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