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Transcript of 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
DongJo Kim, Tokaj 2008
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)
DongJo Kim, Tokaj 2008
• 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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
€
≈−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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
– 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)
DongJo Kim, Tokaj 2008
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
away-side fragments - associated particles pTa
h-h: Leading particle does not fix Energy scale.
Direct gamma - trigger pTt
xEzpout kT
away-side fragments - associated particles pTa
-h: direct gamma does fix Energy scale if no kT
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
1) Initial State Radiation/Final State Radiation OFF,<kT>2=0 GeV/c
xE slope is constant
2) IR/FR ON, <kT>2= 5 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) Initial State Radiation/Final State Radiation OFF,<kT>2=0 GeV/c
xE slope is constant
2) IR/FR ON, <kT>2= 5 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
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
P ( p̂T & p̂Ta) )pT
=p̂T + p̂Ta
p̂T p̂Ta −p̂T2
exp( p̂T + p̂Ta)
2 −4 p̂T2
kT2
⎛
⎝⎜
⎞
⎠⎟
provided kT2 =
2
pT ,pair2
DongJo Kim, Tokaj 2008
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 & p̂Ta) )pT
P ( p̂T ) )pT
P ( p̂Ta ) )pT=
P ( p̂T & p̂Ta) )pT
P ( p̂T ) )pT
α
Lorentz Invariant Gaussian kT smearing -> non-Gaussian distributions even at high-pT. Good agreement between simul. And formulae.
DongJo Kim, Tokaj 2008
3/19/08 DongJo Kim, Tokaj 2008 24
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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 !
DongJo Kim, Tokaj 2008
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 ->
DongJo Kim, Tokaj 2008
3/19/08 DongJo Kim, Tokaj 2008 30
PID FF studiesPID FF studiesPID FF studiesPID FF studies
MLLA + LPHD Sapeta, Wiedeman hep-ph/0707.3494
31
xxEE slopes slopesxxEE slopes slopes
3/19/08 DongJo Kim, Tokaj 2008
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
3/19/08 DongJo Kim, Tokaj 2008
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
3/19/08 33DongJo Kim, Tokaj 2008
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 34DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
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
DongJo Kim, Tokaj 2008
3/19/08 DongJo Kim, Tokaj 2008 37
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
3/19/08 38DongJo Kim, Tokaj 2008
pp @ √s = 200GeV
pp @ √s = 200GeV
Fragmentation photons are isolated ?Fragmentation photons are isolated ?Fragmentation photons are isolated ?Fragmentation photons are isolated ?
3/19/08 DongJo Kim, Tokaj 2008 39
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
DongJo Kim, Tokaj 2008