t highenergy nuclear collisions · highenergy nuclear collisions qgpws, jaipur, 1 st – 3 rd feb...

1QGPWS, Jaipur, 1st – 3rd Feb 2008 David d'Enterria (CERN)

QGP Winter School

Jaipur, India, Feb. 1st 3rd 2008

David d’EnterriaCERN

HighpHighpTT hadrons & jets in hadrons & jets inhighenergy nuclear collisionshighenergy nuclear collisions


OverviewOverview

qhat = ?dNg/dy = ?cs =?

■ Suppressed highpT hadron spectra:

■ Modified highpT dihadron correlations:

■ Full jet reco, jet, modified FFs:

FastkT (D=0.4),area substraction

Hot/dense QCD matter properties via “jet quenching”


QCD matter with heavyions: physics menuQCD matter with heavyions: physics menu

ε /T4

T/Tc

▪ Highdensity QCD at smallx: CGC

▪ QCD at hightemperature: QGP

▪ Gaugegravity duality: AdS/QCD

N = 4

SU(Nc)

BH in

AdS5 x S 5

(s tack of 4 D3 bran es)

✱ (de)confinement✱ chiral symm. restoration✱ early Universe thermodyn.


Early-time probes of QGPEarly-time probes of QGP

▪ HE AA colls. produce expanding QGP: V~O(103 fm3) for ~10 fm/c▪ Collision dynamics: Diff. observables sensitive to diff. reaction stages

Tim

e

Penetrating

probes t~0.1 fm/c

t ~ 10 fm/c

t ~ 107 fm/c

Final state probes

Penetrating probes


Hard probes of hot/dense QCD matterHard probes of hot/dense QCD matter

Z,

“Jet quenching”

J/Ψ & Υ suppression

direct , *, Z(control)

▪ Hard probes: largeQ2 (Q>2 GeV/c), earlytime production (~1/Q<0.1 fm/c) ▪ “Selfgenerated tomographic probes of the hottest and densest phases of AA collisions, well controlled experimentally & theoretically.”


““Jet quenching” as a QGP probeJet quenching” as a QGP probe

� gluonsstrahlung�

∆Eloss(g) > ∆Eloss(q) > ∆Eloss(Q) (color factor) (mass effect)

∝ (q, gluon density, L2)GLV

BDMPS

ˆ

▪ Parton energy loss: multiple nonAbelian (=gluon) radiation off the produced hard parton induced by the dense QCD medium:

▪ Parton energy loss ➠ Medium properties:

▪ transport coefficient:

▪ Flavourdependent energy loss:

▪ Energy lost carried away by gluons in broadened jet cone:

µ

λµ22

ˆ ≈=Lk

q T : Debye mass: mean freepath λ

q̂


25-years of � jet quenching� phenomenology25-years of � jet quenching� phenomenology

▪ Mono-jets:

▪ Jet broadening in :

XNWang&Gyulassy PRL 68, 1480 (1992)

Armesto et alhepph/0405301

▪ Leading hadron suppression:

▪ Medium-modified FFs:

X.N.Wang,A.MajumderSalgado&Wiedemann;Arleo, ...

Bjorken, FERMILABPUB82059THY.1982

▪ Mach-cones in :

θM Trigger

cos M scθ =

Stoecker et al. hepph/0505245.Casalderrey, Shuryak, hepph/0411315

Cerenkov angles, ...

...

Nchjet increases

<zjet> decreases


I. HighpI. HighpTT single inclusive single inclusive hadron spectrahadron spectra


High pHigh pTT (leading) hadrons (leading) hadrons

pT< 2 GeV/c: Expo. (Ed3σ/d3p ~ e-6pT) w/ constant inv. slope: ~ 160 MeV ~ Tcrit

Thermallike soft hadrons: e6pT √sindep.

Hard scatt.: 1/pT

n (√sdepend.)

pT~2GeV/c

■ Above pT~ 2 GeV/c: single spectra dominated by fragmentation hadrons

carrying a large fraction of parent parton pT (<z>=phad/pparton~0.7 @ RHIC)


High-pHigh-pTT hadrons: pQCD factorization theorem hadrons: pQCD factorization theorem

(1) Hadron = collection of partons described by PDFs(x,Q2):

■ Production cross section computable as a convolution of 3 terms: 1 short-

distance (pQCD parton-parton) & 2 long-distance (PDF, FF)

(2) High-Q2 parton-parton x-sections computed

perturbatively at a given O(s):

(3) Parton (jet) fragmentation into hadrons described by a FF(z,Q2):

x1

x2

hadronjet


High-pHigh-pTT hadron spectra: p-p hadron spectra: p-p @ @ 200 GeV200 GeV

■ High pT hadron spectra very well described by NLO pQCD:

PHENIX Collab.

PRD76, 051106(R) (2007)

■ Data sensitive to different parametrizations of gluon FF

M. Ru sscher , QM06


Hard yields in p-A, A-A collisions (no medium effects)Hard yields in p-A, A-A collisions (no medium effects)

A

B

dσAB → hard = A∙B∙dσpp → hard

dNAB → hard (b) = TAB(b)∙dσpp → hard

Nuclear Modification Factor:

At impact parameter b:

geom. nuclear overlap at b nonpQCD prod.

TAB ~ Ncoll (# of nucleonnucleon colls at b)

AB = “simple superposition of pp collisions”⇒ nPDF: independent sum of “free” partons:

dσpA → hard = A∙dσpp → hard

■ Factorization theorem for nuclear collisions:

■ "Ncoll scaling� :


High pHigh pTT hadron spectra: d-Au hadron spectra: d-Au @ 200 GeV@ 200 GeV

π0

PHENIX, nucl-ex/0610036

η

PHENIX,

nucl-ex/0611006

■ Small "cold nuclear matter" modifications (Cronin, shadowing): ~20%

π,h

■ Only protons (factor ~2 enhancement)

deviate from "vacuum" production

STAR: nucl-ex/0604018

p,p_


High pHigh pTT pion spectra: Au-Au pion spectra: Au-Au @ 200 GeV@ 200 GeV

Au+Au→ π0 X (peripheral) Au+Au→ π0 X (central)

Peripheral data agree well with Strong suppression in

p+p (data&pQCD) plus Ncoll scaling central Au+Au collisions


AuAu (dAu) @ 200 GeV:AuAu (dAu) @ 200 GeV: high phigh p

TT (un)suppression ! (un)suppression !

x45 suppression

■ RAA << 1: well belowpQCD expectations for hard scattering xsections in vacuum

π0,h ±

■ AuAu suppression due to finalstate interactions absent in “control” dAu colls.

PRL 91, 0723ii (2003)

PHENIX, PRL 88, 022301 (2002)


High pHigh pT T suppression suppression ⇒⇒ QCD medium properties QCD medium properties■ Medium properties via data vs. � jet quenching� models:

Initial gluon densities (GLV):

dNg/dy = 1400+270

Transport coefficients

■ Other models: Temperatures [AMY]: T ~ 0.4 GeV [G. Moore], Opacities: <n> = L/λ ≈ 3 � 4 [Levai et al.]

Energy losses: dE/dx≈ 0.25 GeV/fm (expanding), dE/dx|eff ≈ 14 GeV/fm (static) [X.N.Wang]

Large opacities imply fast thermalization.

All these values imply energy densities well above εcrit QCD in thermalized syst.

[BDMPS/PQM]

<q0> ~ 13.2+2.1 GeV2/fm

[Vitev & Gyulassy]

PHENIX, arxiv:0801.1655

-150

-3.2


High pHigh pT T suppression (I): hadron “universality”suppression (I): hadron “universality”

■ Photons are unsuppressed but π0,η,h± show a common suppression pattern (magnitude, pT, centrality, ...):

■ Same flat RAA ~ 0.2 up to 10 GeV/c

■ Universal suppression for light mesons consistent with quenching at partonic level prior to q,g fragmentation into leading meson according to vacuum FFs.

PRL 96, 202301 (2006)

✔✔


High pHigh pT T suppression (II): psuppression (II): pTTdependencedependence

■ Flat pTdependence described by parton energy loss models:

■ Underlying LPM interference for single gluon bremsstrahlung would give: ∆Eloss ~ log(pT)

■ Combination of diff. effects (convolution w/ realistic parton radiation energy distrib., local parton pT slope, nuclear PDFs ...) yields constant quenching factor.

PQM – A. Dainese, C. Loizides, G. PaicEPJ C 38, 461(2005)

GLV – I. Vitev 2005

✔✔


High pHigh pT T suppression (III): Excitation functionsuppression (III): Excitation function

■ c.m. energy dependence in agreement with parton energy loss in increasingly dense medium:

RAA ~ 1 @ √s ~ 20 GeV ⇒ dNg/dy ~ 400 , <q0> ~ 3.5 GeV2/fmRAA ~ 0.3 @ √s = 62 GeV ⇒ dNg/dy ~ 650 , <q0> ~ 7 GeV2/fmRAA ~ 0.2 @√s =200 GeV ⇒ dNg/dy ~ 1100 , <q0> ~ 14 GeV2/fm

[RAA @ SPS uses “revised” pp ref.]

Initial gluon density: Medium transport coeff.: SPSRHICRHIC

D.d'E., EJP C 43 (2005)295PHENIX, arXiv:0801.iii

AuAuCuCu

(less suppression in lighter systems)

✔✔


High pHigh pT T suppression (IV): centralitydependencesuppression (IV): centralitydependence

PQM – Loizides EPJ C 38, 461(2005)

■ Increasing centrality i.e. Npart ⇒ increased L, ρ ⇒ larger suppression ■ Theory predicts: log(RAA) ∝Npart

−2/3

■ Agreement data ↔ models as expected for diff. suppressions at diff. (geometrical) parton production points.

PHENIX, arXiv:0801.iii

nEXP~0.58±0.1 consistent with nTH~2/3

✔✔


High pHigh pT T suppression (V): pathlength dependencesuppression (V): pathlength dependence

∆φ = 0°

∆φ = 90°

No apparent Eloss for L< 2 fm“Corona effect” effect? V. Pantuev hepph/0506095

Lε

■ Parton Eloss pathlength ∝ L2 (static), L (expanding):

matter thickness

Less suppression inplane (“short” direction) More suppression outofplane (“long” direction)

~2 fm

Eloss approx. linear with L formost centralities,

PRC76, 034904 (2007)

✔✔


High pHigh pT T suppression (VI): nonAbelian naturesuppression (VI): nonAbelian nature

■ Gluons radiate ✕2 more than quarks:

■ TEST 1: At fixed pT & increasing √s (i.e. at lower x): increased fraction of gluons ⇒ increased quenching

NonAbelian energy loss modelpreferred over “nonQCD” (qloss=gloss)

Gluon: CA = Nc = 3Quark: CF =(Nc

21)/2Nc = 4/3

pT = 5 GeV/c, √s = 105500 GeV

CA /CF=2.25}

SPS=q

RHIC=q,g

LHC=g D.d'E., EJP C 43 (2005)295qrich

q,g~50%

✔✔


High pHigh pT T suppression (VI): nonAbelian nature ?suppression (VI): nonAbelian nature ?

■ TEST 2: A large fraction of highpT (anti)protons from gluonfragmentation ⇒ increased p over quenching

STAR, PRL 97, 152301 (2006)

■ But above 6 GeV/c, similar ,p suppression: no apparent stronger gluon energy loss

(Need new calculations, with latest baryon FF: AKK, DSS)

pT (GeV/ c)

p/ π

40% from gluons

90% p,p from gluons_

dAu

■ However, (anti)proton production not well “calibrated”: enhanced in “cold QCD matter” (extra nonpQCD mechanism ?)

✔✔


High pHigh pT T suppression (VII): Mass effect ?suppression (VII): Mass effect ?

⇒ HeavyQ expected to lose less energy than lightq.■ HighpT e± from heavyquark decays equally suppressed as pions: RAA~0.2 above ~6 GeV/c. Radiative energy loss fails to reproduce data.

■ less bottom fraction ? Additional quenching from collisional energy loss ? ⇒ need to directly reconstruct D (and B) mesons.

■ “Deadcone” effect: Massive quarks cannot radiate gluons at low angles (causality requirement: since vQ<c)

STAR, PRL (2006)

PHENIX, PRL (2006)

[Dokshitzer & Kharzeev]


High pHigh pT T single hadron suppression: summarysingle hadron suppression: summary

▪ Hadrons (but not ) above pT~5 GeV/c suppressed in central AuAu by a factor of ~5 wrt. “vacuum” (pp) or “cold QCD matter” (dAu) parton fragmentation.

▪ Magnitude of quenching consistent with parton energy loss model predictions in a very opaque system: dNg/dy~1400 or q~13 GeV2/fm

❤ Most observed properties of the quenching factor consistent with radiative Eloss: pT, centrality, √s, pathlength, “nonAbelianity”, ...

A few “glitches” in the canonical interpretation: ♦ no deadcone effect for heavyQ (collisional Eloss ?) ♦ ~2fm pathlength “unsuppression” (“corona” effect ?) ♦ (anti)protons not from gluon fragmentation (extra production ?)


High pHigh pT T suppression: outlook (CMS @ LHC)suppression: outlook (CMS @ LHC)

▪ Physics reach (PbPb @ 5.5 TeV, 0.5 nb1, HLT): spectra, RAA

pT~300 GeV/c (Slower rise in BDMPS than in GLV)

▪ RAA at the LHC not independent of pT: more sensitivity to energy loss distribution


II. HighpII. HighpTT dihadron dihadron correlations correlations


Jet reconstruction in Au-Au at RHIC ?Jet reconstruction in Au-Au at RHIC ?

▪ Full jet reconstruction w/ std algorithms is unpractical (but possible?) at

RHIC due to (i) low jet yields, (ii) large soft background (� underlying event� ):

p+p →jet+jet [√s = 200 GeV] Au+Au → X [√sNN = 200 GeV]


�� Jet physics� in Au-Au at RHICJet physics� in Au-Au at RHIC

▪ Alternative I : Study energy modifications suffered by the highest pT hadrons in (“leading” hadron of the jet) in AA compared to pp:




▪ Alternative II : Study the azimuthal correlations in AA relative to pp between highest pT hadron (“trigger”) & any other “associated” hadron:



Dijets via di-hadron Dijets via di-hadron ∆φ∆φ correlations: pp, dAu correlations: pp, dAu

▪ Study dijet events “statistically”: via typical backtoback azimuthal correlations of produced hadron pairs (h± – h±, π0,± – h±):

▪ Clear near-side (∆φ ~ 0) and

away-side (∆φ ~ π) jet signals: 35 GeV/c

d+Au

Nearside

awayside

23 GeV/c

p+p

dAu

pp

pTassoc = 23 GeV/c pT

assoc = 35 GeV/c

▪ Trigger: highest pT (leading) hadron.

▪ Associated ∆φ distribution (e.g. ”assorted”: 2 GeV/c < pT

assoc < pTtrigger)


Dijets via dihadron Dijets via dihadron ∆φ∆φ correlations: central AuAu correlations: central AuAu

▪ AuAu: trigger hadron: from parton at surface awayside hadron: from quenched parton

▪ Same analysis as in pp, dAu but: larger underlying event elliptic flow subtraction

▪ Main experimental findings:

“punchthrough” at high pT

Nearside: approx. unmodified

Awayside: “disappearance” at semihard pT

broadening/softening at low pT

“splitting” at intermediate pT


AuAu dihadron AuAu dihadron ∆φ∆φ correlations: semi-hard, low- p correlations: semi-hard, low- pTT

▪ “Jet remnants” reappear at low pT

as a broader/softened structure:pT trigg= 4 – 6 GeV/cpTassoc = 0.15 – 4 GeV/c

STAR, PRL90, 082302 (03)

1/N t

rigge

r dN/

d(∆φ

)

pT trigg= 4 – 6 GeV/cpTassoc > 2 GeV/c

1/N t

rigge

r dN/

d(∆φ

) ∆φ (radians)

STAR, PRL95,152301(05)

▪ Awayside peak disappears: “monojet” like topology:

<pT> awayside hadrons (pp) ~ 1. GeV/c<pT> awayside hadrons (AuAu) ~ 0.7 GeV/c<pT> inclusive hadrons (AuAu): ~0.6 GeV/c


AuAu dihadron AuAu dihadron ∆φ∆φ correlations: away-side splitting correlations: away-side splitting

▪ Strongly modified awayside correlations at intermediate pT's : (1) Awayside “dip” at (2) Excess of activity (“double peak”, “shoulders”) at: ±1.1 rad

arXiv:0801.iii

0-12%

012%2.5 < pT,trig < 4.0 GeV/c1.0 < pT,assoc < 2.5 GeV/c

▪ Splitting angle doesn't vary much in wide range of centralities

(rads)

arXiv:0801.iii


AuAu dihadron AuAu dihadron ∆φ∆φ correlations: splitting interpretations correlations: splitting interpretations

▪ Large angle gluon rad.

A. Polosa, C. Salgado

Also: Vitev, Phys. Lett. B630 (2005)

Quenchedjet scatters through medium radiates largeangle gluon (“Mercedes” topology)

▪ But also: deflected jets ...

▪ Mach cone

T. Renk, J. Ruppert

hepph/0411315 Casalderrey,Shuryak,Teaneynuclth/0406018 Stoeckerhepph/0503158 Muller,Ruppertnuclth/0503028 A. K. Chaudhuri

▪ Cerenkov radiation

I. Dremin;V. Koch,A. Majumder, XN. Wangnuclth/0507063

Quenchedjet generates a sonic shockboom whilepropagating thru medium. Speedofsound accessible:

Quenchedjet radiates at fixed angle when traversing the medium at v > c. Gluondielectric coeffic. accessible:

( ) nem1cos =θ

cos M scθ =


AuAu dihadron 3-particle AuAu dihadron 3-particle ∆φ∆φ correlations: splitting correlations: splitting

∆φ1

3

∆φ12

0 π 2π

π

2π

Conelike structure

in each event

▪ 3particle help discriminate among various physics mechanisms:

However: Large backgrounds , background shapes not s im p le

Mediumaw ay

near

deflected jets

aw ay

near

Medium

Mach cone

∆φ12

0 π 2π

2π∆φ1

3

πEventbyevent deflection of jets

[M.v Leeuwen, QM06]


AuAu dihadron 3-particle AuAu dihadron 3-particle ∆φ∆φ correlations: results correlations: results

Au+ Au 0- 12%

(∆φ12- ∆φ13)/ 2

(∆φ12+ ∆φ13)/ 2- π

PHENIX Preliminary

C. Prun eau , J. UleryC. Zh an g, N. Ajitan an d

∆ϕ1

3

Cumulant analysis:ModelindependentNonzero 3particle structure

Jet+background analysis:Modeldependent, more sensitiveOffdiagonal peaks consistent with conical emission

(Different coordinates)No ‘deflectedjet peak’consistent with conical emission

∆ϕ12

Conelike emission favoured

3 < pT,t r ig < 4 GeV/ c

1 < pT,as s oc < 2 GeV/ c

[M.v Leeuwen, QM06]


Jet fragmentation: azimuthal � charge ordering�Jet fragmentation: azimuthal � charge ordering�

▪ Strong dynamical charge correlations are expected in jet fragmentation:

▪ Compare ++ and correlations to +

▪ Similar charge ordering observed in pp, AuAu & jetfragmentation MC.

pT > 4 GeV/c: same hadron production mechanism in central AuAu & pp

STAR, PRL , (2002)


High pHigh pT T dihadron correlations: summarydihadron correlations: summary

▪ HighpT 2,3 hadron correlations: allow access mediummodified dijets

▪ Jetlike correlations clearly present: nearside shape, charge ordering

▪ Awayside associated hadrons strongly modified: Low pT: yield strongly enhanced, softened & broadened MidpT: doublepeak structure with conicallike emission at ~1.1 rad Semihard pT: awayside peak strongly suppressed HighpT (pT~8 GeV/c): awayside peak reappears (“punchthrough”)

▪ Rich phenomena at intermediate pT: Tantalizing connections to collective medium response to hard partons (speed of sound, index of refraction, ...) but theorydata comparison challenging.


III. Jet reconstruction, III. Jet reconstruction, jet, jet, fragmentation functionsfragmentation functions


Backup slidesBackup slides


d+Au, 40100%

Au+Au, 05%

STAR preliminary

3 < pT(trig) < 6 GeV2 < pT(assoc) < pT(trig)

[D. Magestro, HP'04]

Dihadron Dihadron ∆η∆η correlations: AuAu (200 GeV) correlations: AuAu (200 GeV)

Significant broadening of pseudo-rapidity

correlations in AuAu compared to pp,dAu. (“stretching” of jet cone along η).

Coupling of g radiation w/ longitud. expanding medium?STAR preliminary p+p

Au+Au, 05%

nearside width


Dijets via dihadron Dijets via dihadron ∆φ∆φ correlations: central AuAu correlations: central AuAu

Ajitanand, ICPAQGP'04and nuclex/0501025

▪ Delicate subtraction procedure (esp. in finite acceptances).

▪ Same dNpair/d analysis as in pp (dAu) but 2 extra � complications�:

(1) Increased � underlying event� background

(2) Collective elliptic flow (harmonic) contribution


Dihadron Dihadron ∆φ∆φ correlations: AuAu away-side splitting correlations: AuAu away-side splitting

PHENIX (nucl-ex/0507004)

p er ip hera l: norm a l je t p a t tern

Emergence of a Volcano Shape

Correlation of soft ~1-2 GeV/c jet partnersCorrelation of soft ~1-2 GeV/c jet partners


Dihadron Dihadron ∆φ∆φ correlations: splitting correlations: splitting

Double peak structure at π ± 1.2 rad reminiscent of Mach wave conical shock (“sonic boom”) in medium ⇒ speed of sound accessible

33.0)(1∫ ττ

τ sf

avs cdc

cos M scθ =

θM Trigger

Mach cone:

θ = arccos(<cs>) ~ 1.2 rad

(timeaveraged)

~ θexp

→ HRG (cs~√0.2)

→ phase transition (cs~0.)

→ QGP (cs~1/√3)

= ~<cs>


Jet properties from dihadron correlationsJet properties from dihadron correlations

Jet “width” j T :

Dijet acoplanarity k T:

(1) 2hadron correlation function:

(2) Fit to 2gaussians: nearside σN, farside σF widths

(3) Extraction of jT, kT from σN, σF via [*], [**] (and dN/dxE from YieldN,F)

⇒

[*]

[**]

nearside farside

[details in J.Jia, nuclex/0409024]


Mean transverse momentum of jet hadrons Mean transverse momentum of jet hadrons (j(jTT): pp, dAu): pp, dAu

Jet (nearangle) “width” jT :jT

p+p

Pythia + GEANT

< jT> ~ 500 MeV/c (from full jet reco) p+p

< jTy> ~350 MeV/c ≡ < jT> ~ 500 MeV/c

• < jT> ~ 500 MeV/c: Agreement between RHIC and ISR data.

• No apparent difference between dAu and pp.

• Fragmentation not affected by cold QCD medium.

[J.Rak, QM'04]


Di-jet acoplanarity (� intrinsic� kDi-jet acoplanarity (� intrinsic� kTT) : pp, dAu) : pp, dAu

Intrinsic kT (dijet acoplanarity):

Tk

Jet 2

Jet 1

∆ϕ

⟨z⟩ = 0.75 taken as constant

• Nonnegligible pp kT broadening: <kTy> ~ 1.1 GeV/c (not observed in high pT spectra <kT>pair≠<kT>incl)

• Nonnull (but small) dAu <kT>nuclear

(constraints models of multiple scattering in cold nuclear medium)

nuclearTppTdAuT kkk 222

R=0.35

d+Au

= +

∆φ=0.22±0.02±0.06

∆φ=0.31±0.05±0.06

(from full jet reco: ET~13 GeV)


Di-jet acoplanarity (� intrinsic� kDi-jet acoplanarity (� intrinsic� kTT): Excitation function (pp)): Excitation function (pp)

Dihadron in pp @ RHIC<kT> ~ 1.8 GeV/c

sqrt(s)dependence of <kT>pair:

(Logarithmic) increase with sqrt(s) consistent with growing gluon radiation contribution (not just intrinsic parton Fermi motion).


Jet properties (jJet properties (jTT, k, k

TT): AuAu (200 GeV)): AuAu (200 GeV)

Preliminary

pp <z><|kTy|>

pp <|jTy|>

pTtrigg =2.5 – 4.0 GeV/c , pTassoc = 1.0 – 2.5 GeV/c

Centrality dependence of ⟨|jTy|⟩ and ⟨z⟩ ⟨|kTy|⟩ in Au+Au:

<jT>AuAu~ <jT>pp: nearside fragmentation unaffected by QCD medium.

Significant kT broadening (kT~3 GeV/c) in AuAu (strongly centrality dependent) indicating substantial finalstate rescattering of awayside fragmenting parton.

[J.Rak, QM'04]


AdS/CFT correspondence and sQGP propertiesAdS/CFT correspondence and sQGP properties

Classical gravity limit

NN = 4 Super-Yang-Mills theory in 4d with SU(NC)

Ap p ly to both d ynam ical and therm od ynam ic observables .

YM observables at in fin ite NC and in fin ite coup ling can be com p uted us ing class ical gravity

A s t r ing theory in 5d Ad S

Fin ite tem p eratu reLarge NC and

s t rong coup ling lim it

Black hole in Ad S5


BDMPS transport coefficient (q) in N=4 SYMBDMPS transport coefficient (q) in N=4 SYM

( )( )

33

45

432/3

69.26ˆ TNTq cSYMSYM αλπ ≈Γ

Γ=

/fm.GeV 4.5ˆ 2=SYMq MeV TCN s 300 ,21 ,3 === α• Take:

Black hole in AdS spacetime: radial coordinate r,• horizon: r=r0

• constant r surface: (3+1)dim Minkowski spacetime

horiz on

€

r0€

r=∞

Recipe: (i) Non pQCD definition of qhat:(ii) Compute qhat in strongly coupled SuperYangMills theory using AdS/CFT

Our (3+1)dim world, Wilson loop C in our world

: area of string worldsheet with boundary C

€

S(C)


Drag force for heavy quarks in N=4 SYMDrag force for heavy quarks in N=4 SYMHerzog, Karch, Kovtun, Kozcaz, Yaffe; Gubser, …….

Drag force for a heavy quark moving in the medium:

CasalderreySolana, Teaney

Fluctuationdissipation theorem

Diffusion coefficient:

Note: D can not be used to find q̂

It is possible to analyze the energy flow pattern (indications of conical flow)

Fluctuationdissipation theorem assumes the quark is in equilibrium with the medium: does not apply to high energy jet

J. J. Friess, S. S. G ubser and

G . M ichalogiorgakis,arXiv:hepth/0605292.

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