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)

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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

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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:

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Application to single-particle spectra

2

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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

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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