Future Measurements to Test Recombination

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 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?
What partons?
Same partons? What is that probability?
4
Usual strong evidences for recombination
Useful to remember in future measurements
5
Quantitative questions about recombination
eventually always become questions about the
nature of partons that are to recombine.
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)?
8
Deep inelastic scattering
e
e
p
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
10
Hwa CB Yang, PRC66(2002) using CTEQ4LQ
11
U
U
D
valon distribution
12
In a pp or AA collision process
U
?
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.
x log
Sea quark dist. Fq c (1-x)7
Saturated sea quark dist. Fq c (1-x)7
14
III. Shower Partons from Fragmentation
Functions
15
Description of fragmentation by recombination
hard parton
meson
16
Meson fragmentation function
S(xi)
Baryon fragmentation function
17
Hwa CB Yang, PRC 73, 064904 (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.
.
19
Hadronic collisions Hwa CB Yang, PRC 66,
025205 (2002)
h p ? h X
20
Leading and non-leading D production
21
pA collisions
h bears the effect of momentum degradation ---
baryon stopping.
22
Transfragmentation Region (TFR)
Theoretically, can hadrons be produced at xF 1?
(TFR)
It seems to violate momentum conservation, pL
vs/2.
In the recombination model the produced p and ?
can have smooth distributions across the xF 1
boundary.
23

• momentum degradation factor

proton-to-pion ratio is very large.
Regeneration of soft parton has not been
considered.
Particles at xF1 can be produced only by
recombination.
Hwa Yang, PRC 73,044913 (2006)
24
V. Large ?
25
AuAu collisions
BRAHMS, nucl-ex/0602018
26
(No Transcript)
27
pT distribution fitted well by recombination of
thermal partons
No jet no associated particles
28
VI. Hadron production at large pT, small pL
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).
29
Backward-forward Asymmetry
Expects more forward particles at high pT than
backward particles
RM has B/F1, since dN/d? of soft partons
decrease as ? increases.
30
STAR (F.Wang, Hard Probes 06)
31
B. p/? Ratio
Success of the recombination model
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
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
(No Transcript)
34
We have assumed RFs for ? ? that may have to be
modified.
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 3and treat them as trigger particles. Look for
associated particles in the 1 36
D. Jet Correlations
37
Trigger-normalized fragmentation function
3. D(zT)
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
4. Three-particle correlation
Ulerys talk at Hard Probes 06
40
Signal Strengths
??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 n2 is much lower than n1 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

42
5. Using Factorial Moments to suppress
statistical background event by event.
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.
44
Proton-to-pion ratio at LHC
? -- probability of overlap of 2 jet cones
Hwa Yang, PRL (to appear), nucl-th/0603053
45
The particle detected has some associated
partners.
There should be no observable jet structure
distinguishable from the background.
46
We predict for 10

Large p/? ratio

• NO associated particles above the background

47
Summary
In general, all hadrons produced with pTare 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.
48
Backup slides
49
Lets look inside the black box of fragmentation.
q
p
1
z
fragmentation
gluon radiation
quark pair creation
50
Shower parton distributions
assume factorizable, but constrained
kinematically.
No gluon column
51
Shower Parton Distributions
Hwa CB Yang, PRC 70, 024904 (04)
52
D. Jet Correlations
1. Correlation of partons in jets
53
b. Two shower partons in a jet in HIC
Hard parton momentum k is not fixed.