was performed on 144473 hadronic decays of the Z ° recorded during 1990 at center-of-mass energies between 88.2 and 94.3 GeV with a luminosity-weighted average energy of 91.31 GeV. The selection of the hadronic event sample relying on the information of the electromagnetic calorimeter and the time-of-flight counters has been described elsewhere [10]. In addi t ion each event was required to have at least five well reconstructed charged tracks.

469


3. The K ° finding algorithm

The search for K~ was performed via the decay into n + n - by systematically pairing opposi tely charged tracks.

Each track had to fulfill the following conditions: A min imum transverse momentum with respect to the beam direction of 150 MeV/c, at least 80 je t chamber hits and at least four z-chamber hits were required; the latter to ensure a good mass resolution by improving the measurement of the polar angle. Due to the geometrical acceptance of the z-chambers, this restricts the range of the polar angle with respect to the beam direction to I cos 01 < 0.7. Furthermore, the radial distance of the track to the beam axis at the point of closest approach was required to exceed 3 mm to reduce the large combinator ia l background.

Intersection points of track pairs in the radial plane were considered to be candidate secondary vertices. Addi t ional cuts were imposed on these pairs: The radial distance from the intersection point to the primary vertex had to be larger than 1 cm and the reconstructed momen tum vector of the I ~ candidate in the plane perpendicular to the beam had to point to the beam axis within 2 ° . In the case where both intersections of the track pair passed these cuts, the one closer to the beam axis was taken.

Finally, all track pairs which had passed the cuts were refit with the constraint to originate from a common three-dimensional vertex. Pairs with an invariant mass of less than 100 MeV/c 2 (assuming both tracks to be electrons) were considered to be photon conversions and rejected.

After applying this procedure to the hadronic event sample and assigning the pion mass to both tracks, the mass dis t r ibut ion shown in fig. la was obtained. A fit with a gaussian for the signal plus a third order polynomial background describes the spec- t rum well and yields mKs0 =497.2 + 0.1 MeV/c 2 and

a = 6.5 ± 0.1 MeV/c 2 in reasonable agreement #~ with the P D G [11] value of 497.7 MeV/c 2 and the expected mass resolution from a Monte Carlo simulation of the OPAL detector, respectively. The peak contains 13816 -4- 118 I ~ (statistical error only).

The given error is statistical only; the remaining difference can be explained by the uncertainty in the mean value of the magnetic field.

>

2000

.2 ~ 1600

E o u1200

~ 800 z

400

0.28

~ 0.24

0.2 ~J

0.16

0.12

0.08

0.04

OPAL

0.5 0.4

(a)

0,5 0,6 0.7 Mass [OeV/c2]

(b)

.... 1 ' o 15 i d 25 36 3'5 :~'d 4 s Momentum [GeM/c]

Fig. 1. (a) Invariant mass spectrum of K~ candidates. (b) Detection efficiency for K~ ~ n+n - .

4. Differential and integrated cross sections

In order to extract the number of I ~ and thus to determine the K ° cross section, it is neccess~ry to est imate the amount of background under the signal peak and to correct for the detection efficiency. For this purpose, fits similar to those described above were performed in different K ° momentum bins. To determine the number of K ° per momentum bin, the entries in the mass range from 450 MeV/c 2 to 550 MeV/c 2 were summed up and the background obtained from the fitted polynomial function was sub- tracted. This was followed by an efficiency correction performed separately in each momentum bin. The detect ion efficiency defined as

= Hreconslructed/Hgenerated,

470


was calculated using a sample of Monte Carlo events that were passed through a detailed simulation of the OPAL detector and subjected to the same analysis

chain as the real data. The agreement between real data and simulated

data was checked and in general found to be good, although it was observed that the fraction of charged tracks having at least four z-chamber hits is 82.2%

in the data compared to 90.3% in the detector simulation. This effect is due to an incorrect estimation of the jet chamber z resolution and of the z-chamber sensitive volume in the simulation. The detection efficiency has been corrected for this difference on a

track by track basis. Fig. lb shows the resulting detection efficiency for

K ° ~ n + n - as a function of the K ° momentum ob-

tained with a hadronic event sample generated with the JETSET Monte Carlo. It shows a maximum of 27% at a momentum of about 3 GeV/c. At high mo-

menta, the efficiency is mainly limited by the require- ment of 80 jet chamber hits which cannot be met by K ° decaying too far from the beam axis. Apart from

the track cut at small transverse momentum, the decrease at low momentum is mainly due to the cut on the radial distance from the intersection point to the

primary vertex. To estimate the uncertainty of the detection effi-

ciency, the same calculation was repeated using events produced with the HERWIG generator. In addition, the K ° selection cuts were varied. From these studies, we determined the detection efficiency uncertainty to be about 5%. It enters as an overall normalization error into the systematic error of our measurement. As further sources of possible systematic errors we considered the following two contributions: An uncertainty in the matching to the z-chamber was ac- counted for by including an error of 3% in the overall normalization error, which brings it up to 6% in total. The uncertainty in the background subtraction described above was determined by varying the fit range and the background shape. It was estimated to be about 7% entering as a bin-to-bin uncertainty; this then contributes 3% to the uncertainty of the total rate by quadratic addition of the contributions from all momentum bins. In total, the systematic uncertainty of the integrated K ° rate was found to be 7% after combining all these effects.

After correcting the data for the unobserved decay

# . . . . i . . . . i . . . . i . . . . i . . . .

° \ + t, OPAL

'~]l ,o " X J JETSET b HERWlG

1

;6

r~ i i , i I + , i L I L i i i I i i i , I , i i ,

l v o 0 . 2 0 . 4 0 . 6 0 . 8

x E

Fig. 2. Differential scale invariant cross section (1/~7hadfl)(dtT/dXE) versus XE for K ° production. The line indicates both the predictions of JETSET and HER- WIG, respectively, since they can not be distinguished from each other within the line width. Indicated errors include statistical and bin-to-bin systematic contributions.

Table l The scaling cross section for K ° production.

XE .XE ( 1/O'had fl ) (do'/dXE)

0.01-0.03 0.02 29.6 4- 2.2 0.03-0.04 0.035 21.1 4- 1.6 0.04-0.06 0.049 15.4 4- 1.1 0.06-0.10 0.078 9.0 4- 0.7 0.10-0.15 0.123 5.0 4- 0.4 0.15-0.20 0.173 2.8 4- 0.2 0.20-0.30 0.242 1.4 4- 0.1 0.30-0.40 0.343 0.75 4- 0.07 0.40-0.60 0.474 0.21 4- 0.03 0.60-1.00 0.693 0.03 4- 0.007

into n°n ° and for K ° production, the scale invari-

ant cross section (1/t&adfl) ( d a / d x E ) for K ° production #2 was obtained as a function of the scaled energy

XE = 2EKo/v'~. It is shown in fig. 2 and table 1. The indicated error bars include statistical and bin-to- bin systematic contributions. In addition there is an overall normalization uncertainty of 6% mentioned

#2 By denoting the particle state we mean both particle and antiparticle state.

471

Volume 264, number 3,4 PHYSICS LETTERS B l August 1991

above. The predict ions of the JETSET 7.2 and HER- WIG 5.0 generators are also shown in fig. 2 along with our data. The fragmentat ion parameters of these pro- grams were tuned to describe the global event shapes as measured by OPALn3 [12]. Whenever referring to the generators throughout this paper, we use these tuned versions. The predict ions of both generators are very similar; they exhibit good agreement with the measurements.

To determine the total K ° rate, the momentum spectrum was integrated, using JETSET to extrapolate over the unobserved momentum region; the size of this correction was 5%. 2.10 + 0.02+ 0.14 K ° per hadronic event were found. The first error quoted is statistical while the second reflects the systematic uncertainties.

Adjusting the Ys parameter in JETSET which con- trois the suppression of s quark pair product ion in the colour field to describe the measured cross section yields 7s = 0.285 + 0.035. The other model parameters were kept fixed. Our measurement is consistent with the default value Ys = 0.3 which has been determined with data from lower center of mass energies, indicat ing the independence of Ys on the center of mass energy. For example, the JADE collaborat ion measured a value of ys = 0.27 • 0.03 + 0.05 [5 ], and the TASSO collaborat ion 7s = 0.35-4-0.02±0.05 [ 13 ], respectively.

5. Comparison with QCD predictions

As previously shown in refs. [14,15] calculations for the gluon momentum spectrum in the modif ied leading log approximat ion (MLLA) [8] (see also ref. [16]) of QCD can describe the momen tum dis- t r ibut ion of all charged particles. These calculations predict a decrease of particle yield at low momenta which is a t t r ibuted to a destructive interference of coherently emit ted soft gluons [ 17]. The agreement between the expected gluon and the observed hadron spectrum can be understood in the context of local pa r ton -hadron duali ty [8]. Fur ther insight into this

~3 In HERWIG 5.0, the parameters determined to fit the event shapes as measured by OPAL are the default values.

mat ter can be gained from a comparison of the predictions for individual particle types.

Denoting ~ = ln (1 /xp) , where xp = 2cp/x/-£ stands for the scaled momentum of the particle, the predicted hadron spectrum can be written as

1 do O'ha d d (

- Nf(Aerf, Qo, x/s,~). (1)

The theoretical predict ions involve three free parameters: an effective QCD scale Aerf which is not directly related to A~--g, a cut-off parameter in the quark-gluon cascade Q0, and the overall normalizat ion factor N that depends on the particle type and is expected to be independent of the center of mass energy. The predicted spectrum shows a max imum which is shifted to lower ~ values with increasing Aeff.

Comparison of the spectrum (1) with the data is not trivial since no rigorous connection between Q0 and the particle mass is available. Instead the measurement of the mass dependence is hoped to provide insight into non-perturbat ive QCD effects. Further- more, formula (1) is difficult to solve numerically. In refs. [14,15], a simplif ied form of (1) has been applied assuming Q0 = A~ff. This assumption is sup- ported by the expectation that the spectrum should be insensitive to the value of Q0 for asymptot ic center of mass energies [8]. The resulting spectrum (the so- called limiting spectrum) is especially convenient for numerical integration. Its explicit form can be found in ref. [18]; it is valid for 1 < ~ < ln(x/~/2A~rf). For massive hadrons, one supposes Q0 > Aeff, and the l imiting formula is expected to be less accurate [ 19 ].

In the case of all charged particles [ 14,15] and ~z ° mesons [15] good agreement with the predicted l imiting spectrum was observed. In the following we compare the measured K ° momentum spectrum in terms of ( 1/O'had) ( d a / d ~ ) with the QCD calculations for Q0 = Aeff. The measured data points are shown in table 2 and together with the result of the fit in fig. 3. The fit range was restricted to 1( - ~maxl < 1 around the posit ion of the maximum ~max. There is good agreement in the range included in the fit; the data points in the low ( region are also reasonably described by the prediction. However, the data show a general tendency towards a broader distr ibution. For the free parameters of the fit we obtain A~ff = 827 + 30 MeV and N = 0.211 + 0.003. The errors of the parameters were determined by varying the K~

472


Table 2 The ~ distribution for K ° production.

( 1 /O 'hadf l ) ( d o ' / d ~ )

0.13-0.93 0.067 -4- 0.009 0.93-1.29 0.261 q- 0.029 1.29-1.60 0.375 + 0.038 1.60-1.80 0.463 -4- 0.047 1.80-2.00 0.545 4- 0.055 2.00-2.20 0.658 4- 0.065 2.20-2.40 0.661 4- 0.065 2.40-2.60 0.726 4- 0.071 2.60-2.80 0.689 4- 0.067 2.80-3.00 0.742 4- 0.072 3.00-3.20 0.738 4- 0.072 3.20-3.40 0.649 4- 0.064 3.40-3.60 0.656 4- 0.065 3.60-3.80 0.547 4- 0.056 3.80-4.04 0.491 4- 0.051 4.04-4.33 0.472 4- 0.050 4.33-4.62 0.342 4- 0.043 4.62-5.02 0.224 4- 0.037

J ~ 0 . 8

0 .6

0 ,4

0 .2

OPAL

- - OCD MLLA Q, = A.., = 8 2 7 MeV

- - - QCD MLLA Q o = 3 0 0 MeV. A ~ = 1 5 0 MeV

\

/

/

~.... / /

00. , ,, 1 . . . . i . . . . i . . . . i , ,

3 4 5

selection cuts and the range of data points included in the fit. We find the posit ion of the max imum at ~mK°ax = 2.91 -4- 0.04. Compared to the values obtained for all charged particles v.n£ '~maxFCharged = 3.603 -4- 0.013 [14], ~charged 3.71 + 0.05 [15], and for n ° mesons of max

~0 ~max = 4.11 + 0.18 [ 15 ], we find that for the more massive K ° the posit ion of the maximum is shifted to lower values of~. This t rend of the max imum posit ion decreasing with increasing particle mass has already been observed at lower center of mass energies by the TASSO collaboration [20]. Corresponding to the shift of the maximum, the l imiting formula yields for the K ° a value of Aerf considerably higher than for

A charged 253 + 30 MeV [14], the light mesons ( elf = n 0 A ch~ged = 220 + 20 MeV [ 15 ] and Aer f 115 ± 40

eft

MeV [15] ). The strong dependence of A~fr on the particle mass is expected to be due to mass effects which are not taken into account in the context of the l imiting formula.

A more natural description of the spectra of massive mesons is expected using the full equation (1) instead of the l imiting spectrum. The same value of A~rf is supposed to describe the spectra of light heavy hadrons, whereas Q0 should be related to the particle mass. In a recent paper [21 ], a method to solve (1) approximately has been proposed and a spectrum for Aeff= 150 MeV, Q0=300 MeV is presented as illus- tration. The value of A~ff was chosen to be consistent with the measurements of the light mesons. This spectrum, normalized to our data, is plot ted as the dashed line in fig. 3. Although no fit to determine the parameters was performed, a reasonable description of the measured data points is found, support ing the above ment ioned expectation of a unique value of Aeff for light and heavy mesons and Q0 increasing with the particle mass.

6. Comparison with data from different center of mass energies

Fig. 3. Measured ~ = In ( 1/xp ) distribution with QCD predictions. Indicated errors include statistical and bin-to-bin systematic contributions. The dotted line shows the result of a fit using the limiting QCD formula (the solid part indicates the fit range); the dashed line illustrates an ap- proximate solution of the full QCD formula.

Fig. 4a shows the number of K ° per hadronic event determined by different experiments [3-5] in a range of center of mass energy from 12 to 91 GeV. The numbers from lower energies stem from a compilat ion recently published by the TASSO collaborat ion [4]. In table 3 the predict ions for the K ° mult ipl ici ty of

473


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Fig. 4. (a) K ° mult ip l ic i ty at different center of mass energies. (b) Differential scale invariant cross section for K ° production as a function of the squared center of mass energy in several XE bins. The dashed line indicates the JETSET prediction for pure photon exchange, whereas the solid line shows the prediction including electroweak effects.

JETSET and HERWIG ~,4 at v~ = 35 GeV and x/~ = 91 GeV are compared with experimental data. The measured K ° multiplicities are well described at both center of mass energies.

Fig. 4b shows the scaling cross section (1/O'hadfl) (da/dXE) as a function of the center of mass energy in various XE bins as measured by OPAL, TASSO and TPC. The evolution of the cross section with the center of mass energy is influenced by two

¢¢4 Also for v'~ = 35 GeV, the tuned parameters were used for the generators.

Table 3 K ° multiplicity at different CMS energies compared with generator predictions.

v~ [GeV] Experimental JETSET HERWIG

35 1.42-1.47 1.46 1.38 91 2.1+0.02±0.14 2.16 2.07

effects: On one hand, scaling violations which are due to gluon emission can be expected. They would lead to a decrease of the cross section at high XE values and to a corresponding increase at low values of XE. On the other hand, electroweak effects become im-

portant if the center of mass energy approaches the Z ° mass. In particular, the flavour composition of the primary produced quarks is different due to the different couplings to photon and Z ° respectively.

The solid line in fig. 4b shows the JETSET prediction for the energy evolution of the K ° cross section including electroweak effects; the dashed line shows the behaviour with pure photon exchange, demon- strating the influence of scaling violations. The full curve exhibits a rise of the cross section compared to the photon exchange case especially at large XE. This is due to the larger coupling of down-type quarks to the Z ° , resulting in a larger fraction of primary strange quarks which yields more strange mesons with high

momenta.

7. Summary

The differential and total cross sections for K ° production in e+e - annihilat ion at v~ -~ Mz0 have been measured from 144473 hadronic events recorded with the OPAL detector in 1990. The yield was found to be 2.10 ± 0.02± 0.14 K ° per event. The total rate

as well as the differential cross section with respect to momentum as predicted by JETSET and HERWlG are in good agreement with the data. Furthermore, the evolution of the K ° multiplicity with x/~ is well described by JETSET and HERWlG. We also compare our measurement to the predictions of analytical QCD formulae derived within the framework of the MLLA approach. A reasonable description of the spectrum is found.

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Acknowledgement

We wish to thank Y.L. Dokshitzer and V.A. Khoze for fruitful and enjoyable discussions and correspon- dence.

It is a pleasure to thank the SL Division for the efficient operat ion of the LEP accelerator, the precise information on the absolute energy, and their contin- uing close cooperat ion with our experimental group. In addi t ion to the support staff at our own institu- tions we are pleased to acknowledge the following: Depar tment of Energy, USA, National Science Foundat ion, USA, Science and Engineering Research Council, UK, Natural Sciences and Engineering Research Council, Canada, Israeli Ministry of Science, Minerva Gesellschaft, The Japanese Minis try of Education, Science and Cul- ture (the Monbusho) and a grant under the Mon- busho International Science Research Program, American Israeli Bi-national Science Foundat ion, Direct ion des Sciences de la Matibre du Commissar ia t

l 'Energie Atomique, France, The Bundesminis ter ium ffir Forschung und Tech- nologie, FRG, and The A.P. Sloan Foundat ion.

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