jet properties from dihadron correlation in phenix
DESCRIPTION
Jet properties from dihadron Correlation in PHENIX. DongJo Kim Norbert Novitzky, Jiri Kral Sami Räsänen, Jan Rak Jyväskylä University & Helsinki Institute of Physics, Finland. High pT Physics at LHC, Feb 4-7 ,2008 Prague. Outline of the talk. Motivation R AA, I AA , gamma-h - PowerPoint PPT PresentationTRANSCRIPT
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
DongJo Kim, Prague High pT 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, Prague High pT 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, Prague High pT 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, Prague High pT 2009
.
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
DongJo Kim, Prague High pT 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, Prague High pT 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, Prague High pT 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, 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.
DongJo Kim, Prague High pT 2009
2/3/09 DongJo Kim, Prague High pT 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, Prague High pT 2009
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.
DongJo Kim, Prague High pT 2009
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
DongJo Kim, Prague High pT 2009
xE =
rpTa ⋅
rpTtr
pTt2 =−
pTa
pTt
cosΔφ≈−pTa
pTt
2/3/09 DongJo Kim, Prague High pT 2009 17
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
DongJo Kim, Prague High pT 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, Prague High pT 2009 19
• 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, Prague High pT 2009 20
(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, Prague High pT 2009 21
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))
2/3/09 DongJo Kim, Prague High pT 2009
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
242/3/09 DongJo Kim, Prague High pT 2009
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
252/3/09 DongJo Kim, Prague High pT 2009
-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.
DongJo Kim, Prague High pT 2009
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
-gluon jet (Annihilation) 17 %
-u quark jet (Compton) 66 %
PYTHIA
-gluon jet (Annihilation) 17 %
-u quark jet (Compton) 66 %
2/3/09 DongJo Kim, Prague High pT 2009
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
∫
2/3/09 DongJo Kim, Prague High pT 2009
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
!
302/3/09 DongJo Kim, Prague High pT 2009
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.