Properties of Vector Mesons in Matter

- Theory and Phenomenology

Ralf Rapp

Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

19. Quark Matter Conference Shanghai, China, 16.11.06

1.) Introduction: Basic Questions

• Vector-meson propagators

Broader Impact: • Are , and alike?• cold vs. hot matter • in-medium hadrons + equation of state• phase transitions (condensates, f, susceptibilities, …)

122 ]mM[)T,;q,M(D VViV

Phenomenology: • production mechanism (elementary: p-A, -A, thermal: A-A) • competing sources (centrality, pT, √s, …)

T

iqx )(j)x(je)x(xdi)q(Π 0emem04

em E.M. Correlation Function:

Imem ~ [ImD+ImD/10+ImD/5]

qq_

4

KK

2.) Constraints from QCD Lattice Sum Rules

3.) Hadronic Spectral Functions Many-Body Theory Bare Parameters Dilepton Rates

4.) Dilepton Phenomenology in URHICs SPS (NA60, NA45) RHIC

5.) Conclusions

Outline

2.1 Lattice QCD: Susceptibilites

Quark-number susceptibilities:

[Allton etal. ’05]

22

20

)m(~)q(~~ ,I,q

I,qI,q

• “dropping” -mass at critical point?

• “smooth” spectral function across phase diagram?!

Isoscalar (“”) Isovector (“”)

2.2 Sum Rules and Order Parameters

)Im(ImsdsI AVn

n

210

21

222

031

q)q(αcI,I

,fI,FrfI

s

πAππ

[Weinberg ’67, Das etal ’67, Kapusta+Shuryak ‘93]

• QCD-SRs:

- lhs: OPE (condensates!) - rhs: spectral function, (0)=1⁄9(0)

[Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl etal ’97, Leupold etal ’98, Kämpfer etal ‘03 ,Ruppert etal ’05]

Promising synergy of lQCD and effective models!

220

2

2 0

Q

)(

sQ

)s(Ims

dsQ

)Q(Π

0.2%1%

• Weinberg-SRs: moments VectorAxialvector

Meson

>>

VB*,a1,K1

...

N,,K…

3.) Medium Effects I: Hadronic Interactions

DV(M,q;B ,T) = [M 2 - mV2 - VP- VB - VM ] -1V-Propagator:

[Chanfray etal, Herrmann etal, RR etal, Koch etal, Weise etal, Mosel etal, Eletsky etal, Oset etal, Lutz etal …]

VP = VB,VM=Selfenergies:V

Constraints: decays: B,M→ VN, V scattering: N/A, N→VN, …

B /0

0 0.1 0.7 2.6

[RR,Wambach etal ’99]

Meson “Melting” Switch off Baryons

3.2Spectral Functions from Free V-N/- Scattering

• fair model agreement (~ compatible with QCDSR)• -broadening somewhat less pronounced

[RR+Wambach ’99]

[Eletsky etal ’01]

[Eletsky etal ’01]-Meson -Meson

• ImV ~ ImTVN N + ImTV ~ VN,V + dispersion relation for ReTV

3.2 Medium Effects II: Dropping Mass

• Hidden Local Symmetry: -mass ↔ “Higgs” mechanism

• Vector Manifestation of Chiral Symmetry: L↔

• In-Medium: thermal -loops, m(0), g→0 (renormalization group)

- dropping -mass - vector dominance violated: a = 2 → 1

[Harada+Yamawaki ‘01]

~(a-2) ~a

• Open Issues: - “flash temperature” Tf ~ 0.7 Tc ( symm.!) - extrapolation to Tc

- no resonances, baryons [Sasaki+Harada ’06: P81]

EM Formfactor

0.85Tc

vac

3.3 Dilepton Emission Rates

• “matching” HG -QGP at ~Tc: “Quark-Hadron Duality” ?! (pQCD↔ chirally symmetric)• anti-/baryons important at RHIC• -meson more stable

)q,M(Im)T(fq

qd

MdM

dR Beeem

c 0

3

2

2

2

Isovector () at SPS

[qq→ee][qq+HTL]

--

Inclusive () at RHIC

4.) Dilepton Spectra in Heavy-Ion Collisions

• evolve over thermal fireball, isentropic QGP-Mix-HG• central In-In: T0-fo=195→120MeV, Tc=175MeV, FB=7fm

Acc),T;q,M(qdxd

dNq

qMd)(Vd

dMdN

i

thermll

FB

thermll

fo

44

0

3

0

Thermal Emission: +

• absolute norm., melting • M>0.9GeV: “4”→and • baryon effects essential

[van Hees+ RR ‘06]

4.2 Chiral Virial Approach vs. NA60• low-density expansion + chiral reduction • also: compare fireball vs. hydrodynamics

• good agreement fireball - hydro (pT-spectra!) • lack of broadening

[van Hees+RR ‘06] [Dusling,Teaney+Zahed ’06]

4.3 NA60 pT-Spectra vs. Hadronic Many-Body

• improved freezeout- (-factor!) + Drell-Yan (pT>1.5GeV) • approx. agreement (local slopes?!) See parallel talks by

H.van Hees, J.Ruppert

4.4 Pb-Au Collisions at SPS: CERES/NA45

• very low-mass di-electrons ↔ low-energy photons[Turbide etal.’03, Alam etal.‘01]

4.5 Dileptons at RHIC

• low mass: thermal! (mostly in-medium )• connection to Chiral Restoration: a1 (1260)→ , 3• intermed. mass: QGP vs. cc → e+e-X (softening?)-

[RR ’01]

[R. Averbeck, PHENIX]

QGP

[Toia etal. ’06]

5.) Conclusions

• Hot+Dense Hadronic Matter:

-broadening matured (melting at ~Tc → hadronic liquid!?)

• Differences between and (critical point)?!• NA45, NA60: - support “quark-hadron duality”

- (anti-)baryon-induced medium effects

Looking forward to further exciting developments …

• Chiral Restoration:

- direct (exp.): measure axialvector ()

- indirect (theo.): chiral + QCD sum rules

• HADES, RHIC, LHC, SPS-09, CBM, …, elementary reactions (cf. working group reports RHIC-II [nucl-ex/0611009], CBM [in prep.])

• “4“ states dominate the vacuum e.m. correlator above M ≈ 1.1GeV

• lower estimate: use vacuum 4 correlator

• upper estimate: O(T2) medium effect → “chiral V-A mixing”:

with

4.2.3 Intermediate-Mass Region

)q()q()()q( AVV001

21)T( c

[Eletsky+Ioffe ‘90]

[van Hees+RR ‘06]

42

[Leupold ’98, Ruppert etal ’05]

0.2% 1%

3.1.3 QCD Sum Rules + (770) in Nuclear Matter

)ss()(s

)s(DImg

m)s(Im

s0

2

4

18

dispersion relation for correlator: sQ

)s(Ims

dsQ/)Q(Π

20

22

• lhs: OPE (spacelike Q2): • rhs: hadronic model (s>0):

...Q

)qq(C

Q

GQ)(

s

ss

6

2

4

22

2

2

2 3ln1

81

[Shifman,Vainshtein+Zakharov ’79]

4-quark condensate!

3.1.2 (770) Spectral Function in Nuclear Matter

In-med -cloud +-N → B* resonances

Relativist.-N → B*(low-density approx)

In-med -cloud + -N → N(1520)

Constraints:N , A N →N PWA

• good agreement: strong broadening + small mass-shift up• constraints from (vacuum) data important quantitatively

N=0

N=0

N=0.50

[Urban etal ’98]

[Post etal ’02]

[Cabrera etal ’02]

3.1 Lattice QCD (QGP)

T=1.5Tc

• lQCD << pQCD at low mass (finite volume?)• currently no thermal photons from lQCD• vanishing electric conductivity!? but: [Gavai ’04]

Dilepton Rate ~ Im(,q=0)/2 EM Correlator Im(,q)/2

[Bielefeld Group ’02, ‘05]

3.) Medium Effects and Thermal Dileptons

4.6 Dropping-Mass Scenarios vs. NA60

• thermal fireball with absolute normalization

• dropping mass disfavored? • free decays at freezeout?• flash temperature? baryons? • chem. potentials? extrapolation to Tc?

[Brown+Rho ’91, Hatsuda+Lee ’92,…, Harada+Yamawaki ‘01]

HLS: [Sasaki+Harada ‘06]

(Tflash=122MeV)

4.2.5 Chiral Virial Approach vs. NA60 (central)

[Steele,Yamagishi+Zahed ’99]

[implementation van Hees+RR ’05]

5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS

Expanding Fireball + pQCD

• pQCD+Cronin at qt >1.6GeV T0=205MeV suff., HG dom.

• addt’l meson-Bremsstrahlung → K→K substantial at low qt

[Liu+ RR’05]

WA98 “Low-qt Anomaly”

[Turbide,RR+Gale’04]

4.2.2 In-In at SPS: Theory vs. NA60

• predictions based on -spectral function of [RR+Wambach ’99]

• uncertainty in fireball lifetime (±25% norm.); or: infer FB≈7fm/c !

• relative strength of thermal sources fix

• good agreement with melting, including pt dependence [van Hees +RR ‘06]