- Email: [email protected]
Inclusive particle production at LEP
PROCEEDINGS SUPPLEMENTS ELSEVIER
Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
Inclusive Particle P r o d u c t i o n at L E P Heinz G e o r g Sander Institut fiir Physik, Johannes Gutenberg-Universit~it Mainz, D-55099 Mainz, Germany Recent results, some still preliminary, on inclusive hadron production at LEP are presented. The high precision data at the Z resonance (LEP I) provide a better understanding of the hadronization dynamics and serve as input for the tuning of Monte Carlo models. First results from the high energy running (LEP II) are still dominated by large statistical uncertainties.
1. R e c e n t r e s u l t s f r o m L E P I
In the years 1989-1995 the e+e - storage ring LEP was operated at the Z pole. In this period each of the four LEP experiments ALEPH, DELPHI, L3, OPAL has recorded about 4 . 1 0 6 hadronic Z decays. This high quality data sample allows detailed studies of ha@on production in e+e--annihilation. More than 40 ha@on species have been identified in hadronic Z decays [1]. The average multiplicities of identified particles are presented elsewhere in these proceedings [2]. It is interesting to note that the results can be described by the phenomenological model of P.V.Chliapnikov and V.A.Uvarov [3]. Figure 1 shows the average multiplicity < n > (without counting the antiparticle) for particles with spin J and modified isospin Im as a function of the particle mass m. A fit of the function + < >= 2 J 11a exp (-bin 2) (1) gives a = 10.4 + 0.2 and b = 3.78 :t: 0.02GeV/c ~ with a X2/ndf = 2, if the pions are excluded. 1.1. M o m e n t u m s p e c t r a Measurements of the inclusive momentum spectra have been published for many different particles. Recently the A L E P H collaboration has measured [4] the neutral pion production using photons in the electromagnetic calorimeter and photons from conversion pairs. Figure 2 shows the inclusive ~.0 spectrum as a function of z v = P/Pb~a,n. Both Monte Carlo models, J E T S E T 7.4 and HERWIG 5.8, are slightly too high at high 0920-5632/98/$19.00 © 1998 ElsevierScienceB.V. All rights reserved. PII S0920-5632(98)00332-6
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1 C-
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v~
+
E
10
-3
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0
1
2
3 2 ("r'l hedron
Figure 1. Particle multiplicity in the Chliapnikov model [1]. The masses are given in GeV.
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
124
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Figure 3. Inclusive cross sections for charged and neutral pions [4].
JETSET 7 . 4
...... HERWIG 5 , 8 0.2
0.4
0.6
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Xp
Figure 2. Inclusive rr° cross section [4]. t(a)
momenta. In Fig.3 the lr ° spectrum as a function of ~ = - I n x v is compared to the charged pion spectrum. The excess of neutral pions is mainly due to decays of the r/mesons. The L3 collaboration has studied [5] the inclusive w and rf production in hadronic Z decays. The w meson was identified via its decay channel w --+ rr+Tr-rr °, while the rf meson was reconstructed in the channels ~' --4 7r+rr-r/ and rf --+ p° 7. The measured spectra (Fig.4 and Fig.5) are compared to predictions of earlier versions of the Monte Carlo models. While the shapes of the distributions are in agreement , significant differences in the production rate are observed. The HERWIG prediction for w production and the J E T S E T 7.3 prediction for Tf are too high. In J E T S E T version 7.4 an extra rf suppression factor has been introduced.
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125
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
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Figure 5. Inclusive rf cross section [5].
Another example of recent LEP results on inclusive hadron production is the OPAL analysis of strange baryon production[6]. Fig.6 shows the measured spectra as a function of zE = E/Ebeam for the j R = 3 1+ octet baryons A and ~-
the J P --- 3+ decuplet baryons E(1385) ~1 2 and ~(1530) °, and the j R _- 3- orbitally excited state A(1520). The curves give the predictions of J E T S E T 7.4, except for the A(1520) baryon, which is not present in JETSET. Here the E(1385) + differential cross section shape from JETSET is compared to the measurement. Generally the predicted spectrum of JETSET 7.4 with default parameters is too soft; an extra parameter is needed to suppress leading baryons. 1.2. T u n i n g o f m o d e l p a r a m e t e r s Based on the high precision data at the Z resonance the LEP collaborations have tuned the popular Monte Carlo models[7],[8]. For example in the global ALEPH fit[8] the following experimental quantities were used:
• event-shape distributions S, A, 1 - T, T,,ino,., - In Y3;
Figure 6. Inclusive cross sections for strange baryons [6].
• charged particle inclusive xp = P/pbe~,m, p~,,t, p±i,~.,
distributions
inclusive spectra of ~ = - In xp for the neutral V ° particles K ° and A °, and for the charged pions, kaons and (anti)protons; inclusive spectra of X E = E/Ebeam for the mesons rl(XE > 0.1), r#(xE > 0.1) p0, K.0, K , + , ¢0, w0; the mean multiplicities of the L = 1 mesons f2, f0 and of the hyperons ~ - , E(1385), =(1530) °, ~ - . Monte Carlo calculations of these quantities at various locations in parameter space were performed and the dependence of each quantity on the model parameters was parametrized. Minimizing the X2 function between data and prediction with respect to the model parameters the following results were found: Table 1 shows the fitted parameter values for the JETSET 7.4 model [9]. The parameters A q c D and Mmin determine the parton shower
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
126
parameter
AQCD (GeV) Mmin (GeV) O'q (GeV) a
b (GeV -2) ~C ~b
p(S = 1)d,u p(S = 1), p(S = 1)c,b
p(JP=2+;L=
1 , S = 1) extra y' suppression
s/u qq/q (suldu)l(slu) leading baryon suppr. switch fragmentation function baryon model azimuthal distrib, in PS
name in program PARJ(81) PAR J(82) PAR J(21) PAtLI(41) PAR J(42) - P A R J(54) - P A R J(55) PARJ(ll) PAR J(12) PAR J(13) PAR J(17) PAtLI(26) PAtLI (2) PARJ(1) PARJ(3) PAR J(19)
default value 0.29 1.0 0.36 0.30 0.58 0.050 0.005 0.50 0.60 0.75 0.0 0.40 0.30 0.10 0.40 1.0
range generated 0.21 - 0.37 1.0 - 2.0 0.28 - 0.44 0.20 - 0.60 0.60- 1.00 0.015 - 0.065 0.0005 - 0.0075 0.40 - 0.70 0.35- 0.65 0.50 - 0.80 0.10 - 0.30 0.05 - 0.55 0.19 - 0.39 0.05 - 0.15 0.4- 1.0 0.2- 1.0
value 0.292 1.57 0.370 0.40 0.796 0.040 0.0035 0.55 0.47 0.65 0.20 0.27 0.285 0.106 0.71 0.57 setting
fit result error + 0.003 4- 0.04 4- 0.002 (fixed) 4- 0.012 adjusted adjusted + 0.02 4- 0.02 adjusted adjusted 4- 0.03 4- 0.004 4- 0.002 4- 0.04 4- 0.03
syst. 4- 0.006 4- 0.13 4- 0.008 4- 0.033
4- 0.06 4- 0.06
44444-
0.09 0.014 0.003 0.07 0.10
MSTJ(11) MSTJ(12) MSTJ(46)
Table 1 Parameters for JETSET 7.4. The parameters describing the higher mesons are assumed to be in the ratio PARJ(17) :PARJ(16) :PARJ(15) = 5 : 3 : 1, and PARJ(14) ----PARJ(16). The diquark-spin suppression parameter PARJ(4) was left at its default value (0.05). No Bose-Einstein correlations are included.
development. The conversion of the partons into hadrons is accomplished with the Lund String model. Since the parameters a and b for light quark fragmentation are highly correlated, the parameter a was fixed to 0.4. The parameters ec and eb in the Peterson function [10] for heavy quarks were adjusted in order to describe the measured charm and bottom spectra. The additional parameters for leading baryon suppression and rf suppression are given in the table. The HERWIG 5.8 model [11] has significantly less explicit parameters (Table 2). The coherent parton branching process is governed by the parameters AQCDand Mgtuon,and the hadronization is modelled with a cluster mechanism. Heavy clusters with masses greater than Md,max can decay into smaller clusters before decaying into hadrons.
Fit results for the ARIADNE 4.08 model are also available [8]. Generally the tuned Monte Carlo models describe the data reasonably well. Significant discrepancies are in the p~Ut spectra for the momentum component out of the event plane (Fig.7) and in the baryon spectra (Fig.S). Similar results have been obtained by the other LEP collaborations. 1.3.
Polarization
measurements
In Z ~ st decays the primary s quark has a longitudinal polarization of PL = --0.94 which is transferred to a directly produced leading A baryon. Other A baryons are decay products of heavier baryons which contain the primary s quark. These A will inherit some fraction of the parent's polarization. A baryons containing a primary u or d quark or coming from the fragmentation process are expected to be unpolarized. The
H.G. Sander~Nuclear Physics B (Proc. Suppl.)
parameter
name in program QCDLAM
AQCD (GeV)
default value 0.18 0.75 3.35 0.0 1.0
RMASS(13) CLMAX CLSMR PWT(3)
Mg,=on (GeV) Mc4ma= (GeV)
40) p(s-quark)
range generated 0.12- 0.18 0.7-1.0 3.0-4.0 0.0-1.0 0.6-1.0
(1999) 123-133
71
fit result error -4- 0.001 + 0.005 ± 0.01 -4- 0.02 -4- 0.01
value 0.147 0.656 3.65 0.73 0.79
127
syst. + 0.005 + 0.015 -4- 0.10 + 0.06 -4- 0.06
Table 2 Parameters for HERWIG 5.8.
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Figure 7. Inclusive distibution ofp~,~'t for charged particles, using the event plane based on the sphericity tensor [8].
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Figure 8. Inclusive A cross section [8].
6
128
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
•2'.'
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Figure 10. The K *° helicity density matrix element P00 as a function of xp [14].
0.2
0.1
0
-0.l
XE
Figure 9. Longitudinal polarization of A baryons [12].
A polarization can be determined from the asymmetry in the weak decay A -4 prr. Figure 9 shows the OPAL measurement [12] of PL as a function of XE. Significant negative values are found for A's with intermediate and high momenta in agreement with ALEPH results [13] and the JETSET prediction. The role of meson spin in the production dynamics has been investigated by OPAL [14] and DELPHI [15]. They measure the spin density matrix of vector mesons in the helicity rest frame using the decay angular distribution. The matrix elements #-1-l,P00,Pll give the relative intensities of the helicity states -1,0,+1, respectively. Since the strong decay cannot disinguish between +1 and -1 helicities, the relevant observable is P00 which is expected to be 1/3 in a simple statistical model [16]. As an example Fig.10 shows the K *° helicity density matrix element p00 as a function of xp, as measured by OPAL. The data for p0, K.0, ¢ and D* show clearly that leading vector mesons are spin aligned with A = 0 preferred.
1.4. F l a v o u r t a g g e d events More information on hadron production in Z decays comes from analyses trying to distinguish the different sources of the observed hadrons: the different initial quark flavours or differences between quark and gluon jets. Since the production of heavy quarks in the fragmentation chain is strongly suppressed, charmed hadrons can either be leading particles from the initial Z -4 c~ decay or decay products of leading bottom hadrons from Z -4 bb decay. There is also a small contribution from gluon splitting into a pair of heavy quarks. The ALEPH collaboration has measured [17] the energy spectrum of D *+ mesons reconstructing the decay chain D *+ -4 D%r + , D O -4 K - 7r+ . Figure 11 shows the experimental result for all Z decays together with the Monte Carlo prediction of the three contributions. The bb contribution has been checked experimentally using a high purity b-tag in the opposite event hemisphere. A fit to the D* spectrum yielded the average number of gluon splitting events per hadronic Z decay to be n(g -4 c~) = (4.7 + 1.0 ± 1.1)%. 1.5. D i f f e r e n c e s b e t w e e n q u a r k a n d g l u o n jets The OPAL collaboration has measured [18] the multiplicity distribution of charged particles in quark and gluon jets using an inclusive jet definition similar to that used for analytic calculations. The method is based on rare events of the type Z -4 qclg, in which the q and Cl jets ap-
H.G. Sander~Nuclear Physics B (Proa Suppl.) 71 (1999) 123-133
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0.7
0.8
0.9
X E = E] Ebeam
[~
~
-- -
Herwig5.9
0.06 ~ 0.114 0.02
Figure 11. Inclusive D *+ cross section. The data points are compared to the model predictions [17].
pear in the same hemisphere of an event. The quark jets are identified by displaced secondary vertices from heavy quark decays. All particles in the opposite hemisphere are taken as the gluon jet. This definitition corresponds closely to single gluon jets produced in gg events from a colour singlet point source. Details of this analysis are given elsewhere in these proceedings [19]. These gluon jets with an average energy of 41.8 GeV are compared to light (u,d,s) quark hemispheres of 45.6 GeV. The corrected charged multiplicity distributions are shown in Fig.12 together with the JETSET and HERWIG predictions. The mean multiplicity values differ by about 50%, the distribution for quark jets is about twice as skewed (asymmetric) as the gluon jet distribution, but the dispersions are found to be the same. Correcting the quark jet result down to 41.8 GeV, OPAL finds r = 1.471-4-0.024-4-0.043 for the multiplicity ratio between gluon and quark jets at 41.8 GeV. The DELPHI collaboration has studied [20] the energy dependence of r, selecting three-jet events with the Durham jet finding algorithm with yc,,t = 0.01. They observe an increase with
0
0
5
10
15
20 rich.
25
30
Figure 12. Corrected distribution of charged particle multiplicity for (a) 41.8 GeV gluon jets, and (b) 45.6 GeV u,d,s quark jets [18].
the jet energy Ejet (Fig.13), which can be described by a linear fit r = (0.92+0.07)+(0.0112+ 0.0024). Ejet(GeV). This result reconciles the CLEO measurement [21] r = 1.04 -4- 0.05 at the T(1S) with the high energy OPAL measurement. The fragmentation function for charged particles in quark and gluon jets has been measured by the ALEPH collaboration [22] selecting nearly symmetric three-jet events with the Durham algorithm with a high jet resolution parameter of y~,t = 0.1. Figures 14 and 15 show the measured inclusive distributions of ZE = Ehad/Ejet for charged particles in quark and gluon jets along with Monte Carlo predictions. As expected from the higher multiplicity, the measured gluon fragmentation function is considerably softer than the quark fragmentation function, however somewhat harder than the model predictions.
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
130
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5
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10 15 20 25 30 35 40 45 50 M e a n charged multiplicity vs jet energy Ej~ (GeV)
Figure 14. Measured quark fragmentation func tion [22].
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2.
0.4
II
After six years of running near the Z resonance the exploration of the high energy regime of LEP started in 1995. The runs in 1995-1996 at centreof-mass energies of 133 GeV ( combined from runs at 130 and 136 GeV ), 161 GeV and 172 GeV provided a total luminosity of around 25 pb-1 per experiment.Since August 1997 LEP is operating at 183 GeV. As shown in Fig.16 the hadronic cross section drops from 30 nb at the Z pole to about 30 pb after cuts, so that these data samples contain only about 300 events per energy point per experiment. At LEP II there is a high probability for initial state photon radiation back to the Z pole. These radiative return events, where the photon remains in the beam pipe, can be rejected using the visible energy E~8 and the imbalance in the energy component parallel to the beam Ell. Figure 17 from L3 [23] shows a clear separation between signal and background events. An important topic for LEP II is the study of W + W pair production with
Figure 17. Scatter plot of variables used to separate radiative from non-radiative events (see text) [23].
cross section up to 17 pb. Hadronic events e+e - --+ W + W - --+ qOqO --+ hadrons cannot be completely separated from e +e- --+ q(:l --4 hadrons, so that the remaining background has to be modelled by Monte Carlo. In the present situation with the small data samples available global event properties are measured first. Figure 18 shows the mean charged multiplicity [24] as a function of centre-of-mass energy compared to the predictions of Monte Carlo models. The models PYTHIA and HERWIG based on parton showers agree with the data, whereas the JETSET O(c~) matrix element model [9] does not predict a fast enough rise in Nch for increasing energy. The charged particle inclusive distribution as a function of ~ = - I n xp, as measured by ALEPH at 172 GeV [25], is shown in Fig.19. The histograms give the model predictions of PYTHIA 5.7 (solid curve)and HERWIG 5.8 (dashed curve), where the model parameters were tuned using the Z data as described earlier. The agreement is very good. The peak position ~* of the inclusive distribution of ~ which was determined by fitting a distorted Gaussian [26] to the central region is
132
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
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Figure 18. Mean multiplicity of charged particles as a function of centre-of-mass energy [24].
shown in Fig.20 along with low energy measurements by the TASSO experiment[27]. The QCD predictions using the double logarithm approximation (DLA) and including higher order corrections (MLLA)[28] have been corrected for the energy dependence of the flavour composition of the primary quarks. The high energy data points are somewhat higher than the MLLA curve. 3. C o n c l u s i o n s The analysis of the LEP I data is still going on. The high statistics available allow detailed studies of many aspects of hadron production. Specific questions like quark/gluon jet differences or spin properties can be answered. The LEP II physics has just started. Many results are still dominated by large statistical errors. Even with the expected luminosity of 500 pb-1 per experiment in the next years this will still not reach the LEP I precision. REFERENCES
. A. BShrer, Inclusive Particle Production in Hadronic Decays of the Z Boson at L E P I,
Siegen SI-96-15.
Figure 19. Charged particle inclusive distribution at 172 GeV [25].
4.5
~"
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3.5
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-QOD MLLA - - - QCD DLA with flovour correction
2.5 2
I
0
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I
l
50
I
I
I
I
J
I
,
I
1O0
I
I
I
150
I
I
I
200
Ecru (OeV) Figure 20. The peak position ~* of the distribution of ~ = - In z v as a function of centre-of-mass energy. The QCD predictions are corrected for the energy dependence of the quark flavour composition [25].
H.G. Sander~NuclearPhysics B (Proc. Suppl.) 71 (1999) 123-133
2. R. Henriques, these proceedings. 3. P. Chliapnikov and V. Uvarov, Phys. Lett. B345 (1995) 313. 4. ALEPH Collaboration, R. Barate et al., Z. Phys. C74 (1997) 451. 5. L3 Collaboration, M. Acciarri et al., Phys. Lett. B393 (1997) 465. 6. OPAL Collaboration, G. Alexander et al., Z. Phys. C73 (1997) 569. 7. DELPHI Collaboration, P. Abreu et al., Z. Phys. C73 (1996) 11. OPAL Collaboration, G. Alexander et al., Z. Phys. C69 (1996) 543. 8. ALEPH Collaboration, R. Barate et al., Studies of Quantum Chromodynamics with the A L E P H Detector, CERN-PPE/96-186, submitted to Physics Reports. 9. T. Sj6strand, Comp. Phys. Comm. 82 (1994) 74. 10. C. Peterson et al., Phys. Rev. D27 (1983) 105. 11. G. Marchesini et al., Comp. Phys. Comm. 67 (1992) 465. 12. OPAL Collaboration, K. Ackerstaff et al., CERN-PPE/97-104, submitted to Z. Phys. C. 13. ALEPH Collaboration, D. Buskulic et al., Phys. Lett. B374 (1996) 319. 14. OPAL Collaboration, K. Ackerstaff et al., CERN-PPE/97-94, submitted to Z. Phys. C. 15. DELPHI Collaboration, P. Abreu et al., CERN-PPE/97-55, submitted to Phys. Lett. B. 16. J.F. Donoghue, Phys. Rev. D19 (1979) 2806. 17. ALEPH Collaboration, R. Barate et al., Study of Charm Production in Z Decays, contribution to the 1997 Lepton-Photon Conference, Hamburg. 18. OPAL Collaboration, K. Ackerstaff et al., CERN-PPE/97-105, submitted to Z. Phys. C. 19. J.W. Gary, these proceedings. 20. DELPHI Collaboration, P. Abreu et al., Updated Results on the Energy Dependence of the Difference between the Quark and Gluon Jet Fragmentation, contribution to the 1997 Lepton-Photon Conference, Hamburg. 21. CLEO Collaboration, ICHEP 96, Warsaw. 22. ALEPH Collaboration, R. Barate et al., Measurements of the Structure of Quark and Gluon Jets in Hadronic Z Decays, contribu-
23. 24.
25.
26. 27. 28.
133
tion to the 1997 Lepton-Photon Conference, Hamburg. L3 Col!aboration, M. Acciarri et al., CERNPPE/97-42, submitted to Phys. Lett. B. G. Cowan, QCD at LEP II, Oxford Workshop on LEP II Physics 1997 and references therein. ALEPH Collaboration, R. Barate et al., QCD Studies with e+e - Annihilation Data from 130 to 172 GeV, contribution to the 1997 Lepton-Photon Conference, Hamburg. C.P. Fong and B.R. Webber, Phys. Lett. B229 (1989) 289. TASSO Collaboration, W. Braunschweig et al., Z. Phys. C47 (1990) 187. Y.L. Dokshitzer et al., Basics of Perturbatire QCD, Edition Fronti~res, Gif-sur-Yvette, 1991.
Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
Inclusive Particle P r o d u c t i o n at L E P Heinz G e o r g Sander Institut fiir Physik, Johannes Gutenberg-Universit~it Mainz, D-55099 Mainz, Germany Recent results, some still preliminary, on inclusive hadron production at LEP are presented. The high precision data at the Z resonance (LEP I) provide a better understanding of the hadronization dynamics and serve as input for the tuning of Monte Carlo models. First results from the high energy running (LEP II) are still dominated by large statistical uncertainties.
1. R e c e n t r e s u l t s f r o m L E P I
In the years 1989-1995 the e+e - storage ring LEP was operated at the Z pole. In this period each of the four LEP experiments ALEPH, DELPHI, L3, OPAL has recorded about 4 . 1 0 6 hadronic Z decays. This high quality data sample allows detailed studies of ha@on production in e+e--annihilation. More than 40 ha@on species have been identified in hadronic Z decays [1]. The average multiplicities of identified particles are presented elsewhere in these proceedings [2]. It is interesting to note that the results can be described by the phenomenological model of P.V.Chliapnikov and V.A.Uvarov [3]. Figure 1 shows the average multiplicity < n > (without counting the antiparticle) for particles with spin J and modified isospin Im as a function of the particle mass m. A fit of the function + < >= 2 J 11a exp (-bin 2) (1) gives a = 10.4 + 0.2 and b = 3.78 :t: 0.02GeV/c ~ with a X2/ndf = 2, if the pions are excluded. 1.1. M o m e n t u m s p e c t r a Measurements of the inclusive momentum spectra have been published for many different particles. Recently the A L E P H collaboration has measured [4] the neutral pion production using photons in the electromagnetic calorimeter and photons from conversion pairs. Figure 2 shows the inclusive ~.0 spectrum as a function of z v = P/Pb~a,n. Both Monte Carlo models, J E T S E T 7.4 and HERWIG 5.8, are slightly too high at high 0920-5632/98/$19.00 © 1998 ElsevierScienceB.V. All rights reserved. PII S0920-5632(98)00332-6
C
73-o
~> 1 0 ®
-TT +
K ' ~ -q+'r]' K° p ~ + c p
1 C-
-1 +10 c-q
y~ Z- ,+
v~
+
E
10
-3
-4
0
1
2
3 2 ("r'l hedron
Figure 1. Particle multiplicity in the Chliapnikov model [1]. The masses are given in GeV.
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
124
~
10 2
• "*
ALEPH
3 lO
0
IO
-I •
--
1o
-2
a~
~1
2
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4
6
ALEPH
Figure 3. Inclusive cross sections for charged and neutral pions [4].
JETSET 7 . 4
...... HERWIG 5 , 8 0.2
0.4
0.6
O.g
Xp
Figure 2. Inclusive rr° cross section [4]. t(a)
momenta. In Fig.3 the lr ° spectrum as a function of ~ = - I n x v is compared to the charged pion spectrum. The excess of neutral pions is mainly due to decays of the r/mesons. The L3 collaboration has studied [5] the inclusive w and rf production in hadronic Z decays. The w meson was identified via its decay channel w --+ rr+Tr-rr °, while the rf meson was reconstructed in the channels ~' --4 7r+rr-r/ and rf --+ p° 7. The measured spectra (Fig.4 and Fig.5) are compared to predictions of earlier versions of the Monte Carlo models. While the shapes of the distributions are in agreement , significant differences in the production rate are observed. The HERWIG prediction for w production and the J E T S E T 7.3 prediction for Tf are too high. In J E T S E T version 7.4 an extra rf suppression factor has been introduced.
10
'
[: I,"
'
'
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. . . .
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-1 i
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Figure 4. Inclusive ~ cross section [5].
i
i
I
0.3
125
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
i(5)
'
'
F
. . . .
I
. . . .
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Figure 5. Inclusive rf cross section [5].
Another example of recent LEP results on inclusive hadron production is the OPAL analysis of strange baryon production[6]. Fig.6 shows the measured spectra as a function of zE = E/Ebeam for the j R = 3 1+ octet baryons A and ~-
the J P --- 3+ decuplet baryons E(1385) ~1 2 and ~(1530) °, and the j R _- 3- orbitally excited state A(1520). The curves give the predictions of J E T S E T 7.4, except for the A(1520) baryon, which is not present in JETSET. Here the E(1385) + differential cross section shape from JETSET is compared to the measurement. Generally the predicted spectrum of JETSET 7.4 with default parameters is too soft; an extra parameter is needed to suppress leading baryons. 1.2. T u n i n g o f m o d e l p a r a m e t e r s Based on the high precision data at the Z resonance the LEP collaborations have tuned the popular Monte Carlo models[7],[8]. For example in the global ALEPH fit[8] the following experimental quantities were used:
• event-shape distributions S, A, 1 - T, T,,ino,., - In Y3;
Figure 6. Inclusive cross sections for strange baryons [6].
• charged particle inclusive xp = P/pbe~,m, p~,,t, p±i,~.,
distributions
inclusive spectra of ~ = - In xp for the neutral V ° particles K ° and A °, and for the charged pions, kaons and (anti)protons; inclusive spectra of X E = E/Ebeam for the mesons rl(XE > 0.1), r#(xE > 0.1) p0, K.0, K , + , ¢0, w0; the mean multiplicities of the L = 1 mesons f2, f0 and of the hyperons ~ - , E(1385), =(1530) °, ~ - . Monte Carlo calculations of these quantities at various locations in parameter space were performed and the dependence of each quantity on the model parameters was parametrized. Minimizing the X2 function between data and prediction with respect to the model parameters the following results were found: Table 1 shows the fitted parameter values for the JETSET 7.4 model [9]. The parameters A q c D and Mmin determine the parton shower
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
126
parameter
AQCD (GeV) Mmin (GeV) O'q (GeV) a
b (GeV -2) ~C ~b
p(S = 1)d,u p(S = 1), p(S = 1)c,b
p(JP=2+;L=
1 , S = 1) extra y' suppression
s/u qq/q (suldu)l(slu) leading baryon suppr. switch fragmentation function baryon model azimuthal distrib, in PS
name in program PARJ(81) PAR J(82) PAR J(21) PAtLI(41) PAR J(42) - P A R J(54) - P A R J(55) PARJ(ll) PAR J(12) PAR J(13) PAR J(17) PAtLI(26) PAtLI (2) PARJ(1) PARJ(3) PAR J(19)
default value 0.29 1.0 0.36 0.30 0.58 0.050 0.005 0.50 0.60 0.75 0.0 0.40 0.30 0.10 0.40 1.0
range generated 0.21 - 0.37 1.0 - 2.0 0.28 - 0.44 0.20 - 0.60 0.60- 1.00 0.015 - 0.065 0.0005 - 0.0075 0.40 - 0.70 0.35- 0.65 0.50 - 0.80 0.10 - 0.30 0.05 - 0.55 0.19 - 0.39 0.05 - 0.15 0.4- 1.0 0.2- 1.0
value 0.292 1.57 0.370 0.40 0.796 0.040 0.0035 0.55 0.47 0.65 0.20 0.27 0.285 0.106 0.71 0.57 setting
fit result error + 0.003 4- 0.04 4- 0.002 (fixed) 4- 0.012 adjusted adjusted + 0.02 4- 0.02 adjusted adjusted 4- 0.03 4- 0.004 4- 0.002 4- 0.04 4- 0.03
syst. 4- 0.006 4- 0.13 4- 0.008 4- 0.033
4- 0.06 4- 0.06
44444-
0.09 0.014 0.003 0.07 0.10
MSTJ(11) MSTJ(12) MSTJ(46)
Table 1 Parameters for JETSET 7.4. The parameters describing the higher mesons are assumed to be in the ratio PARJ(17) :PARJ(16) :PARJ(15) = 5 : 3 : 1, and PARJ(14) ----PARJ(16). The diquark-spin suppression parameter PARJ(4) was left at its default value (0.05). No Bose-Einstein correlations are included.
development. The conversion of the partons into hadrons is accomplished with the Lund String model. Since the parameters a and b for light quark fragmentation are highly correlated, the parameter a was fixed to 0.4. The parameters ec and eb in the Peterson function [10] for heavy quarks were adjusted in order to describe the measured charm and bottom spectra. The additional parameters for leading baryon suppression and rf suppression are given in the table. The HERWIG 5.8 model [11] has significantly less explicit parameters (Table 2). The coherent parton branching process is governed by the parameters AQCDand Mgtuon,and the hadronization is modelled with a cluster mechanism. Heavy clusters with masses greater than Md,max can decay into smaller clusters before decaying into hadrons.
Fit results for the ARIADNE 4.08 model are also available [8]. Generally the tuned Monte Carlo models describe the data reasonably well. Significant discrepancies are in the p~Ut spectra for the momentum component out of the event plane (Fig.7) and in the baryon spectra (Fig.S). Similar results have been obtained by the other LEP collaborations. 1.3.
Polarization
measurements
In Z ~ st decays the primary s quark has a longitudinal polarization of PL = --0.94 which is transferred to a directly produced leading A baryon. Other A baryons are decay products of heavier baryons which contain the primary s quark. These A will inherit some fraction of the parent's polarization. A baryons containing a primary u or d quark or coming from the fragmentation process are expected to be unpolarized. The
H.G. Sander~Nuclear Physics B (Proc. Suppl.)
parameter
name in program QCDLAM
AQCD (GeV)
default value 0.18 0.75 3.35 0.0 1.0
RMASS(13) CLMAX CLSMR PWT(3)
Mg,=on (GeV) Mc4ma= (GeV)
40) p(s-quark)
range generated 0.12- 0.18 0.7-1.0 3.0-4.0 0.0-1.0 0.6-1.0
(1999) 123-133
71
fit result error -4- 0.001 + 0.005 ± 0.01 -4- 0.02 -4- 0.01
value 0.147 0.656 3.65 0.73 0.79
127
syst. + 0.005 + 0.015 -4- 0.10 + 0.06 -4- 0.06
Table 2 Parameters for HERWIG 5.8.
102i
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Figure 7. Inclusive distibution ofp~,~'t for charged particles, using the event plane based on the sphericity tensor [8].
4
5
-- [~ X p
Figure 8. Inclusive A cross section [8].
6
128
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
•2'.'
o.8
t
0.7
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Figure 10. The K *° helicity density matrix element P00 as a function of xp [14].
0.2
0.1
0
-0.l
XE
Figure 9. Longitudinal polarization of A baryons [12].
A polarization can be determined from the asymmetry in the weak decay A -4 prr. Figure 9 shows the OPAL measurement [12] of PL as a function of XE. Significant negative values are found for A's with intermediate and high momenta in agreement with ALEPH results [13] and the JETSET prediction. The role of meson spin in the production dynamics has been investigated by OPAL [14] and DELPHI [15]. They measure the spin density matrix of vector mesons in the helicity rest frame using the decay angular distribution. The matrix elements #-1-l,P00,Pll give the relative intensities of the helicity states -1,0,+1, respectively. Since the strong decay cannot disinguish between +1 and -1 helicities, the relevant observable is P00 which is expected to be 1/3 in a simple statistical model [16]. As an example Fig.10 shows the K *° helicity density matrix element p00 as a function of xp, as measured by OPAL. The data for p0, K.0, ¢ and D* show clearly that leading vector mesons are spin aligned with A = 0 preferred.
1.4. F l a v o u r t a g g e d events More information on hadron production in Z decays comes from analyses trying to distinguish the different sources of the observed hadrons: the different initial quark flavours or differences between quark and gluon jets. Since the production of heavy quarks in the fragmentation chain is strongly suppressed, charmed hadrons can either be leading particles from the initial Z -4 c~ decay or decay products of leading bottom hadrons from Z -4 bb decay. There is also a small contribution from gluon splitting into a pair of heavy quarks. The ALEPH collaboration has measured [17] the energy spectrum of D *+ mesons reconstructing the decay chain D *+ -4 D%r + , D O -4 K - 7r+ . Figure 11 shows the experimental result for all Z decays together with the Monte Carlo prediction of the three contributions. The bb contribution has been checked experimentally using a high purity b-tag in the opposite event hemisphere. A fit to the D* spectrum yielded the average number of gluon splitting events per hadronic Z decay to be n(g -4 c~) = (4.7 + 1.0 ± 1.1)%. 1.5. D i f f e r e n c e s b e t w e e n q u a r k a n d g l u o n jets The OPAL collaboration has measured [18] the multiplicity distribution of charged particles in quark and gluon jets using an inclusive jet definition similar to that used for analytic calculations. The method is based on rare events of the type Z -4 qclg, in which the q and Cl jets ap-
H.G. Sander~Nuclear Physics B (Proa Suppl.) 71 (1999) 123-133
0.12
::•0.012
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0
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5
10
15
20
25
30
35
40
35
40
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0.08 ~0 0 ~ 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
X E = E] Ebeam
[~
~
-- -
Herwig5.9
0.06 ~ 0.114 0.02
Figure 11. Inclusive D *+ cross section. The data points are compared to the model predictions [17].
pear in the same hemisphere of an event. The quark jets are identified by displaced secondary vertices from heavy quark decays. All particles in the opposite hemisphere are taken as the gluon jet. This definitition corresponds closely to single gluon jets produced in gg events from a colour singlet point source. Details of this analysis are given elsewhere in these proceedings [19]. These gluon jets with an average energy of 41.8 GeV are compared to light (u,d,s) quark hemispheres of 45.6 GeV. The corrected charged multiplicity distributions are shown in Fig.12 together with the JETSET and HERWIG predictions. The mean multiplicity values differ by about 50%, the distribution for quark jets is about twice as skewed (asymmetric) as the gluon jet distribution, but the dispersions are found to be the same. Correcting the quark jet result down to 41.8 GeV, OPAL finds r = 1.471-4-0.024-4-0.043 for the multiplicity ratio between gluon and quark jets at 41.8 GeV. The DELPHI collaboration has studied [20] the energy dependence of r, selecting three-jet events with the Durham jet finding algorithm with yc,,t = 0.01. They observe an increase with
0
0
5
10
15
20 rich.
25
30
Figure 12. Corrected distribution of charged particle multiplicity for (a) 41.8 GeV gluon jets, and (b) 45.6 GeV u,d,s quark jets [18].
the jet energy Ejet (Fig.13), which can be described by a linear fit r = (0.92+0.07)+(0.0112+ 0.0024). Ejet(GeV). This result reconciles the CLEO measurement [21] r = 1.04 -4- 0.05 at the T(1S) with the high energy OPAL measurement. The fragmentation function for charged particles in quark and gluon jets has been measured by the ALEPH collaboration [22] selecting nearly symmetric three-jet events with the Durham algorithm with a high jet resolution parameter of y~,t = 0.1. Figures 14 and 15 show the measured inclusive distributions of ZE = Ehad/Ejet for charged particles in quark and gluon jets along with Monte Carlo predictions. As expected from the higher multiplicity, the measured gluon fragmentation function is considerably softer than the quark fragmentation function, however somewhat harder than the model predictions.
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
130
'~ ~~ A 16 14
g q
12
• A ALEPH sym • O DELPHI 0 HRS-PEP • n OPALsym
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5
. . . .
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
10 15 20 25 30 35 40 45 50 M e a n charged multiplicity vs jet energy Ej~ (GeV)
Figure 14. Measured quark fragmentation func tion [22].
A oZ
v 1.8 A z =
~1.6
• ALEPH sym v CLEO • DELPHI o DELPHI sym
0 • [] ¢r
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Figure 15. Measured gluon fragmentation func tion [22].
I31
H.G. Sander/Nuclear Physics B (Proc. Suppl.) 71 (I999) 123-133
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Figure 16. The total hadronic cross section as a function of centre-of-mass energy. The dashed curve is the cross section after cuts against initial state radiation.
2.
0.4
II
After six years of running near the Z resonance the exploration of the high energy regime of LEP started in 1995. The runs in 1995-1996 at centreof-mass energies of 133 GeV ( combined from runs at 130 and 136 GeV ), 161 GeV and 172 GeV provided a total luminosity of around 25 pb-1 per experiment.Since August 1997 LEP is operating at 183 GeV. As shown in Fig.16 the hadronic cross section drops from 30 nb at the Z pole to about 30 pb after cuts, so that these data samples contain only about 300 events per energy point per experiment. At LEP II there is a high probability for initial state photon radiation back to the Z pole. These radiative return events, where the photon remains in the beam pipe, can be rejected using the visible energy E~8 and the imbalance in the energy component parallel to the beam Ell. Figure 17 from L3 [23] shows a clear separation between signal and background events. An important topic for LEP II is the study of W + W pair production with
Figure 17. Scatter plot of variables used to separate radiative from non-radiative events (see text) [23].
cross section up to 17 pb. Hadronic events e+e - --+ W + W - --+ qOqO --+ hadrons cannot be completely separated from e +e- --+ q(:l --4 hadrons, so that the remaining background has to be modelled by Monte Carlo. In the present situation with the small data samples available global event properties are measured first. Figure 18 shows the mean charged multiplicity [24] as a function of centre-of-mass energy compared to the predictions of Monte Carlo models. The models PYTHIA and HERWIG based on parton showers agree with the data, whereas the JETSET O(c~) matrix element model [9] does not predict a fast enough rise in Nch for increasing energy. The charged particle inclusive distribution as a function of ~ = - I n xp, as measured by ALEPH at 172 GeV [25], is shown in Fig.19. The histograms give the model predictions of PYTHIA 5.7 (solid curve)and HERWIG 5.8 (dashed curve), where the model parameters were tuned using the Z data as described earlier. The agreement is very good. The peak position ~* of the inclusive distribution of ~ which was determined by fitting a distorted Gaussian [26] to the central region is
132
H.G. Sander~Nuclear Physics B (Proc. Suppl.) 71 (1999) 123-133
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shown in Fig.20 along with low energy measurements by the TASSO experiment[27]. The QCD predictions using the double logarithm approximation (DLA) and including higher order corrections (MLLA)[28] have been corrected for the energy dependence of the flavour composition of the primary quarks. The high energy data points are somewhat higher than the MLLA curve. 3. C o n c l u s i o n s The analysis of the LEP I data is still going on. The high statistics available allow detailed studies of many aspects of hadron production. Specific questions like quark/gluon jet differences or spin properties can be answered. The LEP II physics has just started. Many results are still dominated by large statistical errors. Even with the expected luminosity of 500 pb-1 per experiment in the next years this will still not reach the LEP I precision. REFERENCES
. A. BShrer, Inclusive Particle Production in Hadronic Decays of the Z Boson at L E P I,
Siegen SI-96-15.
Figure 19. Charged particle inclusive distribution at 172 GeV [25].
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H.G. Sander~NuclearPhysics B (Proc. Suppl.) 71 (1999) 123-133
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