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Hadronization of Partons by Recombination

Hadronization of Partons by Recombination. Rudolph C. Hwa University of Oregon. Summer School on RHIC Physics Wuhan, China, June 2005. Outline. An overview of the recombination model Some questions and answers on the basics Shower partons initiated by hard partons

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Hadronization of Partons by Recombination

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  1. Hadronization of Partons by Recombination Rudolph C. Hwa University of Oregon Summer School on RHIC Physics Wuhan, China, June 2005

  2. Outline An overview of the recombination model Some questions and answers on the basics Shower partons initiated by hard partons Hadronization in heavy-ion collisions

  3. p p H(x) x Parton Recombination First studied for low-pT production in pp collision Das & Hwa, Phys. Lett. 68B, 459 (1977) Ochs observation: H(x) is very similar to the valence quark distribution in a proton.

  4. Valon-recombination model -- better formulation of recombinationHwa, PRD (1980b) Valon model -- to get the proton wave functionHwa, PRD (1980a)

  5. Hadronic collisionsHwa & CB Yang (2002b) h + p  h’ +X h h’ p    K+  + K p+A collisionsHwa & CB Yang (2002a) We studied the centrality dependence (or the number of collisions) in the valon-recombination model good data from NA49

  6. Hadron production at high pT pp collision: mainly by fragmentation AA collision: there were puzzles according to fragmentation Recombination solved those puzzles Hwa & Yang, PRC 67, 034902 (2003); 70, 024905 (2004) Greco, Ko, Levai, PRL 90, 202302 (2003); PRC 68, 034904 (2003) Fries, Muller, Nonaka, Bass, PRL 90,202303(03); PRC 68, 044902 (03) More recent developments -- 2004, 2005 Correlations in jets

  7. Questions: What is the two-parton distribution ? Especially in heavy-ion collisions 2.What are the recombination functions ? Closer examination of the recombination formulas Pion : Proton :

  8. More questions : What about the gluons? Does entropy decrease? What about the spatial considerations? Isn’t the pion a Goldstone boson? Recombination versus fragmentation: Which is more important? 8. What is wrong with string fragmentation? Answer in reverse order.

  9. but not for AA collisions. recombination 8.String fragmentation • String model may be relevant for pp collisions, • String/fragmentation has no phenomenological support in heavy-ion collisions.

  10. High pT physics in pp collisions is well understood. What was a discovery yesterday is now used for calibration today.

  11. hadron momentum Parton distribution (log scale) suppressed by power-law p p q q1+q2 (recombine) (fragment) higher yield heavy penalty 7. Recombination versus Fragmentation

  12. + In Drell-Yan process in -p collisions, the quark contents of pion and proton are probed. p - 6. Pion is a Goldstone boson Is it a boson due to spontaneous symmetry breaking? Or a bound state of quark-antiquark? Both are aspects of the pion. No theory exists that can continuously transform one to the other.

  13. 1. nuclear transverse size RA 2. hadron transverse size rh • If partons are parallel, but far apart, they cannot recombine • If parton trajectories intersect, they must cross at the same space-time region --- relative momentum suppress recombination. 5. Spatial considerations We have formulated recombination in momentum space only so far. Shouldn’t the spatial coordinates be important also? Isn’t hadron size relevant? In heavy-ion collisions there are two sizes:

  14. Our approach: • We consider only collinear partons. • Hard parton defines the direction of the hadron. • Soft partons are restricted to the small spatial spread around the point where hard parton emerges from the nuclear medium. Groups at Duke University and Texas A&M University have Monte Carlo codes to implement space & momentum constraints on recombination. We do not use Monte Carlo code to generate the soft partons throughout the expanding medium. We infer from the soft pion spectrum at low pT what the soft parton distribution is. Momentum space consideration is sufficient, and that is where observation is made.

  15. 4. Entropy color: 3 X 3 1 degrees of freedom decreased spin: 2 X 2 1 depends on wave function momentum conservation Soft gluon radiation: mutates color & carries away spin without changing g RM cannot account for low momentum partons Entropy: a global quantity that should take into account expanding volume.

  16. Gluon conversion to q-qbar Recombination of with saturated sea gives pion distribution in agreement with data. 3. How do gluons hadronize? In pp collisions the parton distributions are x2u(x) x2g(x) Gluons carry ~1/2 momentum of proton but cannot hadronize directly. x [log] Sea quark dist. Fq ~ c (1-x)7 Saturated sea quark dist. F’q ~ c’ (1-x)7

  17. 2. Recombination functions It depends on the wave function. Consider the time-reversed process What are the distributions of the quarks in momentum fractions in the infinite momentum frame?

  18. We need a model to relate to the wave function of the proton Fq U Valon model p U D valons Deep inelastic scattering e e p Fq

  19. Moments by convolution theorem cancel in the ratio valence quark distr in proton valon distr in proton, independent of Q valance quark distr in valon, in proton or in pion known from CTEQ param the ratio can be determined • Basic assumptions • valon distribution is independent of probe • parton distribution in a valon is independent of the hadron U p U D

  20. Single-valon inclusive distribution Hwa & CB Yang, PRC66(2002) proton pion From  initiated Drell-Yan process valon model 3-valon exclusive distribution Recombination function

  21. pp collisions: low pT and large xF Heavy-ion collisions: Low pL (mid-rapidity), large pT 1. Two-parton distributions That is high pT physics. Traditionally, hadronization at high pT is by fragmentation. However, fragmentation model has met some difficulties, most notably in p/ ratio at intermediate pT in nuclear collisions.

  22. Before describing what the two-parton distribution should be at high pT in heavy-ion collisions, we must first • discuss why fragmentation does not work phenomenologically • what are the shower partons in fragmentation? • how does the nuclear medium affect hadronization? Which parton recombines which parton is the core problem in the recombination model.

  23. Rp/π  1 Rp/π Not possible in fragmentation model: u p/ ratio

  24. The black box of fragmentation q p 1 z A QCD process from quark to pion, not calculable in pQCD Momentum fraction z < 1 Dp/q Phenomenological fragmentation function z 1

  25. Let’s look inside the black box of fragmentation. q p 1 z fragmentation gluon radiation quark pair creation Although not calculable in pQCD (especially when Q2 gets low), gluon radiation and quark-pair creation and subsequent hadronization nevertheless take place to form pions and other hadrons.

  26. hard parton meson shower partons fragmentation recombination can be determined known from recombination model known from data (e+e-, p, … ) Description of fragmentation by recombination

  27. valence u d s sea u d L L DSeaKNS L  DVG G  DGL Ls  DKSeaG Gs  DKG s R g 5 SPDs are determined from5 FFs. RK Shower parton distributions assume factorizable, but constrained kinematically.

  28. Shower Parton Distributions Hwa & CB Yang, PRC 70, 024904 (04)

  29. BKK fragmentation functions

  30. If our shower parton distributions are reliable, based on the dynamical independence of the shower partons except for kinematical constraints, then we should be able to calculate the quark fragmentation function into a proton. Nevertheless, there is only a discrepancy of less than a factor of 2 over 4 order of magnitude. Data on Dup(z) not well determined. KKP parametrization has an error.

  31. h Conventional approach D(z) q A A Once the shower parton distributions are known, they can be applied to heavy-ion collisions. The recombination of thermal partons with shower partons becomes conceptually unavoidable.

  32. h Now, a new component Once the shower parton distributions are known, they can be applied to heavy-ion collisions. The recombination of thermal partons with shower partons becomes conceptually unavoidable.

  33. Proton formation: uud distribution usual fragmentation soft component soft semi-hard components (by means of recombination) Pion formation: distribution thermal shower

  34. Shower distribution in AuAu collisions hard parton momentum distribution of hard parton i in AuAu collisions Thermal distribution Contains hydrodynamical properties, not included in our model. Fit low-pT data to determine C & T.

  35. density of hard partons with pT = k Input: parton distributions CTEQ5L nuclear shadowing EKS98 hard scattering pQCD Srivastava, Gale, Fries, PRC 67, 034903 (2003) C, B,  are tabulated for i=u, d, s, u, d, g K=2.5

  36. Shower distribution in AuAu collisions SPD of parton j in shower of hard parton i hard parton momentum distribution of hard parton i in AuAu collisions fraction of hard partons that get out of medium to produce shower calculable Thermal distribution Contains hydrodynamical properties, not included in our model. Fit low-pT data to determine C & T.

  37. soft TT TS hard SS thermal Pion distribution (log scale) fragmentation Transverse momentum Now, we go to REAL DATA, and real theoretical results.

  38. fragmentation thermal  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, 024905 (2004)

  39. TSS Proton production in AuAu collisions TTS+TSS

  40. Proton/pion ratio

  41. All in recombination/ coalescence model Compilation of Rp/ obtained by 3 groups

  42. Cronin Effect Cronin et al, Phys.Rev.D (1975) h q p kT broadening by multiple scattering in the initial state. A p >  Cronin et al, Phys.Rev.D (1975) STAR, PHENIX (2003) Puzzle in pA or dA collisions Unchallenged for ~30 years. If the medium effect is before fragmentation, then  should be independent of h=  or p

  43. (in fragmentation model) PHENIX and STAR experiments found (2002) Can’t be explained by fragmentation. RHIC data from dAu collisions at 200 GeV per NN pair Ratio of central to peripheral collisions: RCP

  44. STAR

  45. d+Au collisions(to study the Cronin Effect) peripheral central d d more T more TS less T less TS

  46. soft-soft No pT broadening by multiple scattering in the initial state. Medium effect is due to thermal (soft)-shower recombination in the final state. d+Au collisions Pions Hwa & CB Yang, PRL 93, 082302 (2004)

  47. Thermal-shower recombination is negligible. Proton Hwa & Yang, PRC 70, 037901 (2004)

  48. 3q  p, each quark has ~1/3 of p momentum 2q  , each quark has ~1/2 of  momentum Nuclear Modification Factor This is the most important result that validates parton recombination.

  49. STAR data Azimuthal anisotropy Molnar and Voloshin, PRL 91, 092301 (2003). Parton coalescence implies that v2(pT) scales with the number of constituents

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