Insights into Hadronization: Probing Matrix Elements and Anomalies at RHIC

1. Hadronization of Dense Partonic Matter Rainer Fries University of Minnesota Talk at SQM 2006 March 28, 2006

2. u  u s d g u g u u d d p g d + Hadronization • Formation of bound states is non-perturbative in QCD. • Hadrons look differently, depending on how we probe them • Probe different matrix elements of different operators. • If we were able to solve QCD completely, we could compute all of them. How we see a hadron depends on … … which process we use to probe … the resolution of the process Hadronization … the reference frame.

3. An Example • E.g. measure form factor in p + *  p Hadronization

4. An Example • E.g. measure form factor in p + *  p • Sensitive to matrix elements •  = wave functions • * describes uud  p: resembles recombination u u d Hadronization

5. Fragmentation • E.g. measure hadrons produced in e+e- • Single parton has to hadronize = fragmentation • Radiation of gluons + pair production • Factorization: • Holds for Q2  • Probing matrix elements like • All these matrix elements are measured, not calculated. Hadronization

6. Dense Parton Systems • Fragmentation = limit of hadronization for very dilute systems (parton density  0) • What happens in the opposite limit (thermalized phase of partons just above Tc)? • No perturbative scale in the problem (T  QCD) • Naively: recombine partons Hadronization

7. Recombination • Simplest realization: • Recombine valence quarks of hadrons • Instantaneous projection of quark states on hadron states • Immediate problems: • Energy not conserved • Where are the gluons? Meson Wigner function Product of quark distributions Hadronization

8. Baryon/Meson Anomaly @ RHIC • Enhanced baryon yield • p/ ~ 1 in Au+Au (for PT ~ 2 …4 GeV/c) • p/ ~ 0.3 in p+p, • p/ ~ 0.1….0.2 in e++e- PHENIX Hadronization

9. Baryon/Meson Anomaly @ RHIC • Enhanced baryon yield • General baryon/meson pattern: p, , ,  versus K, , , K* Hadronization

10. Baryon/Meson Anomaly @ RHIC • Enhanced baryon yield • General baryon/meson pattern: p, , ,  versus K, , , K* • No mass effect:  behaves like a pion (m  mp , m >> m) • Hadron properties don’t matter in this kinematic region. • Only the number of valence quarks! • Do we catch a glimpse at hadronization? STAR Preliminary Hadronization

11. Recombination & Fragmentation • “Dual” model of hadron production: • Recombination + pQCD/fragmentation to describe hadron production at RHIC for PT> 1…2 GeV/c • Competition between Reco und Fragmentation • Fragmentation dominates for power law and high PT. • Recombination dominates for thermal quarks. fragmenting parton: ph = z p, z<1 recombining partons: p1+p2=ph Hadronization

12. Recombination & Fragmentation • “Dual” model of hadron production: • Recombination + pQCD/fragmentation to describe hadron production at RHIC for PT> 1…2 GeV/c • For RHIC: • T = 175 MeV • Radial flow  = 0.55 • Constituent quark masses • Fit to pion data  predictive power for all other hadron species • With B. Muller, C. Nonaka, S. A. Bass Hadronization

13. Hadron Spectra • Recombination of thermal partons dominates up to 4 GeV/c for mesons, 6 GeV/c for baryons Hadronization

14. More Hadron Data • Large baryon/meson ratios • sharp drop beyond PT 4 GeV/c • Nuclear modification factors: • Baryon enhancement can reverse suppression by jet quenching •  RAA > RCP ~ 1 for baryons, • drop in baryon/meson beyond PT 6 GeV/c Hadronization

15. Elliptic Flow Scaling • Assume universal elliptic flow v2p of the partons before the phase transition • Recombination prediction: • Scaling works for all hadrons • Deviations for pions arise mostly from resonance decays (Greco et al.) Hadronization

16. Quark Counting Rule for the QGP • Quark counting rules tell us that there is a quark substructure in hadrons • Classic example: • Counting valence quarks • RHIC 2003: A new quark counting rule • Subhadronic degrees of freedom are explicit!  Partons • Observable v2 describes a collective effect  Bulk matter • Equilibrium reached during the build-up of v2? Thermalization?? • Deconfinement is reached: plasma of constituent (?) quarks at hadronization  QGP phase? Hadronization

17. How robust is v2 scaling? • Scaling law uses the most primitive approximations • Momentum shared equally between constituents • Expect correction for realistic wave function with finite width. • Numerically: effects are small Momentum shared: fractions x and 1-x Hadronization

18. Fate of the Gluons? • Are there gluons or sea quarks? • No effect on particle yields for thermal spectra! • Resulting elliptic flow for hadrons does not obey scaling • For equally shared momenta: Hadronization

19. Zooming in on v2 Scaling • We proposed a new variable: baryon/meson v2 asymmetry (B-M)/(B+M) for scaled v2. • First results: • Size and sign of the effect predicted correctly. • Gluons could be accommodated. P. Sorensen, QM 05 Hadronization

20. A New Scaling? • KET scaling = hydro scaling • Quark number and quark mass scaling don’t interfere with each other! Chiho Nonaka: 3-D Hydro Hadronization

21. Soft (T) partons Shower (S) pT Soft/Hard Recombination • Attempt to treat reco + fragmentation consistently • Hwa and Yang: jets as cones of parton showers at late times; fitted to fragmentation functions • Majumdar, Wang and Wang: 2- and 3- quark constituent quark fragmentation + recombination ( Q2 evolution) • Recombine all partons: • Partons = soft/thermal + showers from jets • Two parton distribution function: Partons from 1 jets soft-soft Partons from 2 jets soft-shower Hadronization

22. Soft/Hard Recombination • Soft/Hard Reco could be important. • Signatures in the p/, /K ratio at largePT. • Produces hadron correlations. Hwa and Yang Hadronization

23. Hadron Correlations • How can hadrons at intermediate PT show jet-like structure? Hadronization

24. STAR preliminary Hadron Correlations • How can hadrons at intermediate PT show jet-like structure? • Actually there are clear deviations from “vacuum” jets D. Magestro Hadronization

25. Hadron Correlations • How can hadrons at intermediate PT show jet-like structure? • Correlations can be introduced by Soft/Hard Recombination • Correlations can arise from correlations between soft partons • Hot spots: fully or partially thermalized jets Hadronization

26. From Parton to Hadron Correlations • Assuming 2-particle correlations • Interesting scaling law ~ nAnB • Blending in fragmentation • Hadron correlations consistent with data can be generated. 4 parton pairs leading to meson correlations Meson trigger Baryon trigger Near side Hadronization

27. Hadronization in Other Systems • Déjà vu: strong dependence of enhancement in RdAu on hadron species. • Traditional explanation for enhancement: initial state scattering. • There must be a much more effective mechanism in the final state, favoring baryons! • Recombination? Hadronization

28. Recombination in d+Au? • We don’t need a QGP, just a certain parton density • Fragmentation is very ineffective for baryons! • It might just be easier to pick up soft partons instead of creating them, even in cold nuclear matter. AA pA pp e+e- Hadronization

29. Recombination in d+Au? • Yields of protons and pions can be explained in a picture containing fragmentation and soft/hard recombination. • Hwa and Yang: Hadronization

30. Summary • Recombination is a very simple model to describe a very complex process. • And it does a remarkable job! • v2 scaling is robust, gluons could be accommodated. • Hadron correlations at intermediate PT are not inconsistent with recombination. • Recombination effects for baryons in d+Au are very likely. Hadronization

31. Backup Hadronization

32. Recombination & Fragmentation • “Dual” model of hadron production: • Recombination + pQCD/fragmentation to describe hadron production at RHIC for PT> 1…2 GeV/c • Fragmentation dominates for power law and high PT. • Recombination dominates for thermal quarks. • For RHIC: • T = 175 MeV • Radial flow  = 0.55 • Fit to pion data  predictive power for all other hadron species Power law: for mesons Exponential: Hadronization

33. Thermal Recombination • Hadron spectrum by convolution of Wigner functions • For PT >> M, kT: collinear kinematics, small mass corrections • Thermal parton distribution  meson ~ baryon Meson Wigner function 2-quark Wigner function Hadronization

34. What is in the Parton Phase? • Recombination: low Q, no hard scattering • No perturbative plasma at hadronization • Effective degrees of freedom; no gluons • Constituent quarks? • We need a field theoretic description including chiral symmetry breaking. • cf. dynamical masses from instantons, lattice, DSE Diakonov & Petrov Bowman et al. Hadronization

35. Hadrochemistry in “Jet Cones” • The baryon/meson ratio is an indicator for the amount of “thermalization” in a jet • Far side produces more baryons than near side Hadronization