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Fragmentation in e + - e - Collisions

Fragmentation in e + - e - Collisions. LEP PETRA. e +. Dave Kettler Correlations and Fluctuations Firenze July 7-9, 2006. p hadron. color dipole. s = Q 2. g , Z 0. e -. QCD Issues for Nuclear Collisions. we observe that a large fraction of RHIC C/F

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Fragmentation in e + - e - Collisions

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  1. Fragmentation in e+-e-Collisions LEP PETRA e+ Dave Kettler Correlations and Fluctuations Firenze July 7-9, 2006 phadron color dipole s = Q2 g, Z0 e-

  2. QCD Issues for Nuclear Collisions we observe that a large fraction of RHIC C/F are due to minijets = low-Q2 parton fragments • How do partons scatter at low Q2 (invariant mass squared) • How do low-Q2 partons fragment to hadrons • What happens to low-Q2 partons in heavy ion collisions to understand the second point we examine the systematics of parton fragmentation in p-p and especially e+-e- collisions

  3. Two-component p-p Spectrum Model 200 GeV p-p S0 replot pt and yt spectra subtractS0 minijets are isolated in single-particle spectra H0 ‘hard’ component: parton scattering and fragmentation hard component vs nch

  4. Parton Scattering and Fragmentation i(pt,f,h)i (x,Q2) parton  hadron jet e´ e+ e-e Q2 x e-p g, Z0 pproton s LEP e Z0 HERA e- pproton fragmentation – two issues: RHIC Q2 x1 x2 s, Q2 how distributed on angle(s) pproton p-p how distributed on momentum p

  5. Parton Fragmentation in e+- e- how are parton fragments (hadrons) distributed on momentum gluon coherence: a QCD triumph LEP PETRA e+ phadron LEP PETRA e-e color dipole s = Q2 ln(pparton) g, Z0 e- ln(phadron) color dipole radiation: s, Q2 an equilibration process LEP, PETRA fragmentation data: 1985-2000 ?

  6. Conventional Fragmentation Studies ‘leading-particle’ strategy trigger vs associated jet is not reconstructed, estimate parton with high-pt leading particle fragmentation function leading particle jet reconstruction ? e+e- CCOR s = 63 GeV xE x A.L.S. Angelis et al., NPB 209 (1982)

  7. xp = ln(1/xp) Fragment Distributions on Momentum fragmentation functions on logarithmic variables non-pQCD physics! conventional: fragment momentum relative to parton momentum D(x,s) D(xp,s) LEP PETRA e-e pQCD scaling violations fragmentation function xp = phadron/pparton D(x,s)  D(y, ymax) D(y,ymax) D(ln(p),s) alternative: fragmentation functions on rapidity y ln(p) rapidity y

  8. Precision Analysis of Fragmentation fragmentation functions well described by simple model function p-p - FNAL p-p e-e - LEP 46 GeV = Q/2 D(y,ymax) 22 7 a form of equilibration g(u,ymax) = ymin STAR redundant dijet multiplicity normalized rapidity (normalized) beta distribution on normalized rapidity u precisely models fragmentation functions

  9. Why a Beta Distribution? Maximum Entropy Distributions with constraints Maximize Shannon Entropy Gaussian Exponential Beta Distribution • Bounded interval • Constraints reflect • parton splitting and • gluon coherence

  10. Identified Hadrons and Partons the flavor/color chemistry of fragmentation identified hadron fragments identified partons pions kaons quark and gluon shapes are different increasing meson mass udsc b gluon heavier fragments stay close to parent parton bottom quark is anomalous

  11. Fragmentation Energy Systematics extrapolation to non-perturbative regime 2n(ymax) (p,q) pQCD fit (p,q) energy sum rule ymax ~ ln( Q/L ) energy systematics fits to quark and gluon jet multiplicities  (p,q) fit parameters (p,q) 400 GeV fragment rapidity non-pQCD g(u,ymax) parton rapidity fits to fragmentation functions with beta distribution  (p,q) fragmentation functions represented over a broad energy range to few %!

  12. Scaling Violations – Conventional g-g data at right excellent agreement with recent measurements Q/2 (GeV) G. Abbiendi et al. (OPAL Collab.), Eur. Phys. J. C 37, 25 (2004)

  13. Scaling Violations – Logarithmic ratio 2.25 related to anomalous dimensions of QCD CA/CF=2.25 near uniformity to right of dotted line ratio 2.25 for xE 1 and s large P. Abreu et al. (DELPHI Collab.), Eur. Phys. J. C 13, 573 (2000)

  14. Comparisons with pQCD MLLA gaussians 10 GeV peak modes 8% form factor on u conventional FF description

  15. Low-Q2 partons play a dominant role in HI collisions Little was known about low-Q2 parton scattering and fragmentation prior to this work We have described all measured e+-e-fragmentation functions with a precise (few %) model function The model function (beta distribution) allows us to extrapolate fragmentation trends to low Q2 That system can then be used to describe low-Q2 parton fragmentation in p-p and HI collisions Summary ‘theoretical’ basis for minijet correlations in nuclear collisions

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