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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. - PowerPoint PPT Presentation
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Di-hadron correlations and parton intrinsic transverse
momentum٭
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
RHIC has moved beyond initial phase
Aug. 5, 2005 QM2005, Budapest 2
1. Di-hadron correlations and back-to-back jets2. Di-jet correlations in proton-proton collisions
3. Jet-jet correlation scenarios2 2 kinematics2 3 kinematicspartial correlation by randomization
4. Degree of randomization 5. Comparison to data6. Application to single-particle spectra
7. Conclusion
Outline
alternative: kT factorization formalism
transverse structure of the proton
Aug. 5, 2005 QM2005, Budapest 3
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
Pedestal&flow subtracted
J. Adams et al. (STAR), Phys. Rev. Lett. 91 (2003) 072304
(single and di) jet tomography
gluon density (Baier, Dokshitzer, Gyulassy, Lévai, Wang, Vitev, …) collective dynamics (Armesto, Salgado, Wiedemann, …)sound speed (Casalderrey, Shuryak, Stöcker, Teaney, …)
Examples:
Aug. 5, 2005 QM2005, Budapest 4
Jet basics
Rcone=0.7 rad
pQCD
fragmentation
parton
parton
Transverse energy deposition in two variables:
hadrons
hard process
Focus on azimuthal angle correlations
Aug. 5, 2005 QM2005, Budapest 6
Jets in various collisions
p + p jet + jet Au + Au stuff + jet + jet
e+ + e jet + jet
measure these… here?!
High pT particle High pT particle
F. Wang, RBRC Workshop, March 10, 2005 “We can do it but with some care…”
Aug. 5, 2005 QM2005, Budapest 7
p + p jet + jet Au + Au stuff + jet + jet
e+ + e jet + jet
Jets in various collisions
High pT particle High pT particleAu + Au collisions substantially more complicated: new results; focus on p + p (pbar) collisions for this talk (but see following 4 presentations and tomorrow’s plenary session)
Aug. 5, 2005 QM2005, Budapest 8
dN
/d
0º 180º
STAR: p-p jet event Analyze jets by measuring between high-pT hadrons
Di-hadron correlations in pp at 200 GeV
B. Cole, RHIC & AGS Users Meeting, June 20, 2005
Rich content already in p + p collisions: widths of the near and away side peaks
Aug. 5, 2005 QM2005, Budapest 9
Charged particle density at the Tevatron
dependence of the charged particle density, dNchg/dd, for pT > 0.5 GeV/c and || < 1 relative to jet#1 (rotated to 270o) for “leading jet” events 30 < ET(jet#1) < 70 GeV.
dNchg/dd, for charged particles in the range pT > 0.5 GeV/c and || < 1 for “min-bias” collisions.
Leading Jet
Charged Particle Density: dN/dd
0.1
1.0
10.0
0 30 60 90 120 150 180 210 240 270 300 330 360
(degrees)
Ch
arg
ed
Pa
rtic
le D
en
sit
y
CDF Preliminarydata uncorrected
Charged Particles (||<1.0, PT>0.5 GeV/c)
30 < ET(jet#1) < 70 GeV
"Transverse" Region
Jet#1
Jet #1 Direction
“Transverse” “Transverse”
“Toward”
“Away”
“Toward-Side” Jet
“Away-Side” Jet R. Field,
ISMD’04
p+pbar2 TeV
Aug. 5, 2005 QM2005, Budapest 10
What can we learn from di-hadron correlations in pp collisions?
Experimental difficulty:extract parton-level
informationGoals:1. separate initial and final-state effects 2. understand fragmentation process3. connect initial state information to
intrinsic transverse momentum of partons in the protonHistory:
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
Aug. 5, 2005 QM2005, Budapest 11
What can we learn from di-hadron correlations in pp collisions?
Near sidefragmentation process (e.g. di-hadron fragmentation
functions)
Away side transverse structure of the proton (e.g. transverse momentum
distribution)
Unidentified
identified hadrons(e.g. baseline for baryon-meson puzzle)
[in addition to fragmentation]
Aug. 5, 2005 QM2005, Budapest 13
What can we learn from di-hadron correlations in pp collisions?
Near sidefragmentation process (e.g. di-hadron fragmentation
functions)
Away side transverse structure of the proton (e.g. transverse momentum
distribution)
Unidentified
identified hadrons(e.g. baseline for baryon-meson puzzle)
Aug. 5, 2005 QM2005, Budapest 16
Starting point: transverse momentum conservation
for a 2 2 partonic process
Gaussian for magnitude of kT
Calculate
Aug. 5, 2005 QM2005, Budapest 18
Jet-jet correlation scenarios
Strongly correlated Partially correlated
due to scattering, gluon radiation, or any combination of collisions and 2 n processes
2 2
Aug. 5, 2005 QM2005, Budapest 20
Degree of randomization
Randomization prescriptions:
uniform in [Φ2 – δΦ, Φ2 + δΦ]
Gauss:
α = 4[< (pT2 sinΔΦ)² > - 2σk²] / pT1²β = 4[< (pT2 cosΔΦ)² > - 2σk²] / pT1²
Aug. 5, 2005 QM2005, Budapest 21
Partially correlated case
Aug. 5, 2005 QM2005, Budapest 22
Partially correlated case
Fit parameters:
Use to describe single-particle spectra at RHIC !
Aug. 5, 2005 QM2005, Budapest 23
To extract width from hadron correlations
Need to take fragmentation into account
Near side Away side
Aug. 5, 2005 QM2005, Budapest 24
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:
Aug. 5, 2005 QM2005, Budapest 25
To extract width from hadron correlations
1. Fix trigger transverse momentum
2. Measure near and away-side widths at given pT
Need to take fragmentation into account
3. Estimate average fragmentation momentum fraction
Procedure:
Aug. 5, 2005 QM2005, Budapest 26
Application to single-particle spectra
2
Aug. 5, 2005 QM2005, Budapest 28
Nuclear effects
Shadowing
Isospin
Broadening
<kT2>pA = <kT
2>pp + C hpA (b)
Shadowing function
Aug. 5, 2005 QM2005, Budapest 29
Reproduces Cronin effect at midrapidity
At ISR and FNAL energies At RHIC energies
Phys. Rev. C65 (2002) 034903 nucl-th/0306019
G.G. Barnaföldi, Monday afternoon
Aug. 5, 2005 QM2005, Budapest 31
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 Au+Au
FOLLOWING TALKS
pTtrig 0
Aug. 5, 2005 QM2005, Budapest 32
Backups
Aug. 5, 2005 QM2005, Budapest 33
kT at RHIC from p+p data
J. Rak, Wed.
J. Rak, DNP03
s=200 GeV
di-hadron
Statistical Errors Only
near-side away-side
nearfar
B. Jacak, Hard Probes 2004
Aug. 5, 2005 QM2005, Budapest 34
Mass number dependence
EVIDENCE FOR MULTIPLE SCATTERING OF HIGH-ENERGY PARTONS IN NUCLEI.By E609 collaboration (M.D. Corcoran et al.) Phys.Lett.B259:209-215,1991
Aug. 5, 2005 QM2005, Budapest 35
CCOR ztrig measurement
Angelis et al (CCOR):Nucl.Phys. B209(1982)
Aug. 5, 2005 QM2005, Budapest 36
2
| |T Ttrigg
ETtrigg
p px
p
Fragmentation Function (distribution of parton momentum among fragments)
In Principle
i | | | | cos( ) parton i parton ii i
p p p p
i| | cos( ) 1
| |i
i iiparton
pz z
p
/( ) z zD z e
jetiip
Fragmentation function
In Practice parton momenta are not known
cos( ) = z T
E triggparton
px z
p
Simple relation E triggz x z
J. Rak, Hot Quarks 2004
Aug. 5, 2005 QM2005, Budapest 37
xE in pp collisions
PHENIX preliminaryCCOR (ISR) s = 63 GeVsee A.L.S. Angelis, Nucl Phys B209 (1982)
Correct +-1/xE -5.31/xE -4 to –5
J. Rak, Hot Quarks 2004
Aug. 5, 2005 QM2005, Budapest 38
z extracted from pp data
E triggz x z 1 / 2( / )Ttrigg
z ztrigg q Txz z e f p z z dz
We measured xE and xTtrigg=2.pTtrigg/s
ztr
igg
PHENIX preliminary
Slope of the fragmentation function in p+p collisions at s=200 GeV
16.16 0.32
z
J. Rak, Hot Quarks 2004
parton distributionFFn D(z)
Aug. 5, 2005 QM2005, Budapest 39
Di-jet fragmentation
pTqpTassoc pTq
z>zz<z
Q2 > Q2
Monte carlo Monte carlo
pTtrig
J. Rak, Hot Quarks 2004