QGP Formation Signals and Quark Recombination Model

1. QGP Formation Signals and Quark Recombination Model Chunbin Yang Central China Normal University Wuhan

2. Outline • Heavy ion collisions and QGP formation • Anomalies at RHIC • Physics ideas in the recombination model • Fragmentation in the recombination model • Applications to Au+Au collisions • NCQ scaling of flow v2 • Violation of the scaling • Particle species dependence of Cronin effect • Discussions

3. time Hot and Dense Cooling down freezing out Initial conditions and interactions

4. QGP formation signals • Strangeness enhancement • Suppression of J/Ψ • Dilepton enhancement • Direct photon • … Parton degree of QGP? QGP signal from the bulk? Experimental probes: 1) Penetrating probes:“jets” energy loss 2) Bulk probes :Elliptic flow, radial flow …

5. Evidence for the formation of QGP Dihadron Single hadron Jet quenching Energy loss ofjets in medium No suppression for p spectrum

6. HOW? Hadron production mechanisms • Partons are produced in high energy collisions like e++e-, e+p, p+p, p+A,A+A • Partons in the final stage of evolution are converted into hadrons

7. Traditional models • String formation and break for low p T • Fragmentation for high p T The string model may not be applicable to heavy ion collisions Fragmentation failed for central Au+Au collisions

8. Anomalies at intermediate pT • B/M • v2(pT) • Jet structure • Cronin effect p/≈1 v2(baryons) > v2(mesons) not the same as in pp • RCPp > RCP Hard to be understood in traditional models

9. Hadronization by recombination • The colliding system generates quarks and gluons in the phase space • The quarks get dressed • The dressed quarks recombine into hadrons to the detector

10. Why Recombination? meson momentum p p q p1+p2 Parton distribution (log scale) (recombine) (fragment) higher yield heavy penalty

11. Features • quark momenta add, higher yield for high produced pT hadrons • soft parton density depends on medium • more quarks for baryons than for mesons • enhanced dependence on centrality for baryons when thermal partons are involved

12. No anomalies in recombination • At intermediate pT, aplenty soft quarks are more important for proton production than for pionsp/1 • For baryons, three quarks contribute to the flow, while only two quarks for mesons  v2(baryons) > v2(mesons), quark number scaling • Soft and semi-soft recombination  Cronin effect • Process dependence of soft partons different jet structure in dA and AA

13. Recombination models • Use just the lowest Fock state i.e. valence quarks • qqqB q qbarM • Gluons converted to quarks first • The probability for two (three) quarks to form a meson (baryon) is given by a process independent recombination function R

14. Different implementations • Duke group etc: • 6-dimensional phase space • using Wigner function from density matrix • Oregon group: • one-dimensional momentum space • using phenomenological recombination function

15. Duke approach • Low pT recombination • high pT fragmentation

16. Texas/Ohio approach Texas A&M/Budapest (Ko, Greco, Levai, Chen) • Monte Carlo implementation (with spatial overlap) • Soft and hard partons • Soft-hard coalescence allowed Ohio State (Lin, Molnar) • ReCo as a solution to the opacity puzzle

17. Basic formulas in Oregon approach

18. Recombination functions Given by the valon distribution of the hadrons

19. Determining R • R p was determined from CTEQ • From the parton distributions in proton • a=b=1.755, c=1.05 at Q2=1GeV2 • R  was determined from Drell-Yan processes • a=b=0 • See Phys. Rev. C 66, 025204

20. Fragmentation? Recombination? Answer:NO FRAGMENTATION only RECOMBINATION • Fragmentation is not a description of the hadronization process. It uses phenomenological functions D(z) that give the probability of momentum fraction z of a hadron in a parton jet

21. Fragmentation D(z) q A A

22. fragmentation h q recombination Initiating parton (hard) Parton shower (semi-hard) Parton shower

23. Recombination for fragmentation Recombination function known in the recombination model Fragmentation function known from fitting e+e- annihilation data S  V  G  S K G K Hwa, Phys. Rev. D (1980). Shower parton distributions K, L, G, Ls, Gs BKK KKP etc

24. Fitted results

25. Shower parton distributions

26. Application to Au+Au collisions • Thermalized low pT (soft) partons • Hard partons (semi-hard) shower partons • Three types of recombination for mesons • thermal parton & thermal parton • thermal parton & shower parton • shower parton & shower parton • Joint parton distribution is not factorizable

27. Parton sources Thermal parton distribution is assumed Hard parton distributions fi(k) can be calculated from • pQCD • nuclear shadowing • nuclear geometry

28. Parton sources Single shower parton distribution is Joint two (three) shower parton distribution can also be written down

29.  Spectrum (0-10%)

30. Nuclear modification RAA

31. p spectrum

32. p/

33. Centrality dependence

34. New physics • Thermal-thermal recombination makes p/ increase from very small value to about 1 at pT3GeV/c • Thermal-shower recombination plays an important role • This recombination can be equivalently regarded as modification of the fragmentation functions

35. NCQ scaling • AMPT model results: • Scaling in v2: partonic dof dominant; • No scaling in v2 : hadronic dof dominant • => • A tool to search for the possible phase boundary! • The beam energy • dependence of the partonic cross sections will not affect the v2 scaling argument. • => • Important for Beam Energy Scan program.

36. NCQ scaling violation

37. Why NCQ scaling ? Assumptions: F(p1,p2)=F(p1)F(p2) collinear φdependence joint distribution Validity of the assumptions?

38. Why NCQ scaling violates? • Because of quark interactions, joint distributions are not products of quark distributions • Recombined quarks not necessarily have the same momentum • Fluctuations: large n=1,3 terms appears in quarks distributions. They contribute to v2 • NCQ at RHIC may be coincident

39. Application to d+Au collisions • Basic formulas the same as for Au+Au collisions • Soft parton distribution the same form, T not temperature but inverse slope • No jet quenching • Nuclear shadowing a little different from that in Au+Au case

40. Pion spectrum

41. Centrality dependence

42. Cronin effect Enhancement of hadron spectrum in pA collisions at high pT Traditional explanation: initial interactions Many soft collisions before the last hard one, each gives a kT kick

43. Cronin effect Shadowing effect is cancelled partially

44. Puzzles • If Cronin effect is really due to initial interactions, dilepton spectrum should show similar effect. • Experimentally, the effect for dilepton is very small, no definite conclusion • Species dependence of the Cronin effect

45. From recombination Medium density depends on centrality Medium effects are different in mesonand baryon production

46. Proton spectrum T different for different centralities

47. RCP for proton

48. RCP for p & 

49. Discussions • QGP signal can be found from the bulk • Hadronization of partons can be described by ReCo for d+Au and Au+Au collisions • ReCo naturally explains species dependence, such as baryon enhancement, v2 scaling... • Cronin effect can be interpreted as from final state interactions

50. Discussions • Combination with other models, such as hydrodynamics etc, is needed and under development • Recombination formulism from pQCD How to calculate the joint distributions?