3/19/080 analysis of the direct photon associated spectra from rhic to lhc dongjo kim rafael diaz,...

3/19/08 1

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

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

DongJo KimDongJo KimRafael Diaz, Norbert Novitzky, Tuomo Kalliokoski

Timo Alho, Sami Räsänen, Jan Rak

Jyväskylä University & Helsinki Institute of Physics, Finland

DongJo Kim, Tokaj 2008

High-pT Physics at LHC, Tokaj'08High-pT Physics at LHC, Tokaj'08

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

1) Open Questions from RHIC

a) RAA

b) Modification of the Fragmentation in AA

2) Two particle correlationa) Kinematics

b) What we learned from di-hadron correlation ?

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

3) Gamma-Hadron Correlation– Still various Contributions to be Understood ?

a) Soft QCD radiations

b) -jet momentum imbalance due to the kT smearing

4) Conclusion and Open Issues

3/19/08 2DongJo Kim, Tokaj 2008

3/19/08 3

On the mission from RHIC to LHCOn the mission from RHIC to LHCOn the mission from RHIC to LHCOn the mission from RHIC to LHCGreat success of RHIC gave us a

• perfect liquid

• sQGP

• test bench for string theory (AdS/CFT)

but also an opportunity to ask why:

• Light and heavy quarks suppression looks so similar:

• Quarks and gluons suppression looks similar:

• Direct photon suppression at high pT looks similar:

Two particle correlations - more detailed view into a nature of parton interactions with QCD medium. Access to parton intrinsic momentum kT -> soft pQCD radiation, jet shape parameters jT -> induced radiation, fragmentation function -> energy loss.

o Di-hadron correlations and conditional yieldso Direct photons-hadron correlations in p+p @ s=200 GeV and 14 TeV

RAAc−quark ≈RAA

u,d

RAAquark ≈RAA

gluon

RAAq,g ≈RAA

gamma


3/19/08 4

PHENIX Charm , PRL. 98, 172301 (2007) PHENIX Charm , PRL. 98, 172301 (2007)

Medium tomography: T. Renk, K. Eskola hep-ph/0610059Medium tomography: T. Renk, K. Eskola hep-ph/0610059

Nuclear Modification Factor for various particles PHENIXNuclear Modification Factor for various particles PHENIX

M. G. Mustafa, Phys.Rev.C72:014905,2005M. G. Mustafa, Phys.Rev.C72:014905,2005

More intuitive exercises….More intuitive exercises….More intuitive exercises….More intuitive exercises….

3/19/08 5

• can’t get error on best fit from 2/d.o.f curves, need 2. N standard deviation errors on fit parameters are given by 2= 2

min + N2, so depending on d.o.f can’t really tell from 2/d.o.f whether IAA gives better constraint than RAA

• However 2min/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

2 (IAA)

2(RAA) Single Di-hadron

y (f

m)

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

• 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 IIAAAA is better than R is better than RAAAA

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

3/19/08 6

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


Phys.Rev.C75:054910,2007

(1)

(2)

(2)

(3)

3/19/08 7

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


3/19/08 8

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

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

€

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


€

≈−pTa

/ ˆ p Ta

pTt/ ˆ p Tt

≈ −za

< zt >

3/19/08 9

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


3/19/08 10

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


3/19/08 11

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 x̂h xh( ) =p̂Ta

p̂Tt

particle pair imbalance xh =pTa

pTt

zt

x̂h

kT2 =

1xh

pout2 − jTy

2 (1+ xh2 )

zt

x̂h

kT2 =

1xh

pout2 − jTy

2 (1+ xh2 )partonic hadronic

Lab frame

Hard scattering rest frame


3/19/08 12

LEP data

xE =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

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)

3/19/08 13

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)


3/19/08 14

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 => 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, Tokaj 2008

3/19/08 15

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

;1x̂h

D(zt)D(ztpTa)xhpTt

)Σ'

xTt

x̂.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)

3/19/08 16

Soft + hard QCD radiationSoft + hard QCD radiation k kTT phenomenology phenomenology

Soft + hard QCD radiationSoft + hard QCD radiation k kTT phenomenology phenomenology

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 radiationHard NLO radiation

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


3/19/08 17

0 Direct

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 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 =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosΔφ≈−pTa

pTt

FF slope


3/19/08 DongJo Kim, Tokaj 2008 18

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)

3/19/08 19

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





3/19/08 20

PYTHIA PYTHIA -h simulation p-h simulation pT,pairT,pair- - correlation correlationPYTHIA PYTHIA -h simulation p-h simulation pT,pairT,pair- - correlation correlation

Δφ

1) IR/FR kT ON

• -h: pT,pair correlated with trigger photon jet balance destroyed by kT. • h-h: jet balance destroyed by kT and zT2) IR Only

Not in the case of “Initial State Radiation”.

• It is due to the collinearity of initial quark with photon


1) IR/FR kT ON 2) IR Only

3/19/08 21

-h correlation and k-h correlation and kTT bias bias-h correlation and k-h correlation and kTT bias bias

Question:

Can one extract the Fragmentation Function from -h associated distribution despite the kT bias?

α

Lorentz invariance:

p̂T g + p̂Ta( )2

= 2 p̂T g p̂Ta - 2cosf p̂T g p̂Ta = 4 p̂T2

the boost:

b =p̂T , pair

Epair

=p̂T , pair

p̂T , pair2 + 4 p̂T

2 h = gb and

p̂T g = ± p̂T + h± h p̂T

1+ g+ p̂T

Ê

ËÁÁÁ

ˆ

¯˜̃˜̃

p̂T g + p̂Ta = 2 p̂T g 2 - 1( ) cosa , sina( ) = p̂T , pair

p̂T g - p̂Ta = 2 p̂T 1+ g - 1( )cos2 a , g - 1( )sina cosa( )

p̂T , pair2 = p̂T g + p̂Ta( )

2- 4 p̂T

2

p̂T , pair = ± p̂T g - p̂Ta( ), ± 2 p̂T g p̂Ta - p̂T2

( )Solve for net-pair momentum


3/19/08 22

-h correlation and k-h correlation and kTT bias bias-h correlation and k-h correlation and kTT bias bias

when changing variable p̂T , pair ,x , p̂T , pair ,y( ) to p̂T g ,x , p̂Ta,y( )

J =p̂T g + p̂Ta

p̂T g p̂Ta - p̂T2

And assuming 2D Gaussian distribution for pT,pair =>

A conditional probability for detecting photon pTt and assoc pTa given parton momentum pT in CMS of hard scattering as:

P ( p̂T & p̂Ta) )pT

=p̂T + p̂Ta

p̂T p̂Ta −p̂T2

exp( p̂T + p̂Ta)

2 −4 p̂T2

kT2

⎛

⎝⎜

⎞

⎠⎟

provided kT2 =

2

pT ,pair2


=p̂T + p̂Ta

p̂T p̂Ta −p̂T2

exp( p̂T + p̂Ta)

2 −4 p̂T2

kT2

⎛

⎝⎜

⎞

⎠⎟

provided kT2 =

2

pT ,pair2


3/19/08 23

-mometum distribution due to the k-mometum distribution due to the kTT smearing smearing-mometum distribution due to the k-mometum distribution due to the kTT smearing smearing

P ( p̂Ta ) )pT=


P ( p̂T ) )pT

P ( p̂Ta ) )pT=


P ( p̂T ) )pT

α

Lorentz Invariant Gaussian kT smearing -> non-Gaussian distributions even at high-pT. Good agreement between simul. And formulae.



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)

3/19/08 25

Folding with a Fragmentation functionFolding with a Fragmentation functionFolding with a Fragmentation functionFolding with a Fragmentation function

Assoc xE distrib for various slopes of D(z)exp(-k*z)

dN

dpTa pT

=D(zt)⊗ ΣQ' (

pTt

zt

)⊗ d∫ p̂T P( p̂T & p̂Ta) p̂T

dN

dpTa pT

=D(zt)⊗ ΣQ' (

pTt

zt

)⊗ d∫ p̂T P( p̂T & p̂Ta) p̂T


Deviation from dashed lines (the true slopes of D(z)) at low pT due to the kT bias.

Unlike the di-hadron correlation it asymptotically converges to the correct value.

Knowing that we could unfold the kT or correct for the bias.

Comparisons to Pythia and PHENIXComparisons to Pythia and PHENIXComparisons to Pythia and PHENIXComparisons to Pythia and PHENIX

3/19/08 26

-h


Pythia

dN

dpTa pT

=D(zt)⊗ ΣQ' (

pTt

zt

)⊗ d∫ p̂T P( p̂T & p̂Ta) p̂T

dN

dpTa pT

=D(zt)⊗ ΣQ' (

pTt

zt

)⊗ d∫ p̂T P( p̂T & p̂Ta) p̂T

27

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

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

Comparison to KKPComparison to KKPComparison to KKPComparison to KKPPYTHIA

-gluon jet (Annihilation) 17 %

-u quark jet (Compton) 66 %

PYTHIA

-gluon jet (Annihilation) 17 %

-u quark jet (Compton) 66 %

3/19/08 DongJo Kim, Tokaj 2008

3/19/08 28

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. 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

• jT near-side jet shape modifications

• 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.

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

• fragmentation photon contribution ?

We are at the beginning of hard-probes exploration in heavy ion environment - LHC (supported by RHIC) will be fun !


3/19/08 29

Direct photons won’t be easy at LHCDirect photons won’t be easy at LHCDirect photons won’t be easy at LHCDirect photons won’t be easy at LHC

Decay photons energy and asymmetry distributions are in the ideal situation (no detector response) flat.

0 E E

Below threshold hits

“Direct” photons from 0 Ecut/E 2% @ E =10 GeV, however, / ratio is also of that order -> Subtraction method we started recently the full PHOS simulation project ->



PID FF studiesPID FF studiesPID FF studiesPID FF studies

MLLA + LPHD Sapeta, Wiedeman hep-ph/0707.3494

31

xxEE slopes slopesxxEE slopes slopes


Hard Process: Uncertainty from FFHard Process: Uncertainty from FFHard Process: Uncertainty from FFHard Process: Uncertainty from FF

• Wide z range– Due to interplay of steep jet pT

distribution and steep fragmentation function.

– z = 0.1 – 0.8• Missing knowledge of gluon

fragmentation at larger z.– Measurement from LEPII is

not still enough for larger z.• 3 jets events or global

analysis.– NLO FF parameters fit failed to

describe the entire kinematic range (= scale violation)

32

EPJC37(2004)25

Wide z distribution


Model HighlightModel HighlightModel HighlightModel Highlight

GLV PQM Modification of D(z)

• Realistic geometry• Bjorken expanding medium• Radiative energy loss – gluon brehmsstralung to all orders in opacity• Calculate a priori (w/o en loss) the average path length to the edge – use it to calculate partonic energy loss

• qhat = product of parton-medium cross-section * color-charge density• BDMPS quenching weights – only coherent radiative energy loss via gluon bremsstrahlung• Realistic geometry• Static• Avg qhat -> time-dependent density = scheme dependent\• No initial state multiple scattering• No modified nuclear parton distribution function

• Longitudinally expanding medium• Hard spheres• PDFs factorized into nucleon ones and HIJING parameterization of the impact parameter dependent nuclear modification factor• radiative gluon energy loss – incorporated in effective medium modified FF


h-h correlations - jet functionsh-h correlations - jet functionsh-h correlations - jet functionsh-h correlations - jet functions

unchanged near-side peak in the final jet functions when moving away from Reaction plane. Away side is clearly modified.


3/19/08 35

Assoc. yield - “Averaged” LO approachAssoc. yield - “Averaged” LO approachAssoc. yield - “Averaged” LO approachAssoc. yield - “Averaged” LO approach

Assumption (Phys.Rev.D74:072002,2006 for details) :

Invariant mass of mass-less partons in hard scattering CMS and in LAB is the same -> non-Gaussian kT-smearing.

zt

kT2 , p

Tt, p

Ta( ) = dzt zn−1 ⋅D (zt

xTt

1

∫ ) ⋅ ′ΣQ zt( )

x̂h kT2 , pTt, pTa( ) = dp̂Tt ̂pTt

n−1 ⋅D pTt

p̂Tt

⎛

⎝⎜⎞

⎠⎟⋅

pTt

s/ 2

∫ ′ΣQ

pTt

p̂Tt

⎛

⎝⎜⎞

⎠⎟

where kT -smeared parton dist. ′ΣQ zt( ) = dp̂T ΣQ p̂T( )0

s/ 2

∫ dφ ̂pn⋅G p̂n, kT2

( )0

∫ ⋅D pTa

p̂Ta

⎛

⎝⎜⎞

⎠⎟⋅1p̂Ta

zt

kT2 , p

Tt, p

Ta( ) = dzt zn−1 ⋅D (zt

xTt

1

∫ ) ⋅ ′ΣQ zt( )

x̂h kT2 , pTt, pTa( ) = dp̂Tt ̂pTt

n−1 ⋅D pTt

p̂Tt

⎛

⎝⎜⎞

⎠⎟⋅

pTt

s/ 2

∫ ′ΣQ

pTt

p̂Tt

⎛

⎝⎜⎞

⎠⎟

where kT -smeared parton dist. ′ΣQ zt( ) = dp̂T ΣQ p̂T( )0

s/ 2

∫ dφ ̂pn⋅G p̂n, kT2

( )0

∫ ⋅D pTa

p̂Ta

⎛

⎝⎜⎞

⎠⎟⋅1p̂Ta

M inv2 =4 p̂T

2 =2 p̂Tt p̂Ta −2 ˆrpTt ˆ

rpTa M inv

2 =4 p̂T2 =2 p̂Tt p̂Ta −2 ˆ

rpTt ˆ

rpTa

zt kT2 , pTt , pTa( )

x̂h kT2 , pTt, pTa( )

kT2 =

1xh

pout2 − jTy

2 (1+ xh2 ) xh =

pTa

pTt

; pout ≈σaway; jT ≈σnear

zt kT2 , pTt , pTa( )

x̂h kT2 , pTt, pTa( )

kT2 =

1xh

pout2 − jTy

2 (1+ xh2 ) xh =

pTa

pTt

; pout ≈σaway; jT ≈σnear

p̂n p̂Tt pTa

-p̂T

pTt p̂Ta

p̂T


3/19/08 36

Final state parton dist and FF from data of pQCD?Final state parton dist and FF from data of pQCD?Final state parton dist and FF from data of pQCD?Final state parton dist and FF from data of pQCD?

in LO: ΣQ( p̂T ) =d3σ

dp̂T2dy1dy2

=1s2

fp x1( ) fp x2( )ab∑

αS2 Q2( )x1x2

Σab cosθ∗( )

or

ΣQ( p̂T ) ∝ p̂T−n

in LO: ΣQ( p̂T ) =d3σ

dp̂T2dy1dy2

=1s2

fp x1( ) fp x2( )ab∑

αS2 Q2( )x1x2

Σab cosθ∗( )

or

ΣQ( p̂T ) ∝ p̂T−n

Effective FS parton distribution:

D z( ) ≡dzz

Ci s;z,αs( )Di x / z,s( )

x

1

∫i∑ or

D (z) =zα ⋅(1−z)b ⋅(1+ z) where α,b, from LEP or fit

D z( ) ≡dzz

Ci s;z,αs( )Di x / z,s( )

x

1

∫i∑ or

D (z) =zα ⋅(1−z)b ⋅(1+ z) where α,b, from LEP or fit

Effective Fragmentation function:

0 invariant cross section provides a constrain:

if 1

p̂T

dσ̂dp̂T

∝ p̂T−n than

1pT

dσ

dpT ;

1pT A⋅D z( )⋅

pT

z⎛

⎝⎜⎞

⎠⎟

−n+1dzz2xT

1

∫ ;A

pT( )

n D z( )⋅zn−3dzxT

1

∫ ⇒

⇒ partons 1p̂T

dσ̂dp̂T

∝ 1pT

dσ

dpT ∝

1

pT( )

8 ⇒ ΣQ p̂T( ) ∝1p̂T8 same power law



kT effectkT effectkT effectkT effect

NLOTsoftTrinsicTTpairT

kkkkp

22

int

22

2

2++==

Outgoing partons carries transverse momentum kT.• momentum imbalance (partons pt are not equal ) due to kTx component• acoplanarity (the transverse momentum of one jet doesn’t lie in the plane determined by the transverse momentum of the second jet and the beam axes) due to kTy component

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 pkkrrr

=+

Direct Photon is isolated in p+p Direct Photon is isolated in p+p Direct Photon is isolated in p+p Direct Photon is isolated in p+p PHENIX PRL 98 (2007) 012002PHENIX PRL 98 (2007) 012002

• Seems to imply Nfrag ≈ 66% of Ndir

• Only Δ from -0.5 - 0.5

(Only ~50% of inclusive photons included )

Which gives you “ Nfrag ≈ 33% of Ndir “

QM08 PHENIXQM08 PHENIX


pp @ √s = 200GeV

pp @ √s = 200GeV

Fragmentation photons are isolated ?Fragmentation photons are isolated ?Fragmentation photons are isolated ?Fragmentation photons are isolated ?


pp @ √s = 14 TeV Pythia

• Isolation done on the pure PYTHIA particles

• || < 0.7, R=0.4, pTth = 1 GeV/c

• Isolation Cut efficiency for direct and frag photons

Gustavo Conesa BalbastreGustavo Conesa Balbastre

QQuark, uark, GGluon Energy Lossluon Energy LossQQuark, uark, GGluon Energy Lossluon Energy Loss

QM08

3/19/08 40

Baryon & meson NMF

STAR Preliminary

Mark Thomas Heinz

Sapeta, Wiedeman hep-ph/0707.3494 Sapeta, Wiedeman hep-ph/0707.3494


3/19/080 analysis of the direct photon associated spectra from rhic to lhc dongjo kim rafael diaz,...

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