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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
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 3rd Nordic "LHC and Beyond" Workshop, Lund
DongJo Kim, LHC and Beyond 2009
Outline of the talkOutline of the talkOutline of the talkOutline of the talk
1) Open Questions from RHIC
a) RAA, IAA
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 ?
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)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, LHC and Beyond 2009
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
DongJo Kim, LHC and Beyond 2009
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
DongJo Kim, LHC and Beyond 2009
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
DongJo Kim, LHC and Beyond 2009
€
pT2
pair
2= kT
2 = kT2
int+ kT
2
soft+ kT
2
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 pkkrrr
=+
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 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, LHC and Beyond 2009
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
DongJo Kim, LHC and Beyond 2009
– 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)
DongJo Kim, LHC and Beyond 2009
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, 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 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, LHC and Beyond 2009
2/3/09 DongJo Kim, LHC and Beyond 2009 12
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
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, LHC and Beyond 2009
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)
PYTHIA
2/3/09 14
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.
DongJo Kim, LHC and Beyond 2009
xE =
rpTa ⋅
rpTtr
pTt2 =−
pTa
pTt
cosΔφ≈−pTa
pTt
2/3/09 15
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 photons
DongJo Kim, LHC and Beyond 2009
xE =
rpTa ⋅
rpTtr
pTt2 =−
pTa
pTt
cosΔφ≈−pTa
pTt
2/3/09 DongJo Kim, LHC and Beyond 2009 16
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 17
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, LHC and Beyond 2009
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
xxEE distribution comparisons ( distribution comparisons (-h)-h)xxEE distribution comparisons ( distribution comparisons (-h)-h)
2/3/09 DongJo Kim, LHC and Beyond 2009 18
• 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
2/3/09 DongJo Kim, LHC and Beyond 2009 19
(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
-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
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
2/3/09 DongJo Kim, LHC and Beyond 2009 20
D(z) ~ exp(-6z)
D(z) ~ z-α(1-z)(1+z)-
Parameters α, and from PRD74 (2006) 072002
Sami Räsänen’s Talk (afternoon)
kT smearing effect
quark vs gluon in KKP
(1)
(2)’
(2)
PHENIX xE BinPHENIX xE Bin
2/3/09 21
PHENIX dir-PHENIX dir- assoc. distributions measures FF assoc. distributions measures FFPHENIX dir-PHENIX dir- assoc. distributions measures FF assoc. distributions measures FF
Run 5+6 p+p @ 200 GeVIsolated photons
DongJo Kim, LHC and Beyond 2009
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<0.80.4<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 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
• 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.
DongJo Kim, LHC and Beyond 2009
23
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
-gluon jet (Annihilation) 17 %
-u quark jet (Compton) 66 %
PYTHIA
-gluon jet (Annihilation) 17 %
-u quark jet (Compton) 66 %
2/3/09 DongJo Kim, LHC and Beyond 2009
NLO :hep-ph/9910252
More intuitive exercises….More intuitive exercises….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 (f
m)
x (fm)
T.Renk, K.Eskola, PRC 75, 054910 (2007)
DongJo Kim, LHC and Beyond 2009
• 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
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)