multijets in e+e- annihilations hasko stenzel. 13.01.2006 frif workshop e+e- multi-jets h.stenzel 2...
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![Page 1: Multijets in e+e- annihilations Hasko Stenzel. 13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 2 Outline Jet rates and algorithms energy evolution](https://reader030.vdocuments.site/reader030/viewer/2022032522/56649d6b5503460f94a4a71c/html5/thumbnails/1.jpg)
Multijets in e+e- annihilations
Hasko Stenzel
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 2
Outline
Jet rates and algorithms energy evolution measurements of αs
4-jet analyses color factors measurements of αs
quark mass effects
Multijet event shapes NP-analysis out-of-plane momentum non-global variables beyond 4-jets
mostly perturbativeQCD
!
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 3
Jet algorithms
jilcut
Jij
ijs
EEJij
pppyy
y ji
cos12
Jet definition based on apair-wise track metric
JADE algorithm
ijsJij
EEy ji cos122
,min2
Durham/kt algorithm
Cambridge ordering parameter ijijv cos1
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 4
Jet rates
Corrections applied for:
background subtraction (LEPII) ISR/FSR QED corrections acceptance/efficiency detector resolution
Corrected distributions represent the hadron level. Hadronisation corrections are applied to perturbative predictions (e.g. for fits).
Hadr. corrections
Exp. uncertainties
Detector corrections
Hadronisation uncertainty claimed
~2% at LEPI < 1 % at LEPII
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 5
Energy dependence of jet observables
As in the case of event-shape Variables, jet rates, mean jet multiplicities anddifferential jet rates are evolving withenergy through the running of αs.
3-jet fraction mea
n j
et m
ult
ipli
city
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 6
Measurements of αs from jet observables
Observables derived from jet rates: differential two jet rate
mean jet multiplicity
mea
n j
et m
ult
ipli
city
232
2
)(y
dy
ydRD
cut
cut
n
cutncut ynyN )(1
)(
differential 2-jet rate
Fits to the data with perturbative prediction O(αs
2)+ NNLA, LogR matching(mostly in the 3-jet region)
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 7
Results from an OPAL analysis
Observables derived from jet rates: differential two jet rate
mean jet multiplicity
Cambridge and Durham
Measurements at LEPI and LEPII
232
2
)(y
dy
ydRD
cut
cut
n
cutncut ynyN )(1
)(
Observable αs (91.2) Δstat Δexp Δpert Δhad Δtot
D2C 0.1147 ±0.0004 ±0.0017 ±0.0030 ±0.0026 ±0.0043
D2D 0.1199 ±0.0004 ±0.0025 ±0.0037 ±0.0017 ±0.0048
<NC> 0.1254 ±0.0005 ±0.0013 ±0.0037 ±0.0033 ±0.0051
<ND> 0.1272 ±0.0004 ±0.0006 ±0.0034 ±0.0039 ±0.0052
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 8
4-jet observables
4-jet observables have been used extensively to determine
QCD color factors
αs (fixing color factors to QCD)
using NLO calculations O(αs3)+
NNLA
L3
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 9
QCD color factors in parton splitting
2
2
2
s
s
s
CF
CA
nfTR
QCD : SU(3) CF=4/3, CA=3, TR=1/2
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 10
Color factors from 4-jets
Leading order diagramsfor 4-jet production
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 11
Observables in 4-jet system
Bengtsson-Zerwas-Angle:
angle between (p1 x p2) and (p3 x p4), ie.angle between planes P1 and P2 spanned by the two
high and the two low energetic jets
P2
P1
p1
p2
p3
p4
Angles between the 4 jets, e.g.
Complete set of observables:
+ R4(ycut) + y23
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 12
NLO fits to angular variables and jet rates
2
; 44
2ln043
42
4
1 FCsOCxOBOBdO
d
Including NLLA
resummation
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 13
Results of simultaneous fit to αs and color factors
αs(MZ) CA CF
ALEPH 0.119±0.006±0.026 2.93±0.14±0.58 1.35±0.07±0.26
OPAL 0.120±0.011±0.020 3.02±0.25±0.49 1.34±0.13±0.22
QCD 3 4/3
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 14
Determination of αs from 4-jet observables (fixing color factors to QCD)
OPAL recently analysed 4-jet rate D-parameter Tminor at LEPI and LEPII
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 15
OPAL results on αs from 4-jet observables
OPAL results αs(MZ) ± Δ stat. Δ exp. Δ had. Δ scale. Δ mass
R4(Durham) 0.1182 ± 0.0003 0.0015 0.0011 0.0012 0.0013 NLO+NLLA
D-parameter 0.1047 ± 0.0014 0.0037 0.0061 0.0052 - NLO xµ=1
Tminor 0.1318 ± 0.0016 0.0056 0.0023 0.0111 - NLO xµ=1
The uncertainty for αs from 4-jet observables is reducedwrt 3-jet case:
4
4
2
1
R
R
s
s
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 16
ALEPH/DELPHI results on αs from R4
αs(MZ) ± Δ stat. Δ sys. Data set
OPAL 0.1182 ± 0.0003 0.0026 91-209 NLO+NLLA
ALEPH 0.1170 ± 0.0001 0.0022 91 NLO+NLLA
DELPHI 0.1175 ± 0.0005 0.0030 LEPI NLO xµopt
DELPHI Logarithmic slope = 1.14 ± 0.36 89-209QCD: 1.27 ± 0.10
bEa
bEd
dsb
bs
log
1:fit exp.
12)log( 0
1
0
1
DELPHI tested the energy dependence of αs from 4-jets at E=150 GeV:
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 17
Testing b-quark mass effects in the 4-jet rate
Cambridge ycut=0.0085 Δ sys.
R4bl 0.898 ± 0.014 0.014
mb(MZ) 3.56 ± 0.33 0.43
Mb 4.61 ± 0.41 0.54
llZ
bbZ
cutbl
R
RyR
4
44 )(
DELPHI analysed flavourtagged 4-jet ratios:
in order to extract the b-quark mass:
LO ; ),()(
NLO ; )()()(2
4
324
bsb
ssl
myByR
yCyByR
preliminary result:
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 18
non-perturbative analysis of 4-jet observables
L3 αs(Mz) α0(2 GeV)
D-parameter0.1046 ± 0.0078 ± 0.0096
0.682 ± 0.094 ± 0.018
all combined0.1126 ± 0.0045 ± 0.0039
0.478 ± 0.054 ± 0.024
L3 analysis of mean valueof D-parameter
Results:
PD
DBD
DDD
spow
sD
sDpert
powpert
2195
22
32
<D-parameter>
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 19
other 4-jet observables
Bn narrow jet broadening
Ml light jet mass
Tminor Thrust Minor, AKA Kout
O Oblateness, TM-Tm
y34 4-jet resolution parameter
… measured at LEPI & LEPII but not analysed in the scope of power corrections …
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 20
out-of-plane momentum for near-to-planar configurations
… with different ycuts …
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 21
non-global variables
… sensitive to local radiation in restricted phase space regions:
single jet mass and single jet broadening
eventper ,
entries two,
NWs
LHs
BBB
MMM
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 22
beyond 4-jets
5- and more jet rates, yij multijet resolution parameters
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13.01.2006 FRIF workshop e+e- multi-jets H.Stenzel 23
Conclusion
Multijet observables (mostly 4-jets) have given access to precision measurements of αs
color factors test of quark mass effects
many variables have been measured
D-parameter, Tminor, Oblateness, y34
out-of-plane momenta non-global variables
few of them have been analysed for power corrections
D-parameter
The potential of ≥5-jet configurations is to be explored.