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Fragmentation Functions and Fragmentation Processes

Fragmentation Functions. Fragmentation Functions and Fragmentation Processes. Stefan Kretzer Brookhaven National Laboratory & RIKEN-BNL. XXXIV International Symposium on Multiparticle Dynamics July 26 - August 1, 2004 Sonoma State University, Sonoma County, California, USA.

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Fragmentation Functions and Fragmentation Processes

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  1. Fragmentation Functions Fragmentation Functions and Fragmentation Processes Stefan Kretzer Brookhaven National Laboratory & RIKEN-BNL XXXIV International Symposium on Multiparticle DynamicsJuly 26 - August 1, 2004Sonoma State University, Sonoma County, California, USA

  2. http://www.pv.infn.it/~radici/FFdatabase/maintained by M. Radici (Pavia) and R. Jakob (Wuppertal) To be updated

  3. Outline: • Status / overview of global analysis of (unpolarized) fragmentation functions (incl. a brief conceptual introduction) • Fragmentation processes [2 examples of hadroproduction at (not-so) high pT]: • The double spin asymmetry • Rho mass shift in at high pT

  4. Factorization and universality p p π π a a c c b b p p

  5. Global analysisofFragmentation Functions (largely avoiding advertisement plots)

  6. The Field & Feynman picture of cascade fragmentation

  7. Bilocal operator hadron P+ = z k+ D(z) k+ quark/gluon

  8. Collinear factorization: e+e- annihilation (1h inclusive)

  9. Fragmentation (or “Decay”) Functions Scale dependence from renormalization or mass factorization: DGLAP

  10. 2 Analysis of e+e-→hX Data Kniehl & Kramer & Pötter Alternative model approaches: Indumathi et al. Bourrely & Soffer Kretzer Bourhis & Fontannaz & Guillet & Werlen

  11. How well are Fragmentation Functions determined from e+e-? u,d,s flavours and gluons Sum over all flavours (singlet combination)

  12. Semi-Inclusive Deep Inelastic Scattering Flavour Separation

  13. E. Christova, SK, E. Leader “valence”“favoured”“rank 1” “sea”“unfavoured”“rank 2” favoured > unfavouredfavoured » unfavoured “strange”“rank 2”

  14. Comparison with previous leading particle guess: As seen in the HERMES pion multiplicities Leading particle ansatz works well.

  15. Hadroproduction: pp→ X at 200 GeV cms Fractional contributions from initial/final state partons Central Rapidity Forward Rapidity gq qg+gq qq initial gg qq gg qg Dq Dq final Dg Dg E [GeV] P? [GeV]

  16. Average Scaling Variables • Symmetric / asymmetric kinematics for central / forward rapidity • Large z fragmentation is probed. Central Rapidity P? [GeV] Forward Rapidity E [GeV]

  17. Factorized NLO pQCD and RHIC pp data STAR forward rapidity PHENIX central rapidity Gluon FF and large-z constraints from hadroproduction.

  18. The gluon fragmentation function has been measured. Hasn’t it?

  19. d σ(3 jet) * fragmentation * tagging-function Laenen & Keller

  20. LO NLO

  21. Onset of pQCD in hadronic collisions soft T. Hirano @ QM04 hard (1/pT)(dN/dpT) pT ??? GeV

  22. The double-spin asymmetry for . can be shown to be (basically) positive definite in the few GeV range (at leading power accuracy).

  23. Taking Moments, e.g.turns the non-local (xa ≠ xb) convolution into a local (in N) product The minimum [by variation δ(Δσ)/δ(Δg)=0] is at

  24. Inverted (from N to x)bounds Δσfrom below:

  25. ALL is (perturbatively) bounded by: Jäger, SK, Stratmann, Vogelsang (PRL 2004) • Positivity • Underlying parton dynamics The upper bound holds up to dependence on the scale where positivity is saturated. The lower bound is obtained under low p? approximations. The order of magnitude must be correct in both cases if the dynamics are:

  26. Perturbative high pT pions are produced in parton scattering and are decoupled (at leading twist) from the remnant. A statistical ensemble can realize J=1 either through angular momentum of spinless (Goldstone) bosons or through the spin of massive baryons. This must be expected to be disfavoured over J=0, i.e. A nonperturbative asymmetry of O(1%), even smaller than 1%, is enough to produce a characteristic transition from negative to positive asymmetry with increasing pT into the perturbative regime around 1-2(?) GeV.

  27. PHENIX hep-ex/0404027 Frank Bauer @ DIS04

  28. Rho mass shift in pp extends to high pT STAR data Does the observation contradict ?

  29. Resonant (p-wave) contribution to the 2-pion fragmentation function. (Bachetta & Radici)

  30. P (Sudakov) k q

  31. Qualitative (dual) features: • Heavier (light) hadrons come with a harder FF. (The low scale evolution is cut-off.) • Heavier hadrons are suppressed. (The virtual parton has to survive a multiple of its perturbative lifetime) • Resonances will be shifted to lower mass.

  32. Quantitative (order of magnitude) estimate: And slowly approaching with increasing .

  33. Summary :(with apologies for the omission of heavy quark fragmentation) • Fragmentation functions are determined from, mostly, e+e- annihilation data. Other processes, such as hadro/photo-production have provided tests of consistency and universality. Next steps: • Include new data & processes in the fit: • Update e+e- fits (large-z data from uds continuum at e.g. BELLE) • Semi-inclusive DIS (flavour) • Hadroproduction (gluons, large-z, RHIC pp norm predictions for AA and spin), enabled by NLO Mellin moment evaluation. • Consistency checks with jet data. • Error analysis and coupled analysis with parton densities (à la CTEQ) • Two recent RHIC measurements – resonance production and the double spin asymmetry for pion production - exemplify the rich phenomenology of identified particle production in hard QCD processes: • The perturbative spin asymmetry can be bounded to be (basically) positive [>O(-103)] for pT < 4 GeV. • Resonance mass shifts of the observed order are to be expected at large pT from parton fragmentation into the resonance decay products. short term not-so-short term

  34. ***** Leftovers *****

  35. Brain(?)storm: MotivationStatus of global fits and issues for updateSIDISenergy sum rule ???Gluon Fragmentation / Jet FF measurement and their interpretation / Tagging FunctionsRecombination in twist expansion ???Parton model limit g->0 ???Low pT exponentialALL: positivity in pQCD and cross-over from statistical contributionrho-meson production and shifted rho mass Collaborations with: E. Christova, E. Leader, W. Vogelsang, H. Yokoya, A. Dumitru, A. Bachetta, M. Radici, …

  36. Energy Conservation: ? kT orderingDGLAP angular orderingMLLA Not a practical constraint.

  37. Parton Distributions: Local operator product expansion in inclusive DIS Bilocal operator definition Fragmentation Functions: No local OPE (no inclusive final state) Bilocal operator definition Some Theory … Just as PDFs, FFs are well defined in terms of Scale dependence enters through renormalization: DGLAP

  38. HERMESDIS  multiplicities (unpolarized hydrogen target) • Curves: • LO • NLO • (“NNLO”)

  39. Factorized cross section pp→π(pT) X “Add” polarization (double-spin asymmetry) p p π π a a c c b b p p

  40. 2→2 channels: • Only (ii) has a negative asymmetry at parton level. • (i) >> (ii) by about a factor 160! • Does this mean that ALL has to be positive? • No: Polarized parton densities may oscillate!

  41. Predictions for ALL are all positive. Is this accidental or is ALL bounded from below? The upper bound on ALL depends on the scale at which positivity |Δg(x,μ)| ≤ g(x,μ)is saturated.

  42. Identified Particle Production in Hard QCD Reactions as in … Fragmentation Functions *** 2004 ***(selected issues) Stefan Kretzer Brookhaven National Laboratory & RIKEN-BNL XXXIV International Symposium on Multiparticle DynamicsJuly 26 - August 1, 2004Sonoma State University, Sonoma County, California, USA

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