Multijets in e+e- annihilations Hasko Stenzel

FRIF workshop e+e- multi-jets H.Stenzel 2 Outline  Jet rates and algorithms  energy evolution  measurements of α s  4-jet analyses  color factors  measurements of α s  quark mass effects  Multijet event shapes  NP-analysis  out-of-plane momentum  non-global variables  beyond 4-jets mostly perturbative QCD !

FRIF workshop e+e- multi-jets H.Stenzel 3 Jet algorithms Jet definition based on a pair-wise track metric JADE algorithm Durham/k t algorithm Cambridge ordering parameter

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

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 and differential jet rates are evolving with energy through the running of α s. 3-jet fraction mean jet multiplicity

FRIF workshop e+e- multi-jets H.Stenzel 6 Measurements of α s from jet observables Observables derived from jet rates:  differential two jet rate  mean jet multiplicity mean jet multiplicity differential 2-jet rate Fits to the data with perturbative prediction O(α s 2 )+ NNLA, LogR matching (mostly in the 3-jet region)

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 Observableα s (91.2)Δ stat Δ exp Δ pert Δ had Δ tot D2CD2C ±0.0004±0.0017±0.0030±0.0026± D2DD2D ±0.0004±0.0025±0.0037±0.0017± ±0.0005±0.0013±0.0037±0.0033± ±0.0004±0.0006±0.0034±0.0039±0.0052

FRIF workshop e+e- multi-jets H.Stenzel 8 4-jet observables 4-jet observables have been used extensively to determine  QCD color factors  α s (fixing color factors to QCD)  using NLO calculations O(α s 3 )+ NNLA L3

FRIF workshop e+e- multi-jets H.Stenzel 9 QCD color factors in parton splitting CFCF CACA nfTRnfTR QCD : SU(3) C F =4/3, C A =3, T R =1/2

FRIF workshop e+e- multi-jets H.Stenzel 10 Color factors from 4-jets Leading order diagrams for 4-jet production

FRIF workshop e+e- multi-jets H.Stenzel 11 Observables in 4-jet system Bengtsson-Zerwas-Angle: angle between (p 1 x p 2 ) and (p 3 x p 4 ), ie. angle between planes P1 and P2 spanned by the two high and the two low energetic jets P2 P1 p1p1 p2p2 p3p3 p4p4 Angles between the 4 jets, e.g. Complete set of observables: + R 4 (y cut ) + y 23

FRIF workshop e+e- multi-jets H.Stenzel 12 NLO fits to angular variables and jet rates Including NLLA resummation

FRIF workshop e+e- multi-jets H.Stenzel 13 Results of simultaneous fit to α s and color factors α s (M Z )CACA CFCF ALEPH0.119±0.006± ±0.14± ±0.07±0.26 OPAL0.120±0.011± ±0.25± ±0.13±0.22 QCD34/3

FRIF workshop e+e- multi-jets H.Stenzel 14 Determination of α s from 4-jet observables (fixing color factors to QCD) OPAL recently analysed  4-jet rate  D-parameter  T minor at LEPI and LEPII

FRIF workshop e+e- multi-jets H.Stenzel 15 OPAL results on α s from 4-jet observables OPAL resultsα s (M Z ) ± Δ stat.Δ exp.Δ had.Δ scale.Δ mass R 4 (Durham) ± NLO+NLLA D-parameter ± NLO x µ =1 T minor ± NLO x µ =1 The uncertainty for α s from 4-jet observables is reduced wrt 3-jet case:

FRIF workshop e+e- multi-jets H.Stenzel 16 ALEPH/DELPHI results on α s from R 4 α s (M Z ) ± Δ stat.Δ sys.Data set OPAL ± NLO+NLLA ALEPH ± NLO+NLLA DELPHI ± LEPINLO x µ opt DELPHILogarithmic slope = 1.14 ± QCD: 1.27 ± 0.10 DELPHI tested the energy dependence of α s from 4-jets at E=150 GeV:

FRIF workshop e+e- multi-jets H.Stenzel 17 Testing b-quark mass effects in the 4-jet rate Cambridge y cut =0.0085Δ sys. R 4 bl ± m b (MZ)3.56 ± MbMb 4.61 ± DELPHI analysed flavour tagged 4-jet ratios: in order to extract the b-quark mass: preliminary result:

FRIF workshop e+e- multi-jets H.Stenzel 18 non-perturbative analysis of 4-jet observables L3α s (M z )α 0 (2 GeV) D-parameter ± ± ± ± all combined ± ± ± ± L3 analysis of mean value of D-parameter Results:

FRIF workshop e+e- multi-jets H.Stenzel 19 other 4-jet observables BnBn narrow jet broadening MlMl light jet mass T minor Thrust Minor, AKA K out OOblateness, T M -T m y 34 4-jet resolution parameter … measured at LEPI & LEPII but not analysed in the scope of power corrections …

FRIF workshop e+e- multi-jets H.Stenzel 20 out-of-plane momentum for near-to-planar configurations … with different y cuts …

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

FRIF workshop e+e- multi-jets H.Stenzel 22 beyond 4-jets 5- and more jet rates, y ij multijet resolution parameters

FRIF workshop e+e- multi-jets H.Stenzel 23 Conclusion Multijet observables (mostly 4-jets) have given access to  precision measurements of α s  color factors  test of quark mass effects many variables have been measured  D-parameter, T minor, Oblateness, y 34  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.