Dileptons at RHIC

Ralf RappCyclotron Inst. + Physics Dept.

Texas A&M UniversityCollege Station, USA

International CCAST Workshop“QCD and RHIC Physics”

Beijing, 10.08.04

… and the Quest for Chiral Symmetry Restoration

1. Introduction

2. Chiral Symmetry in QCD 3. E.M. Correlation Function + Thermal Radiation

4. Low-Mass Dileptons 4.1 Axial-/Vector Correlators

4.2 Medium Effects and Excitation Function

4.3 Lattice QCD

5. Intermediate-Mass Dileptons: QGP Radiation?

6. Perspectives for RHIC

7. Conclusions

Outline

1.) Introduction: Towards QGP Discovery

• So far: RHIC observables ↔ bulk properties of the produced matter:

- energy density ≈20GeVfm-3 ↔ jet quenching (high-pt) - thermalization + EoS ↔ hydrodynamics (v0,v2)

- partonic degrees of freedom ↔ coalescence (p/, v2-scal)

• Future: need to understand microscopic properties (phase transition, “QGP” !?):

- Deconfinement ↔ quarkonia (J/, Y, …) - Chiral Symmetry Restoration ↔ dileptons ( - temperature ↔ photons )

2.) Chiral Symmetry in QCD: Vacuum

2

4

1aq Gq)m̂Aigi(q QCDL SU(2)L× SU(2)R

invariant (mu,d≈0)

Spontaneous Breaking: strong qq attraction Bose Condensate fills QCD vacuum!

0 LRRL qqqqqq >

>

>

>qLqR

qL-qR

-[cf. Superconductor: ‹ee›≠0 Magnet ‹M›≠0 , … ]

-

Profound Consequences:• energy gap: ↔ mass generation!

• massless Goldstone bosons 0,±

• “chiral partners” split, M≈0.5GeV:

qqm*qqq 2

JP=0± 1± 1/2±

2.2 “Melting” the Chiral Condensate

How?

Excite vacuum (hot+dense matter)

• quarks “percolate” / liberated Deconfinement • ‹qq› condensate “melts”, iral Symm. chiral partners degenerate Restoration(-, -a1, … medium effects → precursor!)

0 0.05 0.3 0.75 [GeVfm-3] 120, 0.50 150-160, 20 175, 50 T[MeV], had

PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD

-

1.0 T/Tc

m‹qq›-lattice QCD

2.3 Dilepton Data at CERN-SPS

Low Mass: CERES/NA45 Intermediate Mass: NA50

Central Pb-Pb 158 AGeV

opencharm

Drell- Yan

Mee [GeV] M [GeV]

• strong excess around M≈0.5GeV• little excess in region

• factor ~2 excess• open charm? thermal? …

3.) Electromagnetic Emission Rates

Tiqx jxjexdiqΠ )0()()( emem

4em E.M. Correlation Function:

e+

e-

γ

)T(fqd

dR Bee 24

)T(fqd

dRq B

30

Im Πem(M,q)

Im Πem(q0=q)

= O(1)= O(1)

= O(= O(ααs s ))

also: e.m susceptibility (charge fluct): χ = Πem(q0=0,q→0)

In URHICs:• source strength: dependence on T, B, , medium effects, …• system evolution: V(), T(), B() , transverse expansion, …• nonthermal sources: Drell-Yan, open-charm, hadron decays, … • consistency!

3.2 Two Regimes of Thermal Dilepton Radiation

)M(ImTdM

dRV

dMd

dNem

T/qeeFB

ee

0

3

1 e

q0≈0.5GeV Tmax≈0.17GeV , q0≈1.5GeV Tmax=0.5GeV

Thermal rate:

qq

4.) Low-Mass Dileptons + Chiral Symmetry

Im Πem(M) ~ Im D(M) vector-meson spectral functions

dominated by -meson → chiral partner: a1(1260)

)Im(Im2AVs

dsf

Chiral breaking: Q2 < 3GeV2

Vacuum At Tc: Chiral Restoration

pQCD cont.

+>

>

B*,a1,K1...

N,,K…

Constraints:- branching ratios B,M→N, - N,Aabsorpt.,N→N- QCD sum rules, lattice

4.2 Vector Mesons in Medium: Many-Body Theory

• -meson “melts” in hot and dense matter

• baryon densityB more important than temperature

(i) SPS ConditionsB/0 0 0.1 0.7 2.6

D(M,q:B,T)=[M2-m2--B-M]-1

(ii) Vector Mesons at RHIC

baryon effects important even at Bnet=0 :sensitive to Btot=+B , more robust ↔ OZI -

Dilepton Emission Rates

Quark-Hadron Duality ?!

in-med HG ≈ in-med QGP !

[qq→ee][qq+O(s)]

--

Lower SPS Energy

• enhancement increases!• precision test by NA60!?

4.3 Low-Mass Dileptons in URHICs

Top SPS Energy

• baryon effects important!

BEVALAC/SIS Energy

DLS

• enhancement increases still: DLS puzzle → HADES!?

4.4 Current Status of a1(1260)

>

> >

>

N(1520)…

,N(1900)…

a1 + + . . .

Exp: - HADES (A): a1→(+-) - URHICs (A-A) : a1→

)DImg

mDIm

g

m(

s

dsf a

a

a1

1

1

2

4

2

42

4.5 Comparison of Hadronic Models to LGT

)2/sinh(

))2/1(cosh(),(Im),(

0

00

00 Tq

TqTqdqT

calculate

integrate

More direct!

Proof of principle, not yet meaningful (need unquenched)

Ti≈300MeV, QGP-dominated

Hydrodynamics (chem-eq)

[Kvasnikowa,Gale+Srivastava ’02]

5.) Intermediate-Mass Dileptons: NA50 (SPS)e.m. corr. continuum-like: Im Πem~ M2 (1+s/+…)

Ti≈210MeV , HG-dominated

Thermal Fireball (chem-off-eq)

[RR+Shuryak ’99]

QGP + HG!

• low mass: thermal dominant• int. mass: cc e+X , rescatt.? e-X

[RR ’01]

-

[R. Averbeck, PHENIX]

6.) Dilepton Spectrum at RHIC

MinBias Au-Au (200AGeV)

run-4 results eagerly awaited …

thermal

8.) Conclusions

• Thermal Dileptons in QCD: em(q0,q,B,T)

- low mass: , chiral restoration ↔ -a1 degeneracy

- intermediate mass: QGP radiation (open charm?!) ( - thermal photons )

• extrapolations into phase transition region in-med HG and QGP shine equally bright lattice calculations? deeper reason?

• phenomenology for URHIC’s promising; precision data+theory needed for definite conclusions

• much excitement ahead: PHENIX, NA60, HADES, ALICE,… and theory!

Additional Slides

7.) Thermal Photons

Quark-Gluon Plasma

q

gq

But: other contributions in OO(αs)

collinear enhanced Dg=(t-mD2)-1~1/αs

[Aurenche etal ’00, Arnold,Moore+Yaffe ’01]

Bremsstrahlung Pair-ann.+scatt. + ladder resummation (LPM)

“Naïve” LO: q + q (g) → g (q) + γ

[Kapusta,Lichard+Seibert ’91, … , Turbide,RR+Gale’04]

Hot and Dense Hadron Gas

γ

a1,

Im Πem(q0=q) ~ Im Dvec(q0=q)

Low energy: vector dominance

High energy: meson exchange

Emission Rates

Total HG ≈ in-med QGP ! to be understood…

7.2 Perspectives on Photon Data at RHIC

• large “pre-equilibrium” yield from parton cascade (no LPM)• thermal yields ~ consistent• QGP undersat. small effect

Predictions for Central Au-Au PHENIX Data

• consistent with pQCD only• disfavors parton cascade• not sensitive to thermal yet

4.2 Comparison to Data I: WA98 at SPS

Hydrodynamics: QGP + HG[Huovinen,Ruuskanen+Räsänen ’02]

• T0≈260MeV, QGP-dominated

• still true if pp→X included

[Turbide,RR+Gale’04]Expanding Fireball + pQCD

• pQCD+Cronin at qt >1.5GeV T0=205MeV suff., HG dom.

4.2 Comp. to Data II: WA98 “Low-qt Anomaly”

[Turbide,RR+Gale’04]

Expanding Fireball Model

• current HG rate much below• 30% longer FB 30% increase

Include→ S-wave

• slight improvement• in-medium “” or ?!

2. Thermal Photon Radiation2.1 Generalities

),( 0230 Tqfqd

dRq B

Emission Rate per 4-volume and 3-momentum

γ

Im Πem(q0=q)T

transverse photon selfenergymany-bodylanguage:

kinetictheory:

γ

2

)](1[)()(

(...))2(8

321

)4(9

3,2,1

3,2,13

30

EfEfEf

E

pdN

qd

dRq

|M||M|22

in-medium effects,resummations, …

cut

γ

γ

a1

a1

• Photon-producing reactions:

mostly at dominant (q0>0.5GeV) gauge invariance! q0<0.5GeV a1-strength problematic

[Song ’93, Halasz etal ’98,…]

2.3.1 Hot Hadronic Matter: --a1 Gas

),(][][2

1)]2()[(

422

022

2

'LL ATrmFTrUUMUDTr

f

Chiral Lagrangian + Axial/Vector-mesons, e.g. HLS or MYM:

• (g0,m0,,) fit to ma1 , ,a1

D/S and a1→γ) not optimal HLSMYMKap.’91 (no a1)

• quantitative analysis: account for finite hadron size• improves a1 phenomenology

• t-channel exchange: gauge invariance nontrivial [Kapusta etal ’91]

simplified approach: [Turbide,Gale+RR ’04]

2.3.1.b Hadronic Formfactors

2

2

2

2

2

tΛ

ΛF(t) with

,...a,xmqt x 102

Factor 3-4 suppressionAt intermediate andHigh photon energies

2.3.2 Further Meson Gas Sources

(i) Strangeness Contributions: SU(3)F MYM

(iii) Higher Resonances

Ax-Vec: a1,h1→, Vec: ,’,’’→ other: (1300)→ f1→ , K1→K K*→K a2(1320)→

γ

KK

γ

K* K~25% of

→~40% of→

(ii) t-Channel γ

G large!

potentially important …[Turbide,Gale +RR ’04]

2.3.3 Baryonic Contributions

• use in-medium–spectral funct:

• constrained by nucl. -absorption:

)qq(DImg

mIm med 02

4

em

>

>

B*,a1,K1...

N,,K…

)qq(ImqA

)q(

N

absA 0

0

0 4em

N → N,

N →

NA

-ex

[Urban,Buballa,RR+Wambach ’98]

2.3.3(b) Photon Rates from Spectral Function:

Baryons + Meson-Resonances

• baryonic contributions dominant for q0<1GeV (CERES enhancement!)

• also true at RHIC+LHC: at T=180MeV, B=0

B=220MeV031 .BB

2.3.4 HG Emission Rates: Summary

B=220MeV

[Turbide,RR+Gale ’04]

• t-channel (very) important at high energy

• formfactor suppression (2-4)

• strangeness significant

• baryons at low energy

2.3.5 In-Medium Effects

• many-body approach: encoded in vector-spectral function, relevant below M , q0 ~ 1-1.5 GeV

• “dropping masses”: large enhancement due to increased phase space [Song+Fai ’98, Alam etal ’03]

unless: vector coupling decreases towards Tc (HLS, a→1) [Harada+Yamawaki ’01, Halasz etal ’98]

3.2 Thermal Evolution: QGP→ Mix→ HG

QGP: initial conditions [SPS]

• 0=1fm/c → 0=0.5fm/c: ~2-3• s=CdQGT3; dQG=40 → 32: ~2• pre-equilibrium?!

HG: chemistry [LHC]

T

[GeV

]• conserved BB use entropy• build-up of >0 (N=const)• accelerated cooling

HG: chemistry and trans. flow

• R~exp(3) for → , …• yield up at low qt , down above • large blue shift from coll. flow

Photon Properties in Colorsuperconductors

2.2.4 In-Medium Baryons: (1232)

long history in nuclear physics ! ( A , A )

e.g. nuclear photoabsorption: M, up by 20MeV

little attention at finite temperature

-Propagator at finite B and T [van Hees + RR ’04]

in-medium vertex corrections incl. g’-cloud, (“induced interaction”)(1+ f - f N) thermal -gas

→N(1440), N(1520), (1600)

+ + + + ...

>

>>

> >>

>> NN-1 N-1

3.3 Dilepton Spectrum at RHIC

4.3 Perspectives on Data III: RHIC

• large “pre-equilibrium” yield from parton cascade (no LPM)• thermal yields ~ consistent• QGP undersat. small effect

Predictions for Central Au-Au PHENIX Data

• consistent with initial only• disfavors parton cascade• not sensitive to thermal yet