Jet properties from dihadron Correlation in PHENIX

2/3/09 1

Jet properties from dihadron Correlation Jet properties from dihadron Correlation in PHENIXin PHENIX

Jet properties from dihadron Correlation Jet properties from dihadron Correlation in PHENIXin PHENIX

DongJo KimDongJo KimNorbert Novitzky, Jiri Kral Sami Räsänen, Jan Rak

Jyväskylä University & Helsinki Institute of Physics, Finland

High pT Physics at LHC, Feb 4-7 ,2008 Prague High pT Physics at LHC, Feb 4-7 ,2008 Prague

DongJo Kim, Prague High pT 2009

Outline of the talkOutline of the talkOutline of the talkOutline of the talk

1) Motivation

a) RAA, IAA , gamma-h

b) Modification of the Fragmentation in AA

2) Two particle correlationa) Kinematics

b) What we have learned from di-hadron correlation ?

c) What we can obtain from gamma-hadron correlation ?

3) Gamma-Hadron Correlation Result in p+p ( PHENIX )– Still various Contributions to be Understood ?– Compare the data with KKP and PYTHIA

a) Soft QCD radiations/NLO

b) Quark/Gluon Fragmentation

c) -jet momentum imbalance due to the kT smearing

4) Conclusion and Open Issues 2/3/09 2DongJo Kim, Prague High pT 2009

2/3/09 3

More Exclusive observ. - modification of More Exclusive observ. - modification of D(z)D(z)More Exclusive observ. - modification of More Exclusive observ. - modification of D(z)D(z)

1( )

1 1 1

zD z D

E E E

⎛ ⎞≈ ⎜ ⎟− Δ −Δ⎝ ⎠

%

Wang, X.N., Nucl. Phys. A, 702 (1) 2002

( ) / ; ( ) / ( )D z dN dz z p fragment p jet≡ =

=ln(EJet/phadron)

pThadron~2 GeV for

Ejet=100 GeV

Borghini and Wiedemann, hep-ph/0506218

• MLLA: parton splitting+coherence angle-ordered parton cascade. Theoretically controlled, experimentally verified approach• Medium effects introduced at parton splitting

pp-data also interesting


2/3/09 4

How can one measure How can one measure D(z)D(z)How can one measure How can one measure D(z)D(z)

Assumption:

Leading particle fixes the energy scale of the trigger & assoc. jet

=>

leading particle - trigger pTt

xEzpout kT

away-side fragments - associated particles pTa

€

z = pT / ˆ p T is the jet fragmentation variable: zt and za

€

Dπq (z) = Be−bz

is a simplified Fragmentation Function, b~ 8-11 at RHIC


DELPHI, Eur. Phys. J. C13,543, (1996)

OPAL Z.Phys. C 69, 543 (1996)

associated yield dNassoc

dxE

∝dzz

Ci s;z,αs( )Dih x / z,s( )

x

1

∫i∑ ≡Dh z( )

accoplanarity (CF width) dNassoc

dpout

∝dNassoc

dΔφ∝

dσdkT

xE =rpTa ⋅

rpTtrpTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

associated yield dNassoc

dxE

∝dzz

Ci s;z,αs( )Dih x / z,s( )

x

1

∫i∑ ≡Dh z( )

accoplanarity (CF width) dNassoc

dpout

∝dNassoc

dΔφ∝

dσdkT

xE =rpTa ⋅

rpTtrpTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

€

≈−pTa

/ ˆ p Ta

pTt/ ˆ p Tt

≈ −za

< zt >

2/3/09 5

Azimuthal correlation function in Azimuthal correlation function in pp++pp @ @ s=200 GeVs=200 GeVAzimuthal correlation function in Azimuthal correlation function in pp++pp @ @ s=200 GeVs=200 GeV

d+Au

Phys.Rev.D74:072002,2006

σN

σA

σN jT jet fragmentation transverse momentum

σF kT parton transverse momentum

YA folding of D(z) and final state parton dist.

p + p jet + jet

Δ


2/3/09 6

Two-particle correlations in Two-particle correlations in pp++ppTwo-particle correlations in Two-particle correlations in pp++pp

Fragmentation function D(z) and

Intrinsic momentum kT

Fragmentation function D(z) and

Intrinsic momentum kT


.

2/3/09 7

Correl. fcn width - Correl. fcn width - kkTT and acoplanarity and acoplanarityCorrel. fcn width - Correl. fcn width - kkTT and acoplanarity and acoplanarity

€

pout = 2 kTy

pTa

ˆ p Ta

⇒ pout2 = zt kT

2 xh

ˆ x h

Lorentz boost => pT,pair || kT,t || kT,a colinearity

kT -induced jet imbalance xh xh( ) =pTa

pTt

particle pair imbalance xh =pTa

pTt

zt

xh

kT2 =

1xh

pout2 − jTy

2 (1+ xh2 )

zt

xh

kT2 =

1xh

pout2 − jTy

2 (1+ xh2 )partonic hadronic

Lab frame

Hard scattering rest frame


2/3/09 8

LEP data

yield

Trigger associated spectra are Trigger associated spectra are insensitiveinsensitive to D(z) to D(z)Trigger associated spectra are Trigger associated spectra are insensitiveinsensitive to D(z) to D(z)

bq=8.2

bg=11.4


– Quark FF

--- Gluon FF

– DELPHI, Eur. Phys. J. C13,543, (1996)

--- OPAL Z.Phys. C 69, 543 (1996)

xE =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

Phys.Rev.D74:072002,2006

2/3/09 9

Unavoidable Unavoidable zz-bias in di-hadron correlations-bias in di-hadron correlationsUnavoidable Unavoidable zz-bias in di-hadron correlations-bias in di-hadron correlations

z-bias; steeply falling/rising D(z) & PDF(1/z)

ztrig

zassoc

Varying pTassoc with pTtrigger kept fixed leads to variation of both trigger and associated jet energies.

Fixed trigger particle Fixed trigger particle momentummomentum

does notdoes not fixfix

the the jet energyjet energy!!

Angelis et al (CCOR):Nucl.Phys. B209 (1982)Angelis et al (CCOR):Nucl.Phys. B209 (1982)


ππ00-h x-h xEE distribution from PYTHIA distribution from PYTHIAππ00-h x-h xEE distribution from PYTHIA distribution from PYTHIA

2/3/09 DongJo Kim, Prague High pT 2009 10

• PHENIX shows the increasing trend of xE slopes as you go higher pTt

• PYTHIA – shows the same trend

• Even with higher xE region : PYTHIA fit : 0.2<xE<0.8

PYTHIA

2/3/09 11

kk22TT and and zztt in p+p @ 200 GeV from in p+p @ 200 GeV from 00-h CF-h CFkk22TT and and zztt in p+p @ 200 GeV from in p+p @ 200 GeV from 00-h CF-h CF

Phys.Rev.D74:072002,2006

For D(z) the LEP date were used. Main contribution to the systematic errors comes from unknown ratio gluon/quark jet

Base line measurement for the kT broadening

Still, we would like to extract FF from our own data -> direct photon-h correl.



What about LHC ?What about LHC ?What about LHC ?What about LHC ?

PHENIX measured pTpair=3.360.090.43GeV/c

extrapolation to LHC k2T ~ 6.1 GeV/c €

< pT > pair ≈ log(0.15 ⋅ s) ~ 7.7 GeV /c at s = 14TeV

€

< kT2 > =

2

π⋅< pT

2 > pair (in case 2D Gaussian)

2/3/09 13

D(z)D(z) from gamma tagged correlation from gamma tagged correlation D(z)D(z) from gamma tagged correlation from gamma tagged correlation

leading particle - trigger pTt

xEzpout kT


h-h: Leading particle does not fix Energy scale.

Direct gamma - trigger pTt

xEzpout kT


-h: direct gamma does fix Energy scale if no kT


d 2σdpTtdxE

=dpTa

dxE

⊗d2σ

dpTtdpTa

;1xh

D(zt)D(ztpTa)xhpTt

)Σ'

xTt

x.pTt/ pTa

∫ (pTt

zt

)dzt

d 2σdpTtdxE

=dpTa

dxE

⊗d2σ

dpTtdpTa

;1)pTa

Σ' pTa)pTa

⎛

⎝⎜⎞

⎠⎟D

pTa)pTa

⎛

⎝⎜⎞

⎠⎟

€

xE ≈ −pTa

/ ˆ p Ta

pTt/ ˆ p Tt

≈ −za

< zt >

D(zt) (zt)

PYTHIA

γγ-Jet events-Jet events γγ-Jet events-Jet events

dσdΔ

=( −) dσd)qT

pT=()qT −pT )

dσdΔ

=( −) dσd)qT

pT=()qT −pT )

Back-to-back balanced

Soft QCD radiationSoft QCD radiation

dσdΔ

∝Gauss(Δ ) dσd)qT

pT∝Gauss(pT )

dσdΔ

∝Gauss(Δ ) dσd)qT

pT∝Gauss(pT )

dσdΔ

∝1

Δ −n dσd)qT

pT∝

1pT

−n

dσdΔ

∝1

Δ −n dσd)qT

pT∝

1pT

−n

Hard NLO radiation not in PYTHIAHard NLO radiation not in PYTHIA

q + g→ quark( )qT ) +photon(pT )Compton photo-production

Soft + hard QCD radiation kT phenomenology

142/3/09 14DongJo Kim, Prague High pT 2009

2/3/09 15

0Direct

PHENIX PHENIX s=200 GeV s=200 GeV 00 and dir- and dir- assoc. distributions assoc. distributionsPHENIX PHENIX s=200 GeV s=200 GeV 00 and dir- and dir- assoc. distributions assoc. distributions

Run 5 p+p @ 200 GeVStatistical Subtraction MethodRun 5 p+p @ 200 GeVStatistical Subtraction Method

Arb

itrar

y N

orm

aliz

atio

n

Exponential slopes still vary with trigger pT.

If dN/dxEdN/dz then the local slope should be pT independent.


xE =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

Arb

itrar

y N

orm

aliz

atio

n

2/3/09 16

PHENIX PHENIX s=200 GeV s=200 GeV 00 and dir- and dir- assoc. distributions assoc. distributionsPHENIX PHENIX s=200 GeV s=200 GeV 00 and dir- and dir- assoc. distributions assoc. distributions

Run 5+6 p+p @ 200 GeVIsolated photonsRun 5+6 p+p @ 200 GeVIsolated photons


xE =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

Legend should be corrected, additional *1/10 is missing


PYTHIA PYTHIA -h simulations at RHIC-h simulations at RHICPYTHIA PYTHIA -h simulations at RHIC-h simulations at RHIC1) Initial State Radiation/Final State Radiation OFF,<kT>2=0

GeV/c

xE slope is constant

2) IR/FR ON, <kT>2= 3 GeV/c

xE slope is raising!

Also PYTHIA shows the same trend, though, not as large as in the data, not so trivial even with Direct photons

1)

2)

2/3/09 18

Pythia Initial/Final st. radiation & Pythia Initial/Final st. radiation & kkTTPythia Initial/Final st. radiation & Pythia Initial/Final st. radiation & kkTTIn

itia

l/Fin

a st

ate

ra

dia

tion

OF

F,

k2T=

0 G

eV

/cIn

itia

l/Fin

a st

ate

ra

dia

tion

OF

F,

k2T=

0 G

eV

/c

Initi

al/F

ina

sta

te r

ad

iatio

n O

N,

k2T=

5 G

eV

/cIn

itia

l/Fin

a st

ate

ra

dia

tion

ON

, k2

T=

5 G

eV

/c


1) Initial State Radiation/Final State Radiation OFF,<kT>2=0 GeV/c





1) Initial State Radiation/Final State Radiation OFF,<kT>2=0 GeV/c





xxEE distribution comparisons ( distribution comparisons (-h)-h)xxEE distribution comparisons ( distribution comparisons (-h)-h)


• PHENIX xE distributions and local slopes are compared with PYTHIA and KKP

o PHENIX fitting ranges are limited by statistics

o Local slopes are getting steeper as Trigger pT gets higher

o (1) pT,trigger > ~ 15 , PYTHIA were fitted with fixed range ,0.1<xE<0.3]

o (2)(2)' KKP is much steeper in low xE than PYTHIA

PYTHIA

Nucl. Phys., 2001, B597, 337-369

Parameters α, and from

PRD74 (2006) 072002

Nucl. Phys., 2001, B597, 337-369

Parameters α, and from

PRD74 (2006) 072002

quark vs gluon in KKP

(1)

(2)’

(2)

Local slopes In Various xLocal slopes In Various xEE ranges rangesLocal slopes In Various xLocal slopes In Various xEE ranges ranges


(1) 0.2<xE<0.4

(3) 0.4<xE<0.8

(2) 0.2<xE<0.8

PYTHIA

-u quark jet (Compton) 66 %

-gluon jet (Annihilation) 17 %

PYTHIA



Deviation at low pT due to the kT bias.

Unlike the di-hadron correlation it

asymptotically converges to the correct value ~exp (-6.2z ) in higher xE region

Deviation at low pT due to the kT bias.

Unlike the di-hadron correlation it

asymptotically converges to the correct value ~exp (-6.2z ) in higher xE region

Need to go higher trigger and xNeed to go higher trigger and xEENeed to go higher trigger and xNeed to go higher trigger and xEE


D(z) ~ exp(-6z)

D(z) ~ z-α(1-z)(1+z)-

Parameters α, and from PRD74 (2006) 072002

kT smearing effect

Old Method

Start from balanced b-2-b in hard scattering and boost according

Gaussian pT,pair

Results in complicated numerical integrals

See: PRD74 (2006) 072002

New Method

We start from unbalanced b-2-b in LAB and ask what boost pT,pair leads to

pT,t - pT,a configuration.

Results in much simpler formulae.

Idea: kIdea: kTT to the partonic final state to the partonic final stateIdea: kIdea: kTT to the partonic final state to the partonic final state

222/3/09 DongJo Kim, Prague High pT 2009

Lorentz invariance:

With assumption of Lorentz invariance,

the kinematics can be solved.

In partonic levelIn partonic levelIn partonic levelIn partonic level

23

4 pT

2 =Mpair2 =2( pTt pTa − ˆ

rpTt ⋅ˆ

rpTa) =2 pTt pTa(1−cos(Δφ))


dNdpTa | pTt , pT

∝ pTt + pTa

pTt + pTa+2 pT( ) pTt pTa−pT2e − pTt + pTa( )

2 −4 pT2

pTn2

⎛⎝

⎞⎠

This distribution is folded over

Number distribution of final

State hadrons, dn/dpT and

Fragmentation function D(z)

dNdpTa | pTt

= dpTa Σ ' pTa | pTt( ) 1pTa

D pTa

pTa( )

pTa

s/2

∫

Effect of kT, D(z) ~ exp(-6z):

Trigger photon’s momentum, pTt, grows


Compare Compare -hadron and hadron-hadron-hadron and hadron-hadronCompare Compare -hadron and hadron-hadron-hadron and hadron-hadron

1. -hadron associated distributions are always steeper

2. slope seems to approach fragmentation function (FF) in -hadron

3. hadron-hadron slope does not represent FF


-h -h

h-h h-h

Fitting range mattersFitting range mattersFitting range mattersFitting range matters

2/3/09 26DongJo Kim, Prague High pT 2009

(1) low zT: broad gaussian enhances low

pT particles strongly

(2) medium zT: “optimal” range

(3) large zT: shrinking phase phase

begins to affect the results

(1) (2) (3)

In data: zT (or xE) distributions become steeper when pTt

grows, while in the calculation the trend is exactly opposite!

1. Partonic level needs to be treated carefully?

2. QCD soft radiation matters in accessible range by PHENIX

• Relative yield change from low pT to higher pT

3. The ways of handling kT + something else

In data: zT (or xE) distributions become steeper when pTt

grows, while in the calculation the trend is exactly opposite!

1. Partonic level needs to be treated carefully?

2. QCD soft radiation matters in accessible range by PHENIX

• Relative yield change from low pT to higher pT

3. The ways of handling kT + something else

2/3/09 27

Summary and Open issuesSummary and Open issuesSummary and Open issuesSummary and Open issuesInclusive and two-particle correlation measurement in the high-pT sector at RHIC opened a new window into a QGP physics.

Di-hadron and direct photon-h correlations - base line measurement for nuclear modification study:

• kT and initial/final state QCD radiation, resummation vs NLO

• D(z) : fragmentation function.

• Despite our expectation, FF is not accessible in di-hadron correlations. FF can be extracted from direct photons correlation only at relatively high trigger-photon momenta.

• PHENIX measured the xE distribution associated with isolated photon

• is consistent with KKP, only accessible in low xE or <z> region.

• PYTHIA agrees with Initial/final state radiation on with kT.

• Need to go higher xE (ala . pi0 as associated particle )

• kT-bias still present - pushes the minimum photon-trigger pT above 10 GeV/c at RHIC and 20~30 GeV/c at LHC.


28

points are p+p 14 TeV PYTHIA xE distribution, dashed line KKP FF parameterization

Nucl. Phys., 2001, B597, 337-369

LHC 14TeVLHC 14TeVLHC 14TeVLHC 14TeVPYTHIA



PYTHIA




NLO :hep-ph/9910252

Fold smeared associated distribution over fragmentation function D(z)

In following, use fragmentation variable

– h and h-h correlations – h and h-h correlations – h and h-h correlations – h and h-h correlations

Calculate local slope by negative

logarithmic derivative (NLD)

zT = pTa

pTt

NLD =− ddzT

ln dNdzT( )

29

dNdpTa | pTt

= dpTa Σ ' pTa | pTt( ) 1pTa

D pTa

pTa( )

pTa

s/2

∫


kT2 → kT

2 pT( ) =kT2 −σFermi( )pT

Q0 +pT+σ Fermi

σ Fermi = 0.3 GeV

Q0 = 2.0 GeV

In PYTHIA:

Just an idea, inspired by above:

In future, study how relevant this is to obtained slopes

σ (Q) = max 2.0 GeV ⋅Q7.0 GeV+Q ,PARJ(21)( )

PYTHIA guide:

Eq. (229) in

Chapter 11.3.3

!


dPdxE

: C 1xh

1

1+ xExh( )

n

Trigger biasTrigger biasTrigger biasTrigger bias

Mike

Tannenbaum

For details, see

PRD74 (2006) 072002

Imbalance: Side remark:

xE =−pTa

pTtcos(Δφ) ≈zT

xh =pTa

pTt

pTt→ ∞⏐ →⏐ ⏐ 1

Right trend in the model!

32

““Traditional” way to handle intrinsic kTraditional” way to handle intrinsic kTT““Traditional” way to handle intrinsic kTraditional” way to handle intrinsic kTT

p1 = x1s2 ,0,0,+x1

s2( )

p1 = x2s2 ,0,0,−x2

s2( )

p1 = x1s2 + k1T

2

2x1 s,rk1T ,x1

s2 − k1T

2

2x1 s( )

p1 = x2s2 + k2T

2

2x2 s,rk2T ,−x2

s2 + k2T

2

2x2 s( )

p12 =0 =p2

2

Before kT

Put in kT from

two dimensional

gaussianIdea: partons remain at mass shell:

However, the pair mass:

s = p1 + p1( ) 2=x1x2s−2k1Tk2T cos φ1 −φ2( ) + k1T k2T

x1x2s

(Turns out: need a cut off when kT ≥ pT of the partonic final state)

See J.F. Owens, Rev. Mod.

Phys. 59 No.2, 1987

kT int

NOTE!

Integrate over kT’s with gaussian weights.

Jet properties from dihadron Correlation in PHENIX

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