Dihadron correlations and parton intrinsic transverse momentum

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Di-hadron correlations and parton intrinsic
transverse momentum?
RHIC has moved beyond initial phase

• George Fai, Gábor Papp, Péter Lévai
• ELTE / Kent State University / CRIP

? Supported in part by U.S. DOE
DE-FG02-86ER-40251, NSF INT-0435701,
Szent-Györgyi scholarship 34/2004
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Outline

• Di-hadron correlations and back-to-back jets
• Di-jet correlations in proton-proton collisions
• 3. Jet-jet correlation scenarios
• 2? 2 kinematics
• 2? 3 kinematics
• partial correlation by randomization
• 4. Degree of randomization
• 5. Comparison to data
• 6. Application to single-particle spectra
• 7. Conclusion

transverse structure of the proton
alternative kT factorization formalism
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Why di-hadron (and photon-hadron) correlations?
Statistical tool to study jets (probably the only
way in 200 GeV Au Au collisions)
test of pQCD
modified by the medium, i.e. info on the medium
(single and di) jet tomography
Examples
gluon density (Baier, Dokshitzer, Gyulassy,
Lévai, Wang, Vitev, ) collective dynamics
(Armesto, Salgado, Wiedemann, ) sound speed
(Casalderrey, Shuryak, Stöcker, Teaney, )
J. Adams et al. (STAR), Phys. Rev. Lett. 91
(2003) 072304
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Jet basics
Rcone0.7 rad
Transverse energy deposition in two variables
fragmentation
parton
hard process
pQCD
parton
hadrons
Focus on azimuthal angle correlations
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In ??, ?? variables
pp 200 GeV Near side
4 lt pT(trig) lt 6 GeV
3 lt pT(trig) lt 4 GeV
6 lt pT(trig) lt 12 GeV
?? lt 0.7
STAR preliminary
?? lt 0.7
2 lt pT(assoc) lt pT(trig)

• D. Magestro, Hard Probes 2004

2 lt pT(assoc) lt pT(trig)
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Jets in various collisions
F. Wang, RBRC Workshop, March 10, 2005
We can do it but with some care
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Jets in various collisions
Au Au collisions substantially more
complicated new results focus on p p
(pbar) collisions for this talk (but see
following 4 presentations and tomorrows plenary
session)
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Di-hadron correlations in pp at 200 GeV
STAR p-p jet event
Analyze jets by measuring Df between high-pT
hadrons
dN/dDf
0º
180º
Df
B. Cole, RHIC AGS Users Meeting, June 20, 2005
Rich content already in p p collisions
widths of the
near and away side peaks
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Charged particle density at the Tevatron
ppbar 2 TeV
R. Field, ISMD04

• Df dependence of the charged particle
  density, dNchg/dhdf, for pT gt 0.5 GeV/c and h lt
  1 relative to jet1 (rotated to 270o) for
  leading jet events 30 lt ET(jet1) lt 70 GeV.

dNchg/dhdf, for charged particles in the
range pT gt 0.5 GeV/c and h lt 1 for min-bias
collisions.
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What can we learn from di-hadron correlations in
pp collisions?

• Experimental difficulty
• extract parton-level information

Goals 1. separate initial and final-state
effects 2. understand fragmentation process 3.
connect initial state information to intrinsic
transverse momentum of partons in the proton
History summarized in M.J. Tannenbaum,
nucl-ex/0507020 R.P. Feynman, R.D.
Field, and G.C. Fox, Nucl. Phys. B 128 (1977) 1
A.L.S. Angelis et al. (CCOR), Phys.
Lett. B 97 (1980) 163
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What can we learn from di-hadron correlations in
pp collisions?

• Near side
• fragmentation process
• (e.g. di-hadron fragmentation functions)

identified hadrons
Unidentified
(e.g. baseline for baryon-meson puzzle)

Away side transverse structure of the
proton (e.g. transverse momentum
distribution)
in addition to fragmentation
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What can we learn from di-hadron correlations in
pp collisions?
final state

• Near side
• fragmentation process
• (e.g. di-hadron fragmentation functions)

identified hadrons
Unidentified
(e.g. baseline for baryon-meson puzzle)

Away side transverse structure of the
proton (e.g. transverse momentum
distribution)
initial state
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What can we learn from di-hadron correlations in
pp collisions?

• Near side
• fragmentation process
• (e.g. di-hadron fragmentation functions)

identified hadrons
Unidentified
(e.g. baseline for baryon-meson puzzle)

Away side transverse structure of the
proton (e.g. transverse momentum
distribution)
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Intrinsic vs. radiation contribution toparton
transverse momentum
hypothetical data

final-state radiation

intrinsic (effectively including
initial-state soft gluon radiation)
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Intrinsic vs. radiation contribution toparton
transverse momentum
D. Boer and W. Vogelsang, Phys. Rev. D69 (2004)
094025
STAR
pp
J. Qiu and I. Vitev, Phys. Lett. B570 (2003) 161
radiative tails
J. Jia, APS/DNP Meeting, Oct 30, 2004
B. Cole, Users Meeting, June 20, 2005
pp
PHENIX preliminary
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Starting point transverse momentum conservation

for a 2 ? 2 partonic process
Gaussian for magnitude of kT
Calculate
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2? 3 kinematics
S²
if pT3 uniform in 0,pTmax , then
S² pTmax ²/6
if pT3 uniform in 0,KT , then
S² 2(2sk ²)pTmax ²/6
depends on width of transverse mom distrib.
Economical partially correlated (randomized) 2?
2 scenario
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Jet-jet correlation scenarios

Strongly correlated
Partially correlated
2 ? 2
due to scattering, gluon radiation, or any
combination of collisions and 2? n processes
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Calculational details
Gaussian for magnitude of kT
Evaluate
Notation
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Degree of randomization
a 4lt (pT2 sin?F)² gt - 2sk² / pT1² ß 4lt
(pT2 cos?F)² gt - 2sk² / pT1²
uniform in F2 dF, F2 dF
Randomization prescriptions
Gauss
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Partially correlated case
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Partially correlated case
Fit parameters
Use to describe single-particle spectra at RHIC !
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To extract width from hadron correlations
Need to take fragmentation into account
Near side
Away side
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To extract width from hadron correlations
Approximations

More elaborate approximations available in e.g.

• J. Rak et al. (PHENIX) J. Phys. G 30 (2004)
  S1309
• J. Jia, J. Phys. G 31 (2005) S521
• J. Qiu and I. Vitev, Phys. Lett. B 570 (2003) 161

An example
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To extract width from hadron correlations
Need to take fragmentation into account
Procedure
1. Fix trigger transverse momentum
2. Measure near and away-side widths at given pT
3. Estimate average fragmentation momentum
fraction
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Application to single-particle spectra
2
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Application to single-particle spectra
In the standard collinear factorization
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Nuclear effects

• Shadowing
• Isospin
• Broadening

Shadowing function
ltkT2gtpA ltkT2gtpp C hpA (b)
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Reproduces Cronin effect at midrapidity
At ISR and FNAL energies
At RHIC energies
nucl-th/0306019
Phys. Rev. C65 (2002) 034903
G.G. Barnaföldi, Monday afternoon
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At forward rapidities
G.G. Barnaföldi
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Conclusions

• Di-hadron correlations in proton-proton
  collisions can be described in
• terms of partial randomization
• Degree of randomization extract width
  of intrinsic transverse mom.
• distribution of partons in the proton
• Width can be used as a basis to reproduce
  single-particle spectra
• in proton-proton, proton-nucleus, and
  nucleus-nucleus collisions
• background for jet-quenching studies
• Variation with trigger momentum between pp and
  dAu can provide an
• alternative way to separate initial and
  final-state effects
• Jet quenching observed directly in disappearance
  of away-side peak
• in central AuAu
• FOLLOWING TALKS

pTtrig ? 0
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Backups
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kT at RHIC from pp data
Statistical Errors Only
di-hadron
B. Jacak, Hard Probes 2004
J. Rak, Wed.
J. Rak, DNP03
PHENIX preliminary
Df
near-side
away-side
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Mass number dependence
EVIDENCE FOR MULTIPLE SCATTERING OF HIGH-ENERGY
PARTONS IN NUCLEI. By E609 collaboration (M.D.
Corcoran et al.) Phys.Lett.B259209-215,1991
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CCOR ztrig measurement
Angelis et al (CCOR) Nucl.Phys. B209 (1982)
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Fragmentation Function (distribution of parton
momentum among fragments)
J. Rak, Hot Quarks 2004
jet
In Principle
Fragmentation function
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xE in pp collisions
J. Rak, Hot Quarks 2004
PHENIX preliminary
1/?xE? ? -4 to 5
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?z? extracted from pp data
xTtrigg2.pTtrigg/?s
We measured xE and
parton distribution
J. Rak, Hot Quarks 2004
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Di-jet fragmentation
J. Rak, Hot Quarks 2004
Q2 gt Q2
zgtz
zltz
pTassoc
pTq
pTq
pTtrig
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J. Rak, Hot Quarks 2004