1. Future Measurements to Test Recombination Rudolph C. Hwa University of Oregon Workshop on Future Prospects in QCD at High Energy BNL, July 20, 2006

2. 2 Outline Introduction Recombination model Shower partons Hadron production at low p T Hadron production at large  Hadron production at large p T Summary 1 xFxF pTpT

3. 3 I. Introduction What are the properties of recombination that we want to know and test? What partons? probability of finding partons at probability for recombination to form a pion at p Same partons? What is that probability?

4. 4 Usual strong evidences for recombination number of constituent quarks scaling partons CQ What about gluons? of order 1 or higher impossible by fragmentation Useful to remember in future measurements

5. 5 Two-particle correlation Where are the partons from? Are they independent? Are they from 1 jet, 2 jets, or thermal medium? Quantitative questions about recombination eventually always become questions about the nature of partons that are to recombine.

6. 6 Multiparton distributions in terms of the thermal and shower parton distributions

7. 7 II. Recombination Model Recombination depends on the wave function of the hadron. Constituent quark model describes the bound-state problem of a static hadron. What good is it to help us to know about the distribution of partons in a hadron (proton)? Valons Valons are to the scattering problem what CQs are to the bound-state problem.

8. 8 Deep inelastic scattering e e p FqFq We need a model to relate to the wave function of the proton FqFq Valon model p U U D valons Hwa, PRD 22, 759 (1981)

9. 9 p U U D Basic assumptions valon distribution is independent of probe parton distribution in a valon is independent of the host hadron valence quark distr in proton valon distr in proton, independent of Q valance quark distribution in valon, whether in proton or in pion

10. 10 Hwa & CB Yang, PRC66(2002) using CTEQ4LQ

11. 11 Recombination function It is the time-reversed process of the valon distributions U U D proton pion From  initiated Drell-Yan process valon model U U D recombination function valon distribution

12. 12 In a pp or AA collision process U D _ ++ Is entropy reduced in recombination? The number of degrees of freedom seems to be reduced. Soft gluon radiation --- color mutation without significant change in momentum The number of degrees of freedom is not reduced.

13. 13 How do gluons hadronize? In a proton the parton distributions are Gluons carry ~1/2 momentum of proton but cannot hadronize directly. Sea quark dist. F q ~ c (1-x) 7 Saturated sea quark dist. F’ q ~ c’ (1-x) 7 Gluon conversion to q-qbar Recombination of with saturated sea gives pion distribution in agreement with data. x 2 u(x) x 2 g(x) x [log]

14. 14 III. Shower Partons from Fragmentation Functions The black box of fragmentation  q A QCD process from quark to pion, not calculable in pQCD z 1 Momentum fraction z < 1

15. 15 Description of fragmentation by recombination known from data (e+e-,  p, … ) can be determined hard parton meson fragmentation shower partons recombination

16. 16 Meson fragmentation function Baryon fragmentation function S(x i ) and can be calculated in the RM

17. 17 Has never been done before in the 30 years of studying FF. This is done in the RM with gluon conversion shower partons  valons  hadrons. Hwa & CB Yang, PRC 73, 064904 (2006)

18. 18 IV. Hadron production at low pT. pp x H(x) First studied in pp collision. Parton distributions at low Q 2 Hwa, PRD (1980)

19. 19 Hadronic collisions Hwa & CB Yang, PRC 66, 025205 (2002) h + p  h’ +X h h’ p   K+   + K  + _ Suggested future measurement Better data at higher energy for p   , K , p, Y FNAL P L =100 GeV/c (1982)

20. 20 Leading and non-leading D production Leading (same valence quark)non-leading (sea quark) Asymmetry Hwa, PRD 51, 85 (1995) Suggested future measurement:

21. 21 pA collisions h bears the effect of momentum degradation --- “baryon stopping”. NA49 has good data, but never published. (no target fragmentation, only projectile fragmentation) Hwa & CB Yang, PRC 65, 034905 (2002) Shape depends on degradation. Normalization not adjustable. Suggested future measurement: Measure Need to know well the momentum degradation effect. for all x at higher energy

22. 22 Transfragmentation Region (TFR) Theoretically, can hadrons be produced at x F > 1? It seems to violate momentum conservation, p L > √s/2. In pB collision the partons that recombine must satisfy p B But in AB collision the partons can come from different nucleons BA (TFR) In the recombination model the produced p and  can have smooth distributions across the x F = 1 boundary.

23. 23 proton-to-pion ratio is very large. proton pion Hwa & Yang, PRC 73,044913 (2006)  : momentum degradation factor Regeneration of soft parton has not been considered. Suggested future measurement Determine the x F distribution in the TFR Particles at x F >1 can be produced only by recombination.

24. 24 V. Large  BRAHMS data show that in d+Au collisions there is suppression at larger . BRAHMS, PRL 93, 242303 (2004) Hwa, Yang, Fries, PRC 71, 024902 (2005). No change in physics from  =0 to 3.2 In the RM the soft parton density decreases, as  is increased (faster for more central coll). Suggested future measurement for  and p

25. 25 BRAHMS, nucl-ex/0602018 AuAu collisions

26. 26 TT TS TTT x F = 0.9 x F = 0.8 TFR x F = 1.0 ?

27. 27 No jet => no associated particles p T distribution fitted well by recombination of thermal partons Suggested future measurement Focus on x F >1 region. Determine p/  ratio. Look for associated particles Hwa & Yang (2006)

28. 28 VI. Hadron production at large p T, small p L A. Cronin Effect Cronin et al, Phys.Rev.D (1975) for h= both  and p This is an exp’tal phenomenon. Not synonymous to initial-state k T broadening. In the RM we have shown that final-state recombination alone (without initial-state broadening) is enough to account for CE. We obtained it for both  and p -- impossible by fragmentation. Hwa & Yang, PRL 93, 082302 (2004); PRC 70, 037901 (2004). Suggested future measurement Measure and ratios in d+Au collisions at all , both backward and forward.

29. 29 Backward-forward Asymmetry If hadrons at high p T are due to initial transverse broadening of parton, then backward has no broadening forward has more transverse broadening RM has B/F>1, since dN/d  of soft partons decrease as  increases. Suggested future measurement Measure p and  separately at larger range of , and for different centralities. Expects more forward particles at high p T than backward particles

30. 30 is larger than Au d associated yield in this case x=0.7 x=0.05 Correlation shapes are the same, yields differ by x2. Au d x=0.05x=0.7 associated yield in that case Degrading of the d valence q? STAR (F.Wang, Hard Probes 06) Soft partons -- less in forward, more in backward RM => less particles produced forward, more backward

31. 31 B. p/  Ratio All in recombination/ coalescence model Success of the recombination model Measure the ratio to higher p T If it disagrees with prediction, it is not a breakdown of the RM. On the contrary the RM can be used to learn about the distributions of partons that recombine.

32. 32 C. Strange particles 642 Hwa & CB Yang, nucl-th/0602024 Data from STAR nucl-ex/0601042 This is not a breakdown of the RM. We have not taken into account the different hyperon channels in competition for the s quark in the shower. 40% lower 30% higher

33. 33  production 130 GeV  production small more suppressed

34. 34 We need to do more work to understand the upbending of . It is significant to note that thermal partons can account for the ratio up to pT=4 GeV/c. QGP: s quarks enhanced & are thermalized. We have assumed RFs for  &  that may have to be modified.

35. 35 If  and  are produced mainly by the recombination of thermal s quarks, then no jets are involved. Select events with  or  in the 3<p T <5 region, and treat them as trigger particles. Look for associated particles in the 1<p T <3 region. Predict: no associated particles giving rise to peaks in , near-side or away-side. Suggested future measurement Verify or falsify that prediction

36. 36 2. Correlation of pions in jets Two-particle distribution k q3q3 q1q1 q4q4 q2q2 This can be measured. Hwa & Tan, PRC 72, 024908 (2005) D. Jet Correlations 1. Correlation of partons in jets is negative but not directly measurable

37. 37 3. D(z T ) Trigger-normalized fragmentation function Trigger-normalized momentum fraction X.-N. Wang, Phys. Lett. B 595, 165 (2004) J. Adams et al., nucl-ex/0604018 STAR claims universal behavior in D(z T ) fragmentation Focus on this region violation of universal behavior due to medium effect ---- thermal- shower recombination

38. 38 Suggested future measurement Study z T ~ 0.5 with p T (trigger) ~ 8-10 GeV/c p T (assoc) ~ 4-5 GeV/c Measure p/  ratio of associated particles. My guess: R(p/  ) >> 0.1 if so, it can only be explained by recombination. Do this for both near and away sides.

39. 39 4. Three-particle correlation Conical Flow vs Deflected Jets Medium away near deflected jets away near Medium mach cone Medium away near di-jets 0 0 π π Ulery’s talk at Hard Probes 06

40. 40 Signal Strengths Au+Au Central 0-12% Triggered Δ1Δ1 Δ2Δ2 d+Au Δ1Δ1 Δ2Δ2 Evaluate signals by calculating average signals in the boxes. Near Side, Away Side, Cone, and Deflected.

41. 41 What is the multiplicity distribution (above background) on the away side? If n=2 is much lower than n=1 events (on away side), then the Mach-cone type of events is not the dominant feature on the away side. What is the p/  ratio (above background) on the away side? Evolution with higher trigger momentum should settle the question whether cone events are realistic. Whatever the mechanism is, hadronization would be by recombination for p T <6 GeV/c. More studies are needed.

42. 42 5. Using Factorial Moments to suppress statistical background event by event. Factorial moment for 1 event Normalized factorial moment Event averaged NFM (a) background only (b) bg + 1jet (c) bg + 2jets Try it out, but it is not a way to test recombination. Chiu & Hwa, nucl-th/0605054

43. 43 VII. Two-jet Recombination  and p production at high p T at LHC New feature at LHC: density of hard partons is high. High p T jets may be so dense that neighboring jet cones may overlap. If so, then the shower partons in two nearby jets may recombine. 2 hard partons 1 shower parton from each  p

44. 44 Proton-to-pion ratio at LHC  -- probability of overlap of 2 jet cones Hwa & Yang, PRL (to appear), nucl- th/0603053 single jet If  (p T )~p T -7, then we get

45. 45 The particle detected has some associated partners. There should be no observable jet structure distinguishable from the background. GeV/c That is very different from a super-high p T jet. But they are part of the background of an ocean of hadrons from other jets. A jet at 30-40 GeV/c would have lots of observable associated particles.

46. 46 We predict for 10<p T <20 Gev/c at LHC Large p/  ratio NO associated particles above the background Suggested future measurement Verify or falsify these two predictions

47. 47 Summary In general, all hadrons produced with p T <6 GeV/c are by recombination. Specifically, many measurements have been suggested. Good signatures: large R p/  in some regions no particles associated with high p T trigger. After recombination is firmly established, the hadron spectra can be used to probe the distributions of partons that recombine.

48. 48 Backup slides

49. 49 Let’s look inside the black box of fragmentation.  q fragmentation z 1 gluon radiation quark pair creation

50. 50 Shower parton distributions u g s s d duvalence sea L L  D  Sea K NS L  D  V G G  D  G L L s  D K Sea G G s  D K G RR RKRK 5 SPDs are determined from 5 FFs. assume factorizable, but constrained kinematically. No gluon column

51. 51 Shower Parton Distributions Hwa & CB Yang, PRC 70, 024904 (04)

52. 52 D. Jet Correlations 1. Correlation of partons in jets a. Two shower partons in a jet in vacuum Fixed hard parton momentum k (as in e+e- annihilation) k x1x1 x2x2  0 The two shower partons are correlated. no correlation Hwa & Tan, PRC 72, 024908 (2005) No way to measure this directly.

53. 53 b. Two shower partons in a jet in HIC Hard parton momentum k is not fixed.  f i (k)  f i (k) is small for 0-10%, smaller for 80-92% Also, cannot be measured directly.