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Comparative Study of Comparative Study of Jet-Quenching SchemesJet-Quenching Schemes
Working towards a unified Working towards a unified approach in Jet-modificationapproach in Jet-modification
A. Majumder, Duke University
Thanks to: N. Armesto, S. Bass, C. Gale, S. Jeon, C. Loizides, G. Moore, B. Muller,
T. Renk, C. Salgado, S. Turbide, I. Vitev, U. Wiedemann, X. N. Wang.
OUTLINE A brief history & time-line Four schemes in four dimensions! A comparison of extremes A meeting ground (finding agreement) Going beyond RAA, Space-time Profiles.
Phenomenological extensions (jet correlations) Comprehending the landscape @ RHIC
History, 1990 and after!!History, 1990 and after!! Qiu, StermanHigher twist 1991
Luo, Qiu, StermanA enhancement, 1994
Guo, WangModified fragmentation
2000
Wang,Wang, Zhang, Majumder
HT-2002-2005
Braaten, Pisarski HTL 1990
Aurenche, et.al.
Enhancement1998
AMY2001
Turbide, Jeon, Gale, - AMY
2005
GW model 1994
Wiedemann 2000
ASW 2004
DGLV-2005DGLV-2005Renk,2005Renk,2005
GLV2000
Eskola, HonkanenEskola, HonkanenPQM 2004-05PQM 2004-05
BDMPS-Zakharov 1997
Details of Medium
Classify using scales in the problem2
Q2
2E
E >> Q,
• Difference between schemes relation between Q and
• Extending schemes beyond pQCD with models
Lq i
i 2
ˆx=Eg/E
Higher Twist Approach, E >> Q >> • A medium with a color correlation length << L
• Highly VIRTUAL parton produced in hard collision
• Parton picks up FEW SMALL transverse kicks ~
• Expand diagrams in Q, transverse kick in
• Formal similarity with DGLAP evolution 0<x<1.
• Interference between diagrams leads to LPM suppression
k A FT T
X. Guo, X. N. Wang, Phys. Rev. Lett.
85:3591 (2000); X. N. Wang,
X. Guo, Nucl. Phys. A. A696:788,
(2001); E. Wang, X. N. Wang, Phys.
Rev. Lett.87, 142301,(2001); ibid 89
162301 (2002); B. Zhang, X.N.Wang,
Nucl.Phys. A720:429-451,2003.
• Entire effort is calculating the modification of D(z)
• E-Loss estimate or gluon radiation intensity not needed to get spectra
• Extract length enhanced contributions (Q2)L
• Modification looks like DGLAP X factor
L
GLV, Recursive Operator in Opacity E >> Q ~
• Medium of heavy (static) scattering centers with Yukawa like potentials
• Parton picks up transverse kicks ~
• Operator formalism that sums order by order in opacity • Approximate gluon x 0 (soft gluons), ignore spins ! • Interference between different diagrams leads to the
LPM effect and the L2 length dependence of E-loss.
nz
,n nq a
,n nq a
nznz
,n nq a
,n nq a
nz
,n nq a
,n nq a ++ˆ = R
M. Gyulassy, P. Levai, I. Vitev, Nucl.Phys.B571:197,2000; Phys.Rev.Lett.85:5535,2000; Nucl.Phys.B594:371,2001;
Phys. Lett.B538:282-288,2002.
g
Ln
• Central quantity: radiated gluon intensity, per emission!
• Gives direct measure of E-loss
• Jet loses energy in multiple tries
• To get Hadrons, need to get distribution of E-loss: P(E)
12 2
/ /
0
1( , ) ,
1 1( )med vac
h q h qz
D z Q d D QP
0 1
1
( )1
!
( )
ni
in i
dN ndid
i jet
dNd
n dP
eE
• Used to calculate the energy shifted fragmentation function
• Medium of heavy (static) scattering centers with Yukawa potentials• Parton picks up perp. momentum from kicks in medium• Path-integral in opacity• Two simple limits of calculation a) Few hard scatterings (GLV ) b) Many soft scatterings (BDMPS)
ASW, Path integral in OpacityE>>Q
+ +
L 2
U. Wiedemann, Nucl. Phys. B.582, 409 (2000); ibid. 588, 303 (2000), Nucl. Phys. A.690 (2001); C. Salgado, U. Wiedemann,
Phys.Rev. D. 68 014008 (2003); K. Eskola, H. Honkanen, C. Salgado, U. Wiedemann, Nucl. Phys. A.747, 511(2005);
N. Armesto, C. Salgado, U. Wiedemann, Phys.Rev.D.72,064910 (2005).
g
Ln
• Central quantity: radiated gluon intensity, per emission
• Gives direct measure of E-loss
• To get Hadrons, need to get distribution of E-loss: P(E) and use that to get a fragmentation function
AMY-Finite temperature field theory approach, E>>Q
• Hot thermal medium of quarks and gluons at T ∞• T ∞ implies g 0• Hard parton comes in onshell E ~ T• Picks up multiple soft hits, gT from hard particles of ~
T• The hard lines never go off-shell by more than g2T• Long formation time leads to multiple scattering
P. Arnold, G. Moore, L. Yaffe, JHEP 0111:057,2001; ibid 0112:009,2001 ; ibid. 0206:030, 2002; S. Jeon, G. Moore Phys. Rev.
C71:034901,2005; S.Turbide, C.Gale, S. Jeon, G. Moore, Phys. Rev. C72:014906,2005.
• One calculates the cuts of infinite series of ladder diagrams,
Im• Gives rates of change of
quark and gluon distributions
• The shifted distributions are used to get the medium
modified fragmentation function
QzDppPQzDppPz
zdpnrQzD qifqiffc cgcqq
,';,';'
),;,( //, //
Comparing Results for RComparing Results for RAAAA::GLV vs ASWGLV vs ASW
(non-reweighted)
11 5 .ˆ 2. Gq eV fm q=1GeV2/fm
• ASW with fixed path length 6fm gives similar qhat as GLV
• Introducing realistic geometry gives mean path length = 2 fm
• RE)=q L2, if L L/3, q9q
q=5-15GeV2/fm
PQM
Comparing Results for RComparing Results for RAAAA::HT vs AMYHT vs AMY
• q-hatmax= 3-4 GeV2/fm
• <q-hat> ~ 1 GeV2/fm
• <q-hat> <~ 2GeV2/fm
at T = 370 MeV
The model landscape! The model landscape! A
ssum
ptio
ns a
bout
the
med
ium
Medium scale ~ T s small Jet scale ~ Q
Higher-Twist, Medium sampled with FF,
Finite number of scattering,
Large Q makes s small
Recursive Operator Opacity, (GLV), Medium made of heavy scattering centersFinite number of scattering
Large Q makes s small,
Path Integral Opacity, (ASW)Medium made of heavy scattering centersInfinite number of scatterings resummed
Medium scale Q large makes s small,
Finite temp. resummattion, (AMY)•Equilibrated inifinite medium, HTL dispersion relations •Infinite number of scatterings resummed•T ∞makes s small
Similar models
different q-hatDifferent models
Similar q-hat
AMY based on Hard Thermal Loops: An effective theory of soft modes in a very hot plasma , (Braaten, Pisarski 1990)
Alternate picture, A Vlasov theory of hard particles in soft fields, (Blaizot, Iancu 1992)
Medium enhanced higher twist isolates near on-shell propagation in large nuclei
Mean transverse momentum shift
Propagation of a colored particle in a color field with a short distance correlation,
Langevin Eqn with a lorentz force. Mean transverse momentum shift
)0()(
1
4 ,,2
22 aa
c
RST FsFdsL
N
Ck
)0()(
1
42
22
FsFdsLN
Ck
c
RST
)()( aaaT BvEgQ
dt
tdk
Fields have short correlation lengths
R. Fries Phys. Rev. D. 68,074013,2003
X. Guo, Phys. Rev. D. 58, 114033,1998
But radiation vertex is slightly different
H-T has two kinds of contributions
Original parton comes out of hard scattering off shell
Off shell-ness generated later by multiple scattering
First set of diagrams missing in AMY, but has multiple scattering contributions to second type
And interferences
How important is this difference?
will need to look at differential observables
Differentiating between Model differences with differential observables (More data)!
• Jet-medium and multi-particle correlations• Settle questions of scheme• Phenomenological extensions to lower momenta• Use jets to probe bulk dynamics • And Microscopic degrees of freedom• Understanding q-hat is understanding the medium.• How does the medium:
stop jets, turn jets, distribute lost energy
Q-hat depends on space-time profile of density
• Set a q-hat maximum
• Modulate with space-time profile
• Azimuthally dependent RAA can distinguish
A. Majumder, nucl-th/0608043
• Flow can confuse the difference
• Need many observables in tandem to set the gluon density
• Like RAA vs centrality and back-to –back dihadrons
Central events can give the same answer by adjusting qhat but actual dynamics is different, Renk!, see talk in 1.3
Q-hat is a tensor
Non-Isotropic medium non-isotropic q-hat • Imagine large turbulent magnetic fields produced early in
plasma
• B fields are transverse to the beam
• Will deflect jets, preferentially out to large rapidities
• Near side correlations in effected !!
• Q-hat not just from entropy carrying degrees of freedom
B
L
kkq
TT
ˆ
See talk by M. Strickland
Au+Au 0-10%preliminary
• Note: broadening only in eta and not in phi
• Introducing a transverse momentum into the Yukawa potential or directional q-hat – ASW
• GLV- no broadening, only shift !!
Lead to the formation of an extended ridge on the near side
Talks by M. Calderon, J. Putschke
AM, B. Muller, S. Bass,hep-ph/0611135
How does lost energy show up in bulk matter
Jet correlations • Correlate a hard hadron with a another one
• Hard-Hard correlations understood within p-QCD, Consistency check !
Same side Away side
Majumder Renk
High pT on away side, differential
See talk by H. Z. Zhang, Parallel 2.2
Also understood within pure
jet-quenching schemes,
Higher twist calculations, NLO hard
part, Full geometry
NLO
Vitev, LO
Low pT on the away side, Mach-Cherenkov-Gluon Brem. cone
• More theory that you would ever want!
• Including flow is better for Mach cone explanation
Cassalderry-Solana Renk & Ruppert
Alternate explanations still persist and have not
been ruled out • Cherenkov radiation,
• V. Koch, AM, X-N. Wang
• Not a two state problem, but more complicated !
Regular Gluon radiation with Sudakov form factor for no emissions!
A. Polosa, C. Salgado
• Not a deflected jet! From 3 particle correlations (talk by C. Pruneau), progress..
Conclusions
• Jet-modification in dense matter (Well motivated and unsettled)• Different schemes, using similar physics• Differences in implementation (must be resolved!!)• Multi-particle correlations to high pT • Model extensions at lower pT.
• Explore the space-time profile of the medium• Explore the many dimensions of q-hat• Need more data, need more statistics!
Topics left out: Heavy-quarks, elastic energy loss,
Back up!
Comparing different ST profiles at most central events
• Preliminary
EASW sCR
4n0
2L2 log E / EGLV
E loss formulae!
/( )
/
( ) ( )
( )
asso trigtrig T T
AA T T trigT
trig assoT T
TT T T
trigT
TT T
d dp dpD z p
d dp
d p pdE D D
dE E E
d pdE D
dE E
What is DAA
zT= p/ptrig
The results! Simplest thing RThe results! Simplest thing RAAAA
Dainese, talk at PANIC05
• ASW,PQM
How can such fundamentally different physics produce equally good description of data???,
B. Cole QM2005, problem weirder than you think!
• GLV and ASW are very similar in basic structure (different qhat)
• Difference in implementation, Geometry!
• AMY and HT have truly different origins (similar qhat)
• How can they yield similar physics ???
• Deeper similarity between AMY and HT.
• Within the approximation schemes, they may be similar physics
• Look at Basic theory without radiation in HT and AMY