JET PHYSICS AT LEP AND WORLD SUMMARY OF αs 1 ee Annihilation Data Over the past few ...

18 Pages·1998·0.48 MB·English

JET PHYSICS AT LEP
AND
WORLD SUMMARY OF αs a
S. BETHKE
III. Physikalisches Institut, RWTH
D - 52056 Aachen, Germany
e-mail: [email protected]
Recent results on jet physics and tests of QCD from hadronic final states in
e+e− annihilation at PETRA and at LEP are reviewed, with special emphasis
on hadronic event shapes, charged particle production rates, properties of quark
andgluonjetsanddeterminationsofαs. Thedataintheentireenergyrangefrom
PETRA to LEP-2 arein broad agreement withthe QCD predictions. The world
summary of measurements of αs is updated and a detailed discussion of various
methods to determine the overall error of αs(MZ0) is presented. The new world
averageisαs(MZ0)=0.119±0.004. Thesizeoftheerrordependsonthetreatment
ofcorrelateduncertainties.
1 e+e− Annihilation Data
Overthe pastfewyears,palargeamountofe+e− annihilationdatainthe c.m.
energy range from Q (cid:17) s = 10 to 189 GeV was accumulated at the CESR,
PETRA, PEP, Tristan, LEP and SLC accelerators. The large data samples
at LEP-1, which amount to about 4 million hadronic events around the Z0
resonance for each of the four LEP experiments, and the most recent data at
thehighestenergiesofLEP-2(afewthousandeventsperexperiment),together
with reanalysed PETRA data at lower c.m. energies (about 50.000 hadronic
events), provide powerful tools for precise tests of perturbative QCD.
At energies below or at the Z0 resonance, respectively at PETRA and at
LEP-1, the study of e+e− annihilation events is rather \easy" and straight
forward: apart from two-photon processes, the energy and quantum numbers
ofthe hardscatteringarewellde(cid:12)nedanddi(cid:11)erentprocessescanbe identi(cid:12)ed
and selected with only very little backgrounds or biases. At LEP-2, i.e. at
energies above the Z0 pole, the situation is more complicated:
(cid:15) The annihilation cross section is orders of magnitude lower than at the
Z0 pole; see Figure 1b.
(cid:15) Initialstatephpotonradiationreducestheavailableenergyofthehadronic
c.m. system, s0, see Figure 1a, and causes, together with the resonant
aPresentedattheIVth Int. Symp. onRadiativeCorrections,Barcelona,Sept. 8-12,1998.
1
25
(a) hadrons OPAL(cid:13) OPAL (c)
3 R
10 (preliminary)
Preliminary
(cid:214) s = 189 GeV 20
s
t Inclusive
n
e Born
v
E ‰(cid:13) fi(cid:13) 15
2
10
10
5
PEP/PETRA
TRISTAN
TOPAZ 95
50 100 150 200 0
20 40 60 80 100 120 140 160 180 200
(cid:214)(cid:13) s¢(cid:13) /GeV (cid:214)(cid:13) s /GeV
(b) OPAL
preliminary
104
pb e+e-fi(cid:13) hadrons
n / e+e-fi(cid:13) hadrons; s¢(cid:13)/s>0.7225
o
oss-secti103
cr
102
s¢(cid:13)/s>0.7225
10
60 80 100 120 140 160 180 200
(cid:214)(cid:13) s / GeV
Figure 1: Hadronic cross sections and available data in e+e− annihilation (for details see
text); R:=σ(e+e−→qq)/σ(e+e−→µ+µ−).
crosssectionaroundtheZ0mass,alarge\return-to-the-Z"e(cid:11)ect. Radia-
tivpe evepnts can be suppressed requiring a minimum reconstructed ratio
of s0/ s and other kinematic constraints.
(cid:15) Other processes like e+e− ! W+W− and e+e− ! Z0Z0 emerge above
therespectiveenergythresholds,seetheshadedareainFigure1c,causing
a certain irreducable background for QCD studies.
p
In the following sectiopns, recent QCD tests from LEP-1 ( s (cid:24) 91 GeV;
Section 2), from LEP-2 ( s (cid:24) 130 GeVpto 189 GeV; Section 3) and from a
combination of PETRA and LEP data ( s(cid:24)14 GeV to 172 GeV; Section 4)
are presented. The world summary of αs is updated in Section 5.
2
2 QCD Tests at LEP-1
2.1 αs from Event Shapes using Optimised O(α2s) QCD
DELPHI DELPHI
EEC EEC
AEEC [(cid:79)(a s2); (cid:13) AEEC [xm =1]
JCEF JCEF
1-Thr xm fitted] 1-Thr
O O
C C
B B
Max Max
B B
Sum Sum
r r
H H
r r
S S
r r
D D
DE0 DE0
2 2
DP0 DP0
2 2
DP DP
2 2
DJade DJade
2 2
DDurham DDurham
2 2
DGeneva DCambridge
2 2
DCambridge
2
unw. average : a (M 2) = 0.1165 unw. average : a (M 2) = 0.1243
S Z S Z
r.m.s. = 0.0026(cid:13) r.m.s. = 0.0080(cid:13)
c 2/n = 9.2 / 17 c 2/n = 40 / 16
df df
0.06 0.08 0.10 0.12 0.14 0.06 0.08 0.10 0.12 0.14
a (M2) a (M2)
S Z S Z
Figure 2: Measurements of αs from hadronic event shapes at LEP-1 using O(α2s) QCD
predictionswith(left)andwithout(right)optimisedrenormalisationscalesµ.
The DELPHI collaboration contributed a new measurement of αs from
orientedeventshapedistributionsatLEP-11. 17di(cid:11)erenteventshapeobserv-
ables are measured as a function of the polar angle of the thrust axis, and αs
is determined from (cid:12)ts to O(α2) QCD calculations. As already reported ear-
s
lier2,3,4, good agreement between theory and data can be obtained if both αs
and the renormalisation scale µ are determined simultaneously; see Figure 2.
With optimisedrenormalisationscalesandallowingforscaleuncertainties
between0.5(cid:2)µexp and2(cid:2)µexp, consistentresultsofαs(MZ0)emerge,leading
to a combined average of αs(MZ0) = 0.117(cid:6)0.003. Both the average and
the error,which includes theoretical uncertainties from scale changes as given
above, are smaller than those obtained from resummed O(α2) QCD (cid:12)ts. This
s
3
is basically due to the choice of the averagingprocedure and error de(cid:12)nition.b
The broad consistency between data and optimised O(α2) QCD justi(cid:12)es this
s
procedureandsuggeststoreconsideroptimised(cid:12)xedorderperturbationtheory
as an alternative to resummation which was preferred in the past.
2.2 Differences between Quark- and Gluon-Jets
0.15
OPAL
g jets
incl.
|y| £(cid:13) 2 uds jets
0.1 Jetset 7.4
)
h. Herwig 5.9
c
n
Ariadne 4.08
(
P
0.05 Ariadne 4.08
(reconnected)
0
0 5 10 15 20 25 30 35
n
ch.
Figure 3: Charged particle multiplicites in gluon-inclusive and in light (uds) quark jets in
thecentralrapidity(|y|<2)range.
Di(cid:11)erences between quark- and gluon-jets were studied quite intensively
during the past few years. The aim is to test the basic QCD prediction that
hadrons coming from gluon jets should exhibit a softer energy spectrum and
a wider transverse momentum distribution than those originating from quark
jets, due to the larger colour charge of the gluon. In particular, the ratio R
qg
of the averagemultiplicities of hadrons in gluon jets and in quark jets should,
for in(cid:12)nite jet energies and in leading order QCD, be (cid:25) C /C = 3/(4/3)=
A F
9/4=2.25.
Experimental procedures to separate quark- from gluon-jets are usually
based on vertex tagging of primary b-quark decays. In short, 3-jet like events
bNotethat,forinstance,apreviousstudy4basedon13observablesandusingadifferentpro-
cedure to average results and determine the overall error obtained αs(MZ0)=0.122+−00..000065
which, if the same procedure as used in the DELPHI analysis is applied, converts to
αs(MZ0)=0.116±0.003.
4
>h
c DELPHI
N
< 12
_
qqg events
11 Quark
Gluon
10 QCD Fit
9
8
7
6
k
r
ua 2.25
q
n/ 2
o Ratio of slopes
o glu 11.7.55 Ratio of multiplicities
Rati 1.25 OPAL
CLEO 10 k [GeV]
Figure 4: Charged particle multiplicities in anti-tagged gluon and light quark jets as a
functionoftheenergyscaleκ.
areselectedinwhichoneofthetwolowerenergeticjetsistaggedasab-quark,
while the other low energy jet is then taken to be the gluon jet. From (cid:12)rst
analysesofthis type it wasfound5 that, after correctionfor misidenti(cid:12)ed jets,
R = 1.27(cid:6)0.07. No QCD calculation for this particular type of analysis
qg
exists, such that a direct comparisonof this resultwith theory is not possible.
Theoretical predictions only exist for colour singlet qq and gg (cid:12)nal states,
where however the latter state is not experimentally accessible. In order to
perform an analysis closer to theory, OPAL followed a new strategy in which
events with a high-energetic gluon-jet recoiling against a (vertex-tagged) qq
system6 were selected. Such events are relatively rare, leading to about 550
selected gluon jets from OPAL’s LEP-1 data sample.
Acomparisonofthechargedhadronmultiplicitydistributionofsuchgluon
hemispheres with those of ordinary light quark event hemispheres is shown in
Figure 3, where a signi(cid:12)cant di(cid:11)erence between quark- and gluon-jets is seen.
5
For a central rapidity range, the hadron multiplicity ratio R is found to be
qg
1.87(cid:6)0.13; the remaining di(cid:11)erence to the QCD expectation of 2.25 is likely
to be explained by (cid:12)nite jet energy e(cid:11)ects.
DELPHI has studied the scale dependence of particle multiplicities in
quark-andgluon-jets7. Here,gluon-jets andlightquark-jetsare(anti-)tagged
in3-jet events,andajet energyscale ofκ=E sin(θ/2), where θ is the angle
jet
between the two lowest energetic jets, is de(cid:12)ned. The charged hadron multi-
plicities for quark-and gluon-jets, as a function of κ, are diplayedin Figure 4.
Alsoshownistheratioofmultiplicitiesandtheratioofslopes;thelatterbeing
close to the QCD prediction of 2.25.
From these measurements DELPHI determines the ratio C /C to be
A F
2.27(cid:6)0.012which is ingoodagreementwith QCD,andinparticularwith the
expected colour charge of the gluon.
3 QCD Tests at LEP-2
3.1 Hadronic Event Shapes and Running of αs
103 ALEPH preliminary
O(a s2 ) + NLLA Ecm=183 GeV
102
dT Ecm=172 GeV
/
sd10

s1/ Ecm=161 GeV
1
Ecm=133 GeV
10–1
Ecm=91.2 GeV
10–2
10–3
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 T 1
Figure5: Thrust-distributionsmeasuredbyALEPHatvarious c.m. energies,andcommon
fittoanalyticQCDcalculations inresummednext-to-leadingorderperturbationtheory.
At each new energy point of LEP-2, all four LEP experiments have ex-
tensively studied hadronic event shape distributions and compared the new
measurements with the predictions of QCD Monte Carlo models, as well as
with analytic QCD calculations. In all cases,up to andincluding the most re-
6
L3 Reduced (cid:214)(cid:13) s¢(cid:13)
(cid:214)(cid:13) s =91.2 GeV
0.16
(cid:214)(cid:13) s = 133 GeV
(cid:214)(cid:13) s = 161 GeV
(cid:214)(cid:13) s = 172 GeV
(cid:214)(cid:13) s = 183 GeV
0.14
(cid:214)(cid:13) s = 189 GeV
s QCD Evolution
Constant a
a s
0.12
0.1
50 100 150 200
(cid:214)(cid:13) s (GeV)
Figure6: Runningofαs asmeasuredbyL3.
p
centdataat s=189GeV,goodagreementofdataandtheorywasfound,and
no signi(cid:12)cantdeviation from the standardexpectation was seen. As an exam-
ple, Figure 5 shows the thrust-distributions measured by ALEPH8 at LEP-1
and at four energy points of LEP-2, together with a (cid:12)t to resummed O(α2)
s
QCD calculations which is in good agreement with the data at all energies.
The L3 collaboration has summarised their measurements9 of αs from
various event shape distributions, at LEP-1, at all LEP-2 energy points, and
at hadronic c.m. energies below the Z0 pole, from an analysis of radiative
events recorded at LEP-1. The data, which are displayed in Figure 6, apre in
very good agreement with the QCD prediction of a running coupling αs( s).
3.2 Energy Dependence of Charged Particle Production
Theenergydependenceofparticleproductionwas,similarlyashadronicevent
shapes, continuously monitored by all LEP experiments. The variation of
such observables with energy is found to be in good agreement with QCD
predictions, and also with the \standard" QCD plus hadronisation models.
The energy dependence of the average charged hadron multiplicity and of the
peak position ξ(cid:3) of the ξ =ln(1/x) distribution (x=p/E )9 are shown in
beam
Figure 7.
7
JETSET 7.4 PS 5.0
30 HERWIG 5.8 x * L3 QCD MLLA
ARIADNE 4.06 TASSO QCD DLA
4.5
COJETS 6.23 ALEPH
25 JETSET 7.4 ME DELPHI
4.0 OPAL
>
n ch20 TASSO 3.5
< JADE
TOPAZ
15 AMY 3.0
OPAL
ALEPH
DELPHI 2.5
10 L3
2.0
50 100 150 200
0 50 1(cid:214)(cid:13)00s (GeV15)0 200 250 (cid:214)(cid:13) s (GeV)
Figure 7: Average charged particle multiplicities and peak position ξ(cid:3) of the ξ = ln(1/x)
distribution(compilationbyL3).
4 Power Corrections and Energy Dependence of Event Shapes
The energy dependence of mean values of event shape observables can be
parametrised by the O(α2) perturbative QCD prediction10 plus a term in-
s
cluding the improved two-loop calculations (the \Milan factor") of power-
suppressed 1/Q non-perturbative contributions11, the so-called \power cor-
rections". The latter contains the moment α0 of an e(cid:11)ective coupling below
an infrared scale µ , which is expected to be universal for all applicable event
I
shape observables.
Acompilationofavailabledataonthemeanvalueof(1-thrust)andofthe
C-parameter is shown in Figure 8, which is taken from a recent re-analysis of
JADE data at PETRA energies12. Perturbative QCD plus power corrections
is found to give a very good description of the data, with αs(MZ0) = 0.118(cid:6)
0.002(cid:6)0.004 as determined from these data. However, universality of α0 is
only found to be satis(cid:12)ed at a level of 30%.
Fordifferentialeventshapedistributions,thepowercorrectionsaresimply
a shift of the perturbative (O(α2)) spectra, and these were also studied in a
s
wide c.m. energy range, including the most recent PETRA and LEP data for
a total of four event shape observables13. A (cid:12)t to these data, with αs(MZ0)
andα0 asfreeparametersforeachobservable,leadsto theresultsdisplayedin
Figure 9. Agreement in both αs(MZ0) and α0 is obtained, to a good level of
accuracy, for two of the observables. However, the jet broadening parameters
Bw and Bt deviate signi(cid:12)cantly13 in both αs(MZ0) and α0.
8
Æ(cid:13)1-Tæ(cid:13) Æ(cid:13)Cæ(cid:13)
JADE
JADE
0.18
Mark J 0.35
TASSO ALEPH
0.16 DMEaLrkC IOI DL3ELPHI
AMY 0.3 OPAL
0.14 DELPHI SLD
L3
0.12 AOLPAEPLH 0.25
SLD
perturbative QC(cid:13)D(cid:13)
0.1 0.2
+ improved power corrections
0.08
0.15
0.06
0.1
0.04 (cid:13) power corrections(cid:13)
omitted 0.05
0.02
0 0
0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180
(cid:214)(cid:13) --s [GeV] (cid:214)(cid:13) --s [GeV]
Figure8: Energydependence ofmeanvaluesof(1-Thrust)andoftheC-parameter.
Most recently,the reasonfor these deviations was identi(cid:12)ed and tracedto
the theoretical predictions14; a cure of this problem should soon be available.
5 World Summary of αs
Signi(cid:12)cant determinations of the strong coupling strength, αs, remain to be a
demanding and interesting topic in experimental as well as theoretical study
projects in high energy physics. In the following subsections, previous sum-
maries of αs measurements 15,16 will be updated and a new world average
αs(MZ0) will be determined. Instead of a complete reference to all available
measurements, only the newest results are briefly introduced, and more em-
phasis is spent on a detailed discussion of the overall uncertainty of αs(MZ0),
(cid:1)αs.
5.1 Updates and New Results
The results of all signi(cid:12)cant determinations of αs, i.e. of all those which are
based on QCD calculations which are complete - at least - to next-to-leading
order perturbation theory, are summarised in Table 2. The following entries
were added or updated since summer 199716 (underlined in Table 2):
(cid:15) The most recent determination of αs from the GLS sum rules, based on
new data from ν −N scattering17 is included, replacing the previous
9
0(cid:13) .7(cid:13)
a(cid:13) B(cid:13) W(cid:13)(cid:13) (cid:13) preliminary(cid:13)
0(cid:13) (cid:13)
(cid:13)
(cid:13) 95 % C.L. Contours(cid:13)
0(cid:13) .65(cid:13) (cid:13)
B(cid:13) (cid:13)
T(cid:13) (cid:13)
0(cid:13) .6(cid:13)
0(cid:13) .55(cid:13)
1-T(cid:13)
0(cid:13) .5(cid:13) C(cid:13)(cid:13)
(cid:13)
0.45(cid:13)
(cid:13) 0(cid:13) .0 0.09 0.10 0.11a ( M ) (cid:13) 0.12(cid:13)
s(cid:13) Z(cid:13)
(cid:13) (cid:13) (cid:13)
Figure 9: Fit results for α0 and αs(MZ0) for several differential event shape distributions
measuredinthec.m. energyrangefrom35to183GeV.
result from Chyla and Kataev18.
(cid:15) New measurementsofαs fromhighstatisticsstudies ofvectorandaxial-
vectorspectralfunctionsofhadronicτ-decaysareavailablefromALEPH19
and OPAL20. As the most complete and precise studies of τ decays to
date, these results are combined and taken to replace earlier results21.
(cid:15) H1 has contributed new determinations of αs from (2+1)-jet event rates
at HERA22, replacing a previous measurement23. A combination of
these new results with aformer onefromZEUS24 is updated inTable 2.
(cid:15) A new determination of αs from (cid:7)-decays25 replaces earlier results26.
(cid:15) A recent determination of αs from the total e+e− hadronic cross section
measured by CLEO at E =10.52 GeV27 is added.
cm
(cid:15) Determinations of αs from JADE data, at Ecm = 35 and 44 GeV, were
updated12 by the inclusion of another observable, the C-parameter.
(cid:15) αs from the most recent LEP result on Rl = ΓΓ((ZZ00!!hleapdtroonnss)) was up-
dated28 (these results are still preliminary).
(cid:15) LEP results on αs from event shapes measured at Ecm = 183 and
189 GeV29 are combined and added to the list (some of these results
are still preliminary).
10