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

2. Hadronization2 Rainer Fries 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. … the resolution of the process … which process we use to probe … the reference frame. How we see a hadron depends on … u u d u d u  s d u d g g g p ++

3. Hadronization3 Rainer Fries An Example E.g. measure form factor in p +  *  p

4. Hadronization4 Rainer Fries An Example E.g. measure form factor in p +  *  p Sensitive to matrix elements   = wave functions  * describes uud  p: resembles recombination u u d

5. Hadronization5 Rainer Fries Fragmentation E.g. measure hadrons produced in e + e - Single parton has to hadronize = fragmentation  Radiation of gluons + pair production Factorization:  Holds for Q 2    Probing matrix elements like  All these matrix elements are measured, not calculated.

6. Hadronization6 Rainer Fries 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 T c )?  No perturbative scale in the problem (T   QCD ) Naively: recombine partons

7. Hadronization7 Rainer Fries 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? Product of quark distributions Meson Wigner function

8. Hadronization8 Rainer Fries Baryon/Meson Anomaly @ RHIC Enhanced baryon yield  p/  ~ 1 in Au+Au (for P T ~ 2 …4 GeV/c)  p/  ~ 0.3 in p+p,  p/  ~ 0.1….0.2 in e + +e - PHENIX

9. Hadronization9 Rainer Fries Baryon/Meson Anomaly @ RHIC Enhanced baryon yield General baryon/meson pattern: p, , ,  versus K, , , K*

10. Hadronization10 Rainer Fries Baryon/Meson Anomaly @ RHIC Enhanced baryon yield General baryon/meson pattern: p, , ,  versus K, , , K* No mass effect:  behaves like a pion (m   m p, 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

11. Hadronization11 Rainer Fries Recombination & Fragmentation “Dual” model of hadron production:  Recombination + pQCD/fragmentation to describe hadron production at RHIC for P T > 1…2 GeV/c Competition between Reco und Fragmentation  Fragmentation dominates for power law and high P T.  Recombination dominates for thermal quarks. fragmenting parton: p h = z p, z<1 recombining partons: p 1 +p 2 =p h

12. Hadronization12 Rainer Fries Recombination & Fragmentation “Dual” model of hadron production:  Recombination + pQCD/fragmentation to describe hadron production at RHIC for P T > 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

13. Hadronization13 Rainer Fries Hadron Spectra Recombination of thermal partons dominates up to 4 GeV/c for mesons, 6 GeV/c for baryons

14. Hadronization14 Rainer Fries More Hadron Data Large baryon/meson ratios  sharp drop beyond P T  4 GeV/c Nuclear modification factors:  Baryon enhancement can reverse suppression by jet quenching   R AA > R CP ~ 1 for baryons,  drop in baryon/meson beyond P T  6 GeV/c

15. Hadronization15 Rainer Fries Elliptic Flow Scaling Assume universal elliptic flow v 2 p 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.)

16. Hadronization16 Rainer Fries 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 v 2 describes a collective effect  Bulk matter  Equilibrium reached during the build-up of v 2 ?  Thermalization?? Deconfinement is reached: plasma of constituent (?) quarks at hadronization  QGP phase?

17. Hadronization17 Rainer Fries How robust is v 2 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

18. Hadronization18 Rainer Fries 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:

19. Hadronization19 Rainer Fries Zooming in on v 2 Scaling We proposed a new variable: baryon/meson v 2 asymmetry (B-M)/(B+M) for scaled v 2. First results:  Size and sign of the effect predicted correctly. Gluons could be accommodated. P. Sorensen, QM 05

20. Hadronization20 Rainer Fries A New Scaling? KE T scaling = hydro scaling  Quark number and quark mass scaling don’t interfere with each other! Chiho Nonaka: 3-D Hydro

21. Hadronization21 Rainer Fries 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 (  Q 2 evolution) Recombine all partons:  Partons = soft/thermal + showers from jets  Two parton distribution function: pTpT partons Soft (T) Shower (S) Partons from 2 jets Partons from 1 jets soft-shower soft-soft

22. Hadronization22 Rainer Fries Soft/Hard Recombination Soft/Hard Reco could be important.  Signatures in the p/ ,  /K ratio at large P T.  Produces hadron correlations. Hwa and Yang

23. Hadronization23 Rainer Fries Hadron Correlations How can hadrons at intermediate P T show jet-like structure?

24. Hadronization24 Rainer Fries Hadron Correlations How can hadrons at intermediate P T show jet-like structure? Actually there are clear deviations from “vacuum” jets STAR preliminary D. Magestro

25. Hadronization25 Rainer Fries Hadron Correlations How can hadrons at intermediate P T 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

26. Hadronization26 Rainer Fries Assuming 2-particle correlations  Interesting scaling law ~ n A n B  Blending in fragmentation Hadron correlations consistent with data can be generated. From Parton to Hadron Correlations Meson trigger Baryon trigger 4 parton pairs leading to meson correlations Near side

27. Hadronization27 Rainer Fries Hadronization in Other Systems Déjà vu: strong dependence of enhancement in R dAu 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?

28. Hadronization28 Rainer Fries 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. e+e-e+e- pppAAA

29. Hadronization29 Rainer Fries Recombination in d+Au? Yields of protons and pions can be explained in a picture containing fragmentation and soft/hard recombination.  Hwa and Yang:

30. Hadronization30 Rainer Fries Summary Recombination is a very simple model to describe a very complex process. And it does a remarkable job! v 2 scaling is robust, gluons could be accommodated. Hadron correlations at intermediate P T are not inconsistent with recombination. Recombination effects for baryons in d+Au are very likely.

31. Hadronization31 Rainer Fries Backup

32. Hadronization32 Rainer Fries Recombination & Fragmentation “Dual” model of hadron production:  Recombination + pQCD/fragmentation to describe hadron production at RHIC for P T > 1…2 GeV/c  Fragmentation dominates for power law and high P T.  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 Exponential: Power law: for mesons

33. Hadronization33 Rainer Fries Thermal Recombination Hadron spectrum by convolution of Wigner functions For P T >> M, k T : collinear kinematics, small mass corrections Thermal parton distribution  meson ~ baryon 2-quark Wigner function Meson Wigner function

34. Hadronization34 Rainer Fries 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.

35. Hadronization35 Rainer Fries 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