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Event shapes and other QCD studies at LEP
Sw. Banerjee
To cite this version:
Sw. Banerjee. Event shapes and other QCD studies at LEP. International conference on high-energy
physics 30 ICHEP, Jul 2000, Osaka, Japan. �in2p3-00007904�
Event Shapes and other QCD studies at LEP
Swagato Banerjee
LAPP, IN2P3-CNRS, Chemin de Bellevue, BP110, Annecy-le-Vieux, France 74941.
Abstract
QCD results on jet rates, event shapes and inclusive charged particle spectra in hadronic events from e
−e
+annihilations at LEP up to a center-of-mass energy of 208 GeV are presented.
Talk given at the XXX
thInternational Conference on High Energy Physics (ICHEP),
27 July-2 August 2000, Osaka, Japan.
1
Event Shapes and other QCD studies at LEP
Swagato Banerjeea
aLAPP, IN2P3-CNRS, Chemin de Bellevue, BP 110, Annecy-le-Vieux, France 74941.
QCD results on jet rates, event shapes and inclusive charged particle spectra in hadronic events from e−e+ annihilations at LEP up to a center-of-mass energy of 208 GeV are presented.
1. Introduction
With the increase of center-of-mass energy (√
s), LEP provides an ideal environment for pre- cise tests of QCD over a wide energy range with small hadronization corrections, which scale in- versely as √
s. In this paper, results up to√ s = 208 GeV from the LEP experiments: ALEPH [1], DELPHI [2], L3 [4,5] and OPAL [6,7] are re- viewed. Radiative Z-decay events with isolated photons, provide information on the hadronicsys- tem down to√
s = 30 GeV [2,4]. From quark and gluon jet multiplicities measured at the Z peak, colour factors are obtained [3].
2. Jet Rates
Hadronicevents are characterised by a multi- jet topology. Jets have been studied using the Jade, Durham and Cambridge algorithms.
Figure 1 shows the different jet rates for year 2000 data using the Cambridge algorithm [5]. Satis- factory agreement with the predictions of QCD models is obtained.
NLO predictions for 4 jet rates are now avail- able [8]. αsmeasured by DELPHI [2] usingCam- bridge algorithm (ycut = 0.004) are compared toO(αs3) calculations in figure 2. Fit to d log Edαs−1 gives 1.17±0.28, in agreement with expectationcm
of 1.27 for 5 flavours.
3. Event Shapes
The energy flow in hadronic events can be con- veniently studied in terms of collinear and in- frared safe global event shape variables. The energy dependence comes from logarithmic be-
0.2 0.4 0.6 0.8 1
10-2 10-1
Data (205.3 GeV) (Cambridge)
2-JETS 3-JETS 4-JETS 5-JETS
L3
PRELIMINARY
ARIADNE 4.08 HERWIG 5.9 JETSET 7.4 PS
ycut
Jet Rate
Figure 1. Jet rates using the Cambridge algo- rithm.
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15
80 100 120 140 160 180 200 220
O(α3s) statistical errors only
ECM/GeV αs(ECM)
Figure 2. αs from 4 jet rates.
from non-perturbative effects.
For some event shape variables, like thrust (T), heavy jet mass (ρ), total and wide jet broadenings (BTand BW) and the C-parameter (C), complete theoretical calculations exist up to O(αs2) and the leading and next-to-leading order terms have been resummed up to all orders. While the sec- ond order calculations work well in the multi-jet region, the resummed calculations are necessary to describe the data in the two jet region. Thus the whole distribution of the event shapes can be used, giving reduced statistical errors in the de- termination ofαs.
4. Determination of αs
4.1. Power Law ansatz
Assuming the soft gluon emission is controlled by an effective coupling (αeff), which differs from αs in the infrared region, the hadronization cor- rection to the non-perturbative component of mo- ments as well as the differential distributions of event shapes can be parameterised using a power law ansatz. The mean values and the distribu- tions have been simultaneously fitted to αs(MZ) and the non-perturbative parameter α0(µI)(=
1 µI
µI
0 dqαeff(q)) at a scaleµI= 2 GeV, using sec - ond order calculations for the perturbative part.
The results ofαsandα0from fits to moments and distributions are shown in the figure 3. The scat- ter in the measurements from different variables between the different experiments being large, universality ofα0 is verified within±20%.
Phenomenological study [2] shows that the rel- ative size of the power law contribution is large for event shapes variables with large relative second order term. L3 studied [4] the second moment of the event shapes using an additional 1/s term in the power law parametrization. The contribution is small forρ, negative for BWand substantial for others.
4.2. Resummed LL & NLL + O(αs2) The standard determination of αs from event shape variables uses matching of second order predictions with resummed NLLA calculation.
Quark mass effects are included in the O (αs2)
ALEPH MEAN ALEPH DIST
1-Tρ BT BW C
αs(MZ) α0(2 GeV)
World Average 0.2
0.3 0.4 0.5 0.6 0.7 0.8
0.1 0.11 0.12 0.13
Figure 3. Summary of αs-α0 measurements.
calculations: while the effect is 1% at MZ, it scales as 1/s down to 0.2% at 200 GeV. Fits to the five event shape variables measured by L3 [5] at √
s
= 206 GeV are shown in the figure 4.
The measurements of αs using the different event shapes are averaged for each value of √
s, and evolved to MZfor comparison in the figure 5.
The average of all the measurements gives:
αs(MZ) = 0.1204±0.0007(exp)±.0034(theo) From a fit to the slope of theαsmeasured between 30 and 208 GeV by the L3 [5], the number of active quark flavours is obtained to be 5.1±1.3 (exp) ± 1.9 (theo), in agreement with DELPHI measurements [2] of d log Edαs−1
cm. 5. Charged Particle spectra
Beyond the leading logarithmicapproximation, the intrajet coherence phenomena arising from destructive interference between the soft gluon emission within the jets, reduces the phase space available for further parton emission to an angu- lar ordered region. This dynamical suppression of the soft momenta leads to energy and emission angle ordering of successive parton radiations. It results in reduced parton multiplicities and a dip in the parton momenta in the low momentum re- gion.
3
0 5 10 15 20
0.5 0.6 0.7 0.8 0.9 1 T
1/Ntot dN/dT
0 10 20 30
0 0.1 0.2 0.3
ρ 1/Ntot dN/dρ
0 5 10 15
0 0.1 0.2 0.3 BT 1/Ntot dN/dBT
0 5 10 15 20
0 0.1 0.2
BW 1/Ntot dN/dBW
0 2 4 6 8 10
0 0.2 0.4 0.6 0.8 C 1/Ntot dN/dC
√s = 206 GeV Data QCD fit PRELIMINARY
L3
Figure 4. O (αs2) + resummed calculations fit.
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 ALEPH
DELPHI L3 OPAL
√s (GeV)
αs (MZ)
41.255.3 65.475.4 82.385.1 89.593.0 91.2
133.0
161.0
172.0
183.0
189.0
195.0 198.0 200.0 201.0 205.0
207.0
Figure 5. αsmeasurements from event shapes.
The charged particle momentum spectrum is studied in terms of the variable ξ = −ln(2√|p|s) (where p is the momentum). The energy evolu- tion of the charged particle multiplicity and the measured peak position (ξ) (figures 6, 7) provide evidence for gluon coherence: predictions without coherence effects fail to describe the data.
TASSO JADE TOPAZ AMY ALEPH DELPHI OPAL L3
PRELIMINARY JETSET 7.4 PS
HERWIG 5.9 ARIADNE 4.08 COJETS 6.23 JETSET 7.4 ME
√s (GeV)
< nch >
10 15 20 25 30
0 50 100 150 200 250
Figure 6. Energy evolution of charged particle multiplicity.
6. Quark and gluon multiplicities
The evolution of the charged particle multiplic- ity has been studied as a function of the opening angle (θ) between the sub-leading jets in mirror symmetric 3 jet events [3]. Correcting for the case when the gluon fragments into the leading jet, large opening angles translate into harder gluon jets, giving higher multiplicities.
Recent theoretical calculations relate the derivatives of quark-gluon multiplicities to the QCD colour factors [9]. From a fit to the data from hadronicZ decays, DELPHI updated their analysis using theCambridgejet algorithm, and obtained: CA/CF= 2.221±0.047(exp)±0.058 (had)±0.075(theo), in good agreement with the QCD prediction of 9/4.
The gluon-gluon multiplicity is extracted at scales given by √
s and pT using the relation:
2.0 2.5 3.0 3.5 4.0
4.5 TASSO L3 ALEPH DELPHI OPAL
QCD DLA QCD MLLA
√ s (GeV)
ξ
*PRELIMINARY
50 100 150 200
Figure 7. Energy evolution of peak position of ξ-spectra.
Ngg= 2[Nq¯qg(θ)−Nqq−N0], estimating the non- perturbative offset term (N0) from CLEO data.
Measurements of the quark and gluon jet multi- plicities are shown in the figure 8.
5 10 15 20 25
10 102
Ecm , pT[GeV] Nch
Nch from e+e- to qq Fit
Ngg=2(Nqqg - Nqq) Ngg (CLEO) Ngg (OPAL) Eden (a)
DELPHI
Figure 8. Charged particle multiplicity in quarks and gluon jets.
Different aspects of hard and soft gluon radi- ation have been studied in hadronicevents with
√s in the range 30 to 208 GeV. Evidence of gluon coherence and higher gluon colour charge have been observed. The strong coupling constant, the number of active quark flavours and QCD colour factors have been measured.
Acknowledgements
I thank all the 4 LEP experiments for shar- ing with me the preliminary results and thank Sunanda Banerjee, Dominique Duchesneau, John Field, Klaus Hamacher and Oliver Passon for in- teresting discussions.
REFERENCES
1. ALEPH coll., contributed paper #164.
2. DELPHI coll., contributed paper #638.
3. DELPHI coll., contributed paper #640.
4. L3 coll., Physics lettersB489(2000) 65.
5. L3 coll., contributed paper #630.
6. OPAL coll., Eur.Phys.J.C16(2000) 185.
7. OPAL coll., contributed paper #252.
8. Zoltan Trocsanyi, these proceedings.
9. P.Edenet al., JHEP 09 (1998) 15.
P.Edenet al., Eur.Phys.J.C11(1999) 345.
