Hadronization of Partons by Recombination

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Hadronization of Partons by Recombination

• Rudolph C. Hwa
• University of Oregon

Summer School on RHIC Physics Wuhan, China, June
2005
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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
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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.
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Valon model -- to get the proton wave function
Hwa, PRD (1980a)
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pA collisions Hwa CB Yang (2002a)
We studied the centrality dependence (or the
number of collisions) in the valon-recombination
model
good data from NA49
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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
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Closer examination of the recombination formulas
Pion
Proton
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More questions

• What about the gluons?
• Does entropy decrease?
• What about the spatial considerations?
• Isnt the pion a Goldstone boson?
• Recombination versus fragmentation
• Which is more important?
• 8. What is wrong with string fragmentation?

Answer in reverse order.
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8. String fragmentation

• String model may be relevant for pp collisions,
  

• String/fragmentation has no phenomenological
  support in heavy-ion collisions.

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High pT physics in pp collisions is well
understood.
What was a discovery yesterday is now used for
calibration today.
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7. Recombination versus Fragmentation
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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.
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5. Spatial considerations
We have formulated recombination in momentum
space only so far.
Shouldnt the spatial coordinates be important
also? Isnt hadron size relevant?
In heavy-ion collisions there are two sizes
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Groups at Duke University and Texas AM
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.
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4. Entropy
Entropy a global quantity that should take into
account expanding volume.
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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. Fq c (1-x)7
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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?
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Deep inelastic scattering
e
e
p
Fq
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• Basic assumptions
• valon distribution is independent of probe
• parton distribution in a valon is independent of
  the hadron

U
p
U
D
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3-valon exclusive distribution
Recombination function
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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.
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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.
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p/? ratio
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(No Transcript)
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The black box of fragmentation
q
p
1
z
A QCD process from quark to pion, not calculable
in pQCD
Momentum fraction z lt 1
Dp/q
Phenomenological fragmentation function
z
1
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Lets 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.
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Description of fragmentation by recombination
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Shower parton distributions
assume factorizable, but constrained
kinematically.
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Shower Parton Distributions
Hwa CB Yang, PRC 70, 024904 (04)
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BKK fragmentation functions
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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.
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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.
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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.
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Pion formation
distribution
thermal
shower
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Thermal distribution
Contains hydrodynamical properties, not included
in our model.
Fit low-pT data to determine C T.
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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 iu, d, s, u, d, g
K2.5
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Thermal distribution
Contains hydrodynamical properties, not included
in our model.
Fit low-pT data to determine C T.
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thermal
Pion distribution (log scale)
fragmentation
Transverse momentum
Now, we go to REAL DATA, and real theoretical
results.
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? production in AuAu central collision at 200 GeV
Hwa CB Yang, PRC70, 024905 (2004)
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Proton production in AuAu collisions
TTSTSS
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Proton/pion ratio
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Compilation of Rp/? obtained by 3 groups
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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
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RHIC data from dAu collisions at 200 GeV per NN
pair
Ratio of central to peripheral collisions RCP
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STAR
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dAu collisions (to study the Cronin Effect)
peripheral
central
d
d
more ?T ? more TS
less ?T ? less TS
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dAu collisions
Pions
Hwa CB Yang, PRL 93, 082302 (2004)
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Proton
Hwa Yang, PRC 70, 037901 (2004)
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Nuclear Modification Factor
This is the most important result that validates
parton recombination.
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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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Forward-backward asymmetry in dAu collisions
If initial transverse broadening of parton gives
hadrons at high pT, then
Expects more forward particles at high pT than
backward particles
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Backward-forward asymmetry at intermediate pT
in dAu collisions
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Forward-backward asymmetry by recombination
Less soft partons in forward (d) direction than
backward (Au) direction.
Less TS recombination in forward than in backward
direction.
It is natural for parton recombination to result
in forward-backward asymmetry
More interesting behavior found in large pT and
large pL region.
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Forward production in dAu collisions
BRAHMS data
Hwa, Yang, Fries, PRC 71, 024902 (2005)
Underlying physics for hadron production is not
changed from backward to forward rapidity.
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Summary

• We have discussed
• some basic issues about recombination
• application to intermediate and high pT
  physics in heavy-ion collisions
• resolved several puzzles on single-particle
  distributions in HIC

We have not covered Correlation of hadrons in
jets (Thursday)