analysis of the direct photon associated spectra from rhic to lhc

2/3/09 1

Analysis of the Direct photon associated Analysis of the Direct photon associated spectra from RHIC to LHCspectra from RHIC to LHC

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

Jyväskylä University & Helsinki Institute of Physics, Finland

3rd Nordic "LHC and Beyond" Workshop, Lund

DongJo Kim, LHC and Beyond 2009

Outline of the talkOutline of the talk

1) Open Questions from RHICa) RAA, IAA

b) Modification of the Fragmentation in AA2) Two particle correlation

a) Kinematicsb) 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 ?

a) Soft QCD radiations b) Quark Fragmentation only ?c) -jet momentum imbalance due to the kT smearing

(Details in Sami Räsänen’s Talk)

a) Conclusion and Open Issues

2/3/09 2DongJo Kim, LHC and Beyond 2009

2/3/09 3

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

1( )1 1 1

zD z DE 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)

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

∝dzzCi s;z,αs( )Δ i

h / z,s( )

1

∫i∑ ≡Δ h z( )

αccoplαnαrity (CF width) dNαssoc

dpout

∝dNαssoc

dΔφ∝

dsdkT

E =rpTα ⋅

rpTtrpTt2 =−

pTαpTt

cosΔφ≈−pTαpTt

€

≈−pTa

/ ˆ p Ta

pTt/ ˆ p Tt

≈ −za

< zt >

djdisk:Applications:MathType%206:MathType.app

2/3/09 5

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

d+Au

Phys.Rev.D74:072002,2006

sN

sA

sN jT jet fragmentation transverse momentum

sF 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++pp

Fragmentation function D(z) and

Intrinsic momentum kT


€

pT2

pair

2= kT

2 = kT2

int+ kT

2soft

+ kT2

NLO

R. P. Feynman, R. D Field, and G. C. Fox, Phys Rev D18 1978J. Rak and M. Tannenbaum hep-ex/0605039 v1

• Intrinsic : Fermi motion of the confined partons inside the proton.• NLO : Hard gluon radiation• Soft : Initial and Final state radiation, resummation techniques (hep-ph/9808467) .

pairTTaTt pkk rrr=+

2/3/09 7

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

€

pout = 2 kTypTa

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( )=pTαpTt

pαrticle pαir im bαlαnce h =pTαpTt

zt

xh

kT2 =

1h

pout2 − φTy

2 (1+ h2 )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)

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 =

rpTα ⋅rpTtrpTt

2 =−pTαpTt

cosΔφ ≈−pTαpTt

Phys.Rev.D74:072002,2006

2/3/09 9

Unavoidable Unavoidable zz-bias in di-hadron correlations-bias in di-hadron correlationsz-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)


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

2/3/09 DongJo Kim, LHC and Beyond 2009 10

• Even with higher xE region Slope gets larger as you go higher pt

• PYTHIA fit : 0.2<xE<0.8

• Unknown quark/gluon contributions increase the systematic higher

PYTHIA

2/3/09 11

kk22TT and and zztt in p+p @ 200 GeV from in p+p @ 200 GeV from pp00-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 => D(z) slope.

Base line measurement for the kT broadening - collisional energy loss. Direct width comparison is biased.

Still, we would like to extract FF from our own data -> direct photon-h correl.DongJo Kim, LHC and Beyond 2009


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 > =

2π⋅< pT

2 > pair (in case 2D Gaussian)

2/3/09 13

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 2s

dpTtdE=dpTαdE

⊗d 2s

dpTtdpTα;

1h

Δ(zt)Δ(ztpTα)hpTt

)Σ'

Tt

.pTt/ pTα

∫ (pTtzt

)dzt

d 2s

dpTtdE=dpTαdE

⊗d 2s

dpTtdpTα;

1)pTα

Σ' pTα)pTα

⎛⎝⎜

⎞⎠⎟Δ

pTα)pTα

⎛⎝⎜

⎞⎠⎟

€

xE ≈ −pTa

/ ˆ p Ta

pTt/ ˆ p Tt

≈ −za

< zt >

D(zt)d (zt)

PYTHIA

2/3/09 14

p0 Direct

PHENIX PHENIX s=200 GeV s=200 GeV pp00 and dir- and dir- assoc. distributions assoc. distributions

Run 5 p+p @ 200 GeVStatistical Subtraction Method

Arb

itrar

y N

orm

aliz

atio

n

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 =

rpTα ⋅rpTtrpTt

2 =−pTαpTt


2/3/09 15

PHENIX PHENIX s=200 GeV s=200 GeV pp00 and dir- and dir- assoc. distributions assoc. distributions

Run 5+6 p+p @ 200 GeVIsolated photons


xE =

rpTα ⋅rpTtrpTt

2 =−pTαpTt



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

GeV/cxE slope is constant

2) IR/FR ON, <kT>2= 3 GeV/cxE 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 17

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

itial

/Fin

a st

ate

radi

atio

n O

FF,

k2 T=0

GeV

/c

Initi

al/F

ina

stat

e ra

diat

ion

ON

, k2 T

=5 G

eV/c


1) Initial State Radiation/Final State Radiation OFF,<kT>2=0 GeV/cxE slope is constant

2) IR/FR ON, <kT>2= 5 GeV/cxE slope is raising!Also PYTHIA shows the same trend, though, not as large as in the data, not so

trivial even with Direct photons

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, b and from

PRD74 (2006) 072002

quark vs gluon in KKP

(1)

(2)’

(2)

Local 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 %

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 xEE


D(z) ~ exp(-6z)

D(z) ~ z-α(1-z)b(1+z)-

Parameters α, b and from PRD74 (2006) 072002

Sami Räsänen’s Talk (afternoon)

kT smearing effect

quark vs gluon in KKP

(1)

(2)’

(2)

PHENIX xE Bin

2/3/09 21

PHENIX dir-PHENIX dir- assoc. distributions measures FF assoc. distributions measures FFRun 5+6 p+p @ 200 GeVIsolated photons


o PHENIX measures FF in low xE or low <z> ?

o PYTHIA and KKP shows the similar trend as data in 5<pTt< 15 GeV

o KKP steeper than PYTHIA in low xE region

0.4<xE<0.8

o as xE gets higher, KKP ~ PYTHIA

o Finalizing the data and go to higher xE ( pi0 in associated bin )

2/3/09 22

Summary 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. LHC will be an ideal laboratory - larger xsection and center-of-mass energy available for hard-probes production.

As a next goal after “day one” 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

• fragmentation function - can be measured using jets - not from the first data. 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.

• 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 30 GeV/c at LHC : Sami’s talk.


23

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

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

LHC 14TeVLHC 14TeVPYTHIA

-gluon jet (Annihilation) 17 %

-u quark jet (Compton) 66 %

2/3/09 DongJo Kim, LHC and Beyond 2009

NLO :hep-ph/9910252

http://www.slac.stanford.edu/spires/find/hep/www?j=EPJ,C13,347

More intuitive exercises….More intuitive exercises….

2/3/09 24

• can’t get error on best fit from c2/d.o.f curves, need c2. N standard deviation errors on fit parameters are given by c2= c2

min + N2, so depending on d.o.f can’t really tell from c2/d.o.f whether IAA gives better constraint than RAA

• However c2min/d.o.f=2.8 for IAA fit

seems too large to be acceptable. (?)

Zhang,Owens,Wang, PRL 98 212301 (2007)

NLO pQCD + KKP FF + expanding medium

c2 (IAA)

c2(RAA) Single Di-hadron

y (fm

)

x (fm)T.Renk, K.Eskola, PRC 75, 054910 (2007)


• IAA better than RAA at RHIC and LHC

• RAA similar situation between RHIC and LHC

• IAA looks better probe in LHC

IIAAAA is better than R is better than RAAAA

Gamma-h will be better Gamma-h will be better

2/3/09 25

6< pT trig < 10 GeV

STAR Preliminary

Inconsistent with Parton Quenching Model calculation

(1) C. Loizides, Eur. Phys. J. C 49, 339-345 (2007) Modified fragmentation model better

(2) H. Zhang, J.F. Owens, E. Wang, X.N. Wang –Phys. Rev. Lett. 98: 212301 (2007) Di-Hadron correlation is more sensitive for jet tomography than RAA (2)(3)

Gamma-h will be better but current results with very wide bins , not much different at this moment

(3) K.Eskola, T.Renk ,Phys.Rev.C75:054910,2007 DongJo Kim, LHC and Beyond 2009

Phys.Rev.C75:054910,2007

(1)

(2)

(2)

(3)

analysis of the direct photon associated spectra from rhic to lhc

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