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. Outline Introduction Recombination model Shower partons1 xF pT
Introduction
Recombination model
Shower partons
Hadron production at low pT
Hadron production at large 
Hadron production at large pT
Summary

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

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

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

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

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

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

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

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

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

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

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

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

17. Has never been done before in the 30 years of studying FF.
Hwa & CB Yang, PRC 73, (2006)
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.

18. IV. Hadron production at low pT
First studied in pp collision.
Parton distributions at low Q2 p x
H(x)
Hwa, PRD (1980) .

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

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

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

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

24. BRAHMS data show that in d+Au collisions there is suppression at larger .
BRAHMS, PRL 93, (2004)
V. Large 
Hwa, Yang, Fries, PRC 71, (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. AuAu collisions
BRAHMS, nucl-ex/

26. xF = 0.9
xF = 1.0
xF = 0.8
TFR ? TT TS
TTT

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

28. VI. Hadron production at large pT, small pL
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 kT 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, (2004); PRC 70, (2004).
Suggested future measurement
Measure and ratios in d+Au collisions at all , both backward and forward.

29. Backward-forward Asymmetry
If hadrons at high pT are due to initial transverse broadening of parton, then
backward has no broadening
forward has more transverse broadening
Expects more forward particles at high pT than backward particles
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.

30. STAR (F.Wang, Hard Probes 06)
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.
associated yield in that case
Degrading of the d valence q?
Soft partons -- less in forward, more in backward
RM => less particles produced forward, more backward

31. B. p/ Ratio Success of the recombination model
All in recombination/ coalescence model
Measure the ratio to higher pT
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. C. Strange particles 6 4 2
Hwa & CB Yang, nucl-th/
Data from STAR nucl-ex/
40% lower
30% higher
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.

33.  production
130 GeV
 production
small
more suppressed

34. We need to do more work to understand the upbending of .
We have assumed RFs for  &  that may have to be modified.
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.

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<pT<5 region, and treat them as trigger particles. Look for associated particles in the 1<pT<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. D. Jet Correlations 1. Correlation of partons in jets is negative
but not directly measurable
D. Jet Correlations
2. Correlation of pions in jets
Two-particle distribution k q3 q1 q4 q2
Hwa & Tan, PRC 72, (2005)
This can be measured.

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

38. Suggested future measurement
Study zT ~ 0.5 with pT(trigger) ~ 8-10 GeV/c pT(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. Conical Flow vs Deflected Jets
4. Three-particle correlation
Conical Flow vs Deflected Jets
Medium
away
near
deflected jets
mach cone
di-jets π
Ulery’s talk at Hard Probes 06

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

41. More studies are needed.
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 pT<6 GeV/c.

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

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

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

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

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

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