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 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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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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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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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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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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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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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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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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Color factors from 4-jets

Leading order diagramsfor 4-jet production

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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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NLO fits to angular variables and jet rates

2

; 44

2ln043

42

4

1 FCsOCxOBOBdO

d

Including NLLA

resummation

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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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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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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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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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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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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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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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out-of-plane momentum for near-to-planar configurations

… with different ycuts …

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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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beyond 4-jets

5- and more jet rates, yij multijet resolution parameters

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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.