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Quark and Gluon Jet Fragmentation Differences

In this talk, we explore the differences in fragmentation between quark and gluon jets, focusing on data from the Tevatron (CDF) and DELPHI experiments. We analyze charged particle multiplicities in 3-jet events and two-gluon systems, discussing theoretical implications and challenges in perturbative QCD calculations. Historical perspectives on the ratio of multiplicities, comparative studies between different energy scales, and ongoing research trends in jets are reviewed. We also summarize the experiments' findings regarding the ratio of charged particles in gluon and quark jets.

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Quark and Gluon Jet Fragmentation Differences

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  1. Quark and Gluon Jet Fragmentation Differences Andrey Korytov • Abstracts covered in this talk • 5-0081 Fragmentation differences of quark and gluon jets at the Tevatron (CDF) • 5-0437 Charged particle multiplicities in 3-jet events and two-gluon systems (DELPHI)

  2. CDF kT=1 GeV/c Multiplicity in Gluon and Quark Jets: Theory • Parton shower stage—challenge for pQCD calculations in very soft domain (kT < 1 GeV): • resummation at LLA and NLLA precision: - start out from color singlet - small opening angles around jet direction - r = Ng/Nq = CA/CF = 9/4 = 2.25 • continues flow of papers since mid-1980 to include corrections going beyond the NLLA accuracy most recent r = Ng/Nq = 1.4-1.7 (Q=20-100 GeV) • Hadronization stage—still a mystery: • Believed to be local, independent of jet origin: Nhadrons = K  Npartons (Local Parton-Hadron Duality) kT

  3. Multiplicity in Gluon and Quark Jets: Experiment • Proved to be a hard measurement: • continuous flow of papers from e+e- experiments (15+ papers over last 15 years): r = Ng/Nq ranged from 1 to 1.5

  4. r-measurement history 2.5 NLL extensions 2.0 HRS OPAL 1.5 SLD r = Ng / Nq ALEPH DELPHI 1.0 CLEO CDF 0.5 0.0 1980 1985 1990 1995 2000 2005 Year Gluon vs. Quark Jets: Historical Perspective Ratio r = Nch(gluon jet) / Nch(quark jet) CA /CF =9/4 (LLA, NLLA)

  5. DELPHI: Theory behind the new analysis • Eden et al., 1998: New look at relationship between Ngg and Nqq multiplicities • - Predict Ngg from Nqq (e+e-) data. • - Match Integration constant to reproduce • experimental Nch multiplicity in Υ-decays. • Eden et al., 1999: Multiplicity in 3-jet events (e+e- data) can be written as a sum of • a) restricted multiplicity in qq-system (two energy scales) • b) half of unrestricted multiplicity in gg-system (single energy scale) •  Eden “A” • No consensus on proper scales! • Eden “B” • Various scales appearing in formulae above:

  6. Jet 1 3 1 Jet 3 Jet 2 DELPHI: Multiplicity in 3-jet events • DATA • s=91 GeV • Events clustered in 3 jets • Two independent variables: • 1 and 3 • q- and g-jets are not identified • on event-by-event basis • THEORY (with experimental input): • Eden “A” • Eden “B”

  7. DELPHI: Ngg from 3-jet events • Use preferred Eden “A”: • Ngg(kLe) is obtained from • 1) Nqqg = N3-jet(1, 3): measured multiplicity • 2) Constrained Nqq(Lqq, kLu): evaluated from unconstrained multiplicity in e+e- data, using: Theory curve for Ngg is based on Nqq(s) data and normalized on this point

  8. DELPHI: r = (Ngg from 3-jet events) / Nqq

  9. Jet 2 cone p p Jet 1 CDF: Data analysis strategy • Dijet and g-jet events with Mjj and Mgj ~80-100 GeV • tracks are not used in jet reconstruction • Dijet events (~60% gluon jets) and g-jet events (~80% quark jets) • small uncertainties in energy range used (well known range of PDFs) • Dijet or g-jet center of mass frame: Ejet = ½Mjj or ½Mgj • Nch multiplicity in cones with opening angle q from ~0.3 to ~0.5 rad • Energy scale Q = 2Ejettan(qcone/2)  Ejetqcone •  Q=11-25 GeV (no controversy on proper scales for small opening angles) Some leading-order diagrams for g-jet events Some leading-order diagrams for dijet events

  10. two-parameter fit to CLEO (10 GeV) and OPAL (80 GeV) data CDF: Nch multiplicities in gluon and quark jets • Multiplicities measured in range of Q=11-25 GeV • Tevatron and e+e- data (Q>10 GeV) agree • E-scaling observed • Tevatron and e+e- data (Q>10 GeV) follow 3NLL trends e+e- model-dependent results

  11. CDF: ratio r = Ng / Nq • Ratio measured in range of Q=11-25 GeV: e.g., r=1.640.17 at Q=19 GeV • E-scaling observed • Data agrees with the recent NLL extensions

  12. CDF: Data vs. Monte Carlo Gluon Jets: Herwig 5.6 & Pythia 6.115 reproduce multiplicity in gluon jets fairly well Quark Jets: Herwig 5.6 & Pythia 6.115 over-estimate multiplicity in quark jets by ~30% Side Note on Pythia vs Herwig: Pythia gives ~3-4% higher multiplicity in comparison to Herwig

  13. x = p/Ejet = 1 0.5 0.1 0.05 CDF: momentum distributions of particles dN/d • Gluon jets: Herwig and Pythia are in reasonable agreement with data Quark jets: Herwig and Pythia disagree with data

  14. CDF: momentum-dependent ratio r() • Momentum distributions of charged particles in gluon and quark jets • Ratio reaches max and flattens for soft part of spectrum at ~1.80.2 • Same pattern was observed at LEP x = p/Ejet = 1 0.5 0.1 0.05

  15. Summary • CDF: • Multiplicities in gluon and quark jets and their ratio are measured for energy scales Q=11-25 GeV (analysis is model-independent): r = 1.640.17 at Q=19 GeV • Ejetcone-scaling is observed • Multiplicities and their ratio follow recent pQCD calculations pushing resummation precision beyond the Next-to-Leading Log Approximation • DELPHI: • Multiplicities in gluon jets are measured for energy scales Q=13-53 GeV (analysis is model-dependent): r ~ 1.35 ( about 1% error) at Q=20 GeV • Ratio of multiplicities in gluon and quark jets agrees with recent pQCD calculations at Q>20 GeV and is systematically lower at Q<20 GeV • Multiplicities of charged particles in 3-jet events may help to sort out uncertainties with scales to be used for describing events of complicated topologies

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