Thermal Photons in Strong Interactions

Ralf RappCyclotron Inst. + Physics Dept.

Texas A&M UniversityCollege Station, USA

College Station, 24.09.04

Introduction I: E.M. Probes in Strong Interactions

0 0.05 0.3 0.75 [GeVfm-3] 120 150-160 175 T [MeV] ½ 20 50 hadron

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

• -ray spectroscopy of atomic nuclei: collective phenomena• DIS off the nucleon: - parton model, PDF’s (high Q2) - nonpert. structure of nucleon [JLAB] • thermal emission: - compact stars (?!) - heavy-ion collisions What is the electromagnetic spectrum of matter?

1. Introduction

2. Thermal Photon Emission Rates 2.1 Generalities 2.2 Quark-Gluon Plasma: Complete LO

2.3 Hadronic Matter: - Meson Gas - Baryonic Contributions - Medium Effects

3. Relativistic Heavy-Ion Collisions 3.1 Nonthermal Sources 3.2 Thermal Evolution 3.3 Comparison to SPS and RHIC Data

4. High-Density QCD: Colorsuperconductor

5. Conclusions

Outline

Introduction II: Electromagnetic Emission Rates

Tiqx jxjexdiqΠ )0()()( emem

4em E.M. Correlation Function:

e+

e-

γ

Bee fxqdd

dN 244

Bfxqdd

dNq

430

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: depend. on T, B, ; medium effects, …• system evolution: V(), T(), B() ; transverse expansion, …

• nonthermal sources: e+e-: Drell-Yan, open-charm; : initial/ • consistency! pre-equil.

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

2.2 Quark-Gluon Plasma“Naïve” Leading Order Processes: q + q (g) → g (q) + γ

T

qT

qd

dRq

s

Ts 0/q-2230 4

912.2lne

30

[Kapusta etal ’91, Baier etal ’92]

But: other contributions to OO(αs)

collinear enhanced Dg=(t-mD2)-1 ~ 1/αs

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

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

q

gq

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]

2.3.6 Hadron Gas vs. QGP Emission• complete LO QGP rate ~2-3 above tree-level rate • in-med HG + Meson-Ex (bottom-up) ≈ complete LO QGP (top-down)

“quark-hadron duality” ?! • Similar findings for thermal dilepton rates

not yet understood …

“Freeze-Out” Hadron Gas

QGP ?!

Au + Au

3. Relativistic Heavy-Ion Collisions

Au + Au → X

e+

e-

Signatures of the QGP?• Suppression of J/ Mesons

• Decays of -Mesons

• Photons …

J/

3.1 Nonthermal Sources

Initial hard production: pp → γX

scaling with xT=2pT /√s , + power-law fit [Srivastava ’01]

Nuclear Effects: pA → X

•“Cronin”: gaussian kt-smear.• cf. pA → πX• AA: <kt

2>AA≈ 2<kt2>pA

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

3.3 Comparison to Data I: WA98 at SPSHydrodynamics: QGP + HG

[Huovinen,Ruuskanen+Räsänen ’02]

• T0≈260MeV, QGP-dominated

• still true if pp→X included

[Turbide,RR+Gale’04]

Expanding Fireball + Initial

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

3.3 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 ?!

3.3 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

4. Photon Emission from Colorsuperconductor

Cold Quark Matter → (qq) Cooper pairs, qq≈100MeV

q » ms2 : u-d-s symmetrically paired (Color-Flavor-Locking)

iral symmetry broken, Goldstone bosons,

m2 ~ mq

2 ≈ (10MeV)2

Effective theory descriptionof “hadronic” processes:

γ

γ

Photon Emissivities

exceeds e+e-→γγ for T≥5MeV[Vogt,Ouyed+RR]

5. Conclusions

• significant progress in E.-M. radiation from QCD matter: - QGP: soft collinear enhancement → complete leading order - HG: more complete (strangeness, baryons, t-chan, FF’s)

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

• phenomenology for URHIC’s compares favorably with existing data

• consistency with dileptons

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

Additional Slides

Photon Properties in Colorsuperconductors

(i) (770)

+>

>

B*,a1,K1...

N,,K…

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

Significance of high B at low M Elab=20-40AGeV optimal?!

2.2.2 1± Mesons:

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

(i) Check: in Vacuum and in Nuclei

),(),()2(

4)( 03

3

0 qpqEGEfpd

qG NNpN

N

)(Re

)(Imtan)( 1

33 MG

MGM

232

2

),(3

2)( cmcm

NN kFkM

M

m

fM

→ ok !

(ii) (1232) in URHICs

broadening: Bose factor, →B repulsion: N-1, NN-1

not yet included: (N→ ),( pEGmedN

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)

2.2.6 Observables in URHICs

(i) Lepton Pairs (ii) Photons

),(1

023

2

4Tqf

Mqd

dR Bee

Im Πem(M,q) ),( 0230 Tqfqd

dRq B

Im Πem(q0=q)

e+

e- γ

baryon density effects!

[Turbide,Gale+RR ’03]

• consistent with dileptons• Brems with soft at low q?