r Mesons in Medium at RHIC + JLab

Mesons in Medium at RHIC + JLab

Ralf Rapp Cyclotron Institute +

Dept. of Physics & Astronomy Texas A&M University College Station, USA

Theory Center SeminarJefferson Lab (Newport News, VA), 28.03.11

1.) Introduction: QCD Hadron and Phase Structure

• Electromagn. spectral function - √s ≤ 1 GeV : non-perturbative - √s ≥ 2 GeV : pertubative (“dual”)

• Disappearance of resonances ↔ phase structure changes: - hadron gas → Quark-Gluon Plasma - realization of transition?

√s=M

e+e → hadrons

)T,q(fMqdxd

dN Bee023

2em

44 Im Πem(M,q;B,T)

• Thermal e+e emission rate from hot/dense matter (em >> Rnucleus )

• Temperature? Degrees of freedom?• Deconfinement? Chiral Restoration?

1.2 Intro-II: Low-Mass Dileptons at CERN-SPS

CERES/NA45 [2000]

mee [GeV]

• strong excess around M ≈ 0.5GeV (and M > 1GeV) • little excess in and region

NA60 [2005]

1.) Introduction

2.) Resonances + Chiral Symmetry Spontaneous Chiral Symmetry Breaking + Chiral Partners

3.) Meson in Medium Hadronic Lagrangian + Empirical Constraints Many-Body Theory + Spectral Functions

4.) Dilepton Spectra in Heavy-Ion Collisions Thermal Emission Rates, Lattice QCD Phenomenology in URHICs

5.) Dilepton Spectra in Nuclear Photo-Production Elementary Amplitude, CLAS Phenomenology

6.) Conclusions

Outline

2.1 Chiral Symmetry Breaking + Hadron Spectrum

“Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85]

Quark Level: Const. Mass Observables: Hadron Spectrum

• Mq* ~ ‹0|qq|0›

• chiral breaking: |q2| ≤ 1 GeV 2

-

350000 fm|qqqq||qq| LRRLCondensates fill QCD vacuum:

• energy gap• massless Goldstone mode• “chiral partners” split (½ GeV)

JP=0± 1± 1/2± 3/2±

(1700)N(1520)

(1232)

M

[GeV

]

• spectral distributions!

2.2 Q2-Dependence of Chiral Breaking

Axial-/Vector Mesons

pQCD cont.

F2-Structure Function (spacelike)

JLAB Data

≈ x

• average → Quark-Hadron Duality• lower onset-Q2 in nuclei?

[Niculescu et al ’00]

p

d• Weinberg Sum Rule(s)

)Im(Ims

dsf IA

IV

112

1.) Introduction





6.) Conclusions

Outline

3.1 -Meson in Vacuum and Hot/Dense Matter

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

[Chanfray et al, Herrmann et al, Urban et al, Weise et al, Oset et al, …]

• Pion Cloud

>>

R=, N(1520), a1, K1 ...

h=N, , K …

=• -Hadron Scattering

= +

[Haglin, Friman et al, RR et al, Post et al, …]

• constrain effective vertices: R→ h, scattering data (N→N, N/A)

• Vacuum: chiral Lagrangian +

→ P-wave phase shift, el.-mag. formfactor

• Hadronic Matter: effective Lagrangian for interactions with heat bath In-Medium -Propagator

3.2 Scattering Processes from Spectral Function↔ Cuts (imag. parts) of Selfenergy Diagrams:

N-1

>

N-1

meson-exchange scattering

resonanceexcitation

meson-exchange current

N →

N → → N

NN →

3.3 Constraints from Nuclear Photo-Absorption -absorption cross section in-medium spectral function

)q,M(D)qq(qA

)q(

N

absA 04

00

0 medem ImIm

NA

-ex

[Urban,Buballa, RR+Wambach ’98]

Nucleon Nuclei

• melting of 2.+3. resonances• quantitative determination of interaction vertex parameters

3.4 Spectral Function in Nuclear Matter

In-med. -cloud +N→B* resonances

N→B* resonances (low-density approx.)

In-med -cloud + N → N(1520)

Constraints:N , A N →N PWA

• strong broadening + small upward mass-shift• empirical constraints important quantitatively

N=0

N=0

N=0.50

[Urban et al ’98]

[Post et al ’02]

[Cabrera et al ’02]

3.5 Spectral Function in Heavy-Ion Collisions

• -meson “melts” in hot /dense matter• medium effects dominated by baryons

B /0

0 0.1 0.7 2.6

Hot+Dense Matter

[RR+Gale ’99]

Hot Meson Gas

[RR+Wambach ’99]

1.) Introduction





6.) Conclusions

Outline

“Freeze-Out”QGPAu + Au

4.1 Strong-Interaction Matter in the Laboratory

Hadron GasNN-coll.

Sources of Dilepton Emission:

• “primordial” (Drell-Yan) qq annihilation: NN→e+eX -

e+

e

• emission from equilibrated matter (thermal radiation) - Quark-Gluon Plasma: qq → e+e , … - Hot+Dense Hadron Gas: → e+e , …

-

• final-state hadron decays: ,→ e+e , D D → e+eX, … _

4.2 Thermal Dilepton Emission

Rate:e+

e-)T,q(f

Mqdxd

dN Bee023

2em

44

Im Πem(M,q;B,T)

Imem ~ [Im D+ Im D/10 + Im D/5]

M ≤ 1 GeV: non-perturbative M > 1.5 GeV: perturbativeIm em ~ Nc ∑(eq)2

√s=M

e+

e-

e+

e-

q

q

-

ee→had / ee→ ~ Im em(M) / M2

“Hadronic Spectrometer” (T ≤ Tc) “QGP Thermometer” (T > Tc)

4.2.2 Dilepton Rates: Hadronic vs. QGP dRee /dM2 ~ ∫d3q f B(q0;T) Im em

• Hadronic and QGP rates tend to “degenerate” toward ~Tc

• Quark-Hadron Duality at all M ?! ( degenerate axialvector SF!)

[qq→ee]-[HTL] F2-Structure Function

p

d

JLAB Data

[RR,Wambach et al ’99]

4.3 Lattice-QCD Dilepton Rate

• low-mass enhancement in lattice rate!• similar to hard-thermal-loop resummed perturbation theory

[Kaczmarek et al ’10]

[Braaten,Pisarski+Yuan ‘90]

dRee/d4q 1.4Tc (quenched) q=0

4.3.2 Euclidean Correlators: Lattice vs. Hadronic

]T/q[)]T/(q[

)T;q,q(dq

)T;q,(G VV 221

2 0

00

0

0sinh

coshIm

• Euclidean Correlation fct.

)T,(G

)T,(G

V

V

free

Hadronic Many-Body vs. Lat. [’02] Lattice [Kaczmarek et al ‘10]

• “Duality” of lattice (1.4 Tc) and hadronic many-body (“Tc”) rates?!

4.3.3 Back to Spectral Function

• corroborates approach to chiral restoration !?

-Im

em

/(C

T q

0)

4.4 Dileptons in Heavy-Ion Collisions

• invariant-mass spectrum directly reflects thermal emission rate: - M<1GeV: broadening - M>1GeV: Tslope ~ 160-180 MeV

+ Spectra at CERN-SPS In-In(158AGeV) [NA60 ‘09]

M[GeV]

Thermal Emission Rate

• Evolve rates over fireball expansion:

[van Hees +RR ’08]

qd

dRqqd

)(VddM

dN thermee

FB

thermee

fo

40

3

2 20

M[GeV]

4.4.2 Conclusions from Dilepton “Excess” Spectra

• thermal source (T~120-200MeV)

• M<1GeV: in-medium meson - no significant mass shift - avg. (T~150MeV) ~ 350-400 MeV

(T~Tc) ≈ 600 MeV → m

- driven by baryons

• M>1GeV: radiation around Tc

• fireball lifetime “measurement”: FB ~ (6.5±1) fm/c (semicentral In-In)

[van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08]

• approach seems to fail at RHIC

1.) Introduction





6.) Conclusions

Outline

5.1 Nuclear Photoproduction: Meson in Cold Matter

+ A → e+e X

[CLAS+GiBUU ‘08]

E≈ 1.5-3 GeV

e+

e

• extracted “in-medium” -width ≈ 220 MeV - small?!

5.2 Equilibrium Approach

N

(a) Production Amplitude: t-channel [Oh+Lee ‘04] + resonances ( spectr. fct.!)

[Riek et al ’08, ‘10]

(b) Medium Effects:

propagator in cold nuclear matter

- broadening much reduced with increasing 3-momentum

ee*NeeXA |D||T|f~

dMd

22

prod

N→ N

d → e+eX

Im D

[

1/M

eV2 ]

M[GeV]

+ CLAS

• average q ~ 2GeV average N(Fe) ~ 0.40

• free norm: 2 =1.08 vs. 1.55 in-med vs. vac spectral function• need low momentum cut + absolute cross section!

Density at Decay Point

5.2.2 Application to CLAS DataE≈1.5-3 GeV, uniform production points, decay distribution with in-med

• low-momentum yield small, but spectral broadening strong

3-Momentum Cuts Transparency Ratio

5.3 Predictions for Photoproduction

X.) Axialvector in Medium: Dynamical a1(1260)

+ + . . . =

Vacuum:

a1

resonance

InMedium: + + . . .

• in-medium + propagators• broadening of - scattering amplitude

[Cabrera et al. ’10]

6.) Conclusions• EM spectral function ↔ excitations of QCD vacuum - ideal tool to probe hot/dense matter

• Effective hadronic Lagrangian + many-body theory: - strong broadening in (baryonic) medium, suppresed at large momentum (CLAS!)

• Dileptons in heavy-ion collisions: - spectro- /thermo-meter (CERES, NA50,NA60) - melting at “Tc” = 160-190 MeV

→ quark-hadron duality?! hadron liquid?!

• Sum rules + axialvector spectral function to tighten relations to (partial) chiral restoration

• Future experiments at RHIC-2, FAIR +LHC; JLAB?!

4.2.4 Intermediate-Mass Dileptons: Thermometer• QGP or Hadron Gas (HG) radition? • vary critical temperature Tc in fireball evolution

• partition QGP vs. HG depends on Tc

(spectral shape robust: dilepton rate “dual” around Tc! )

• Initial temperature Ti ~ 190-220 MeV at CERN-SPS

green: Tc=190MeVred: Tc=175MeV (default)blue: Tc=160MeV

qq →

→ (e.g. a1 → )

-

4.4 Sum Rules and Order Parameters

)Im(ImsdsI AVn

n 2

102

122

2 031 q)q(αcI,I,fI,FrfI sπAππ

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

• QCD-SRs

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

Promising synergy of lQCD and effective models

• Weinberg-SRs: moments VectorAxialvector

sQ

)s(Ims

dsQ

)Q(Π

20

2

2

...

Q

)qq(C

Q

GQ)()Q( ss

s 6

2

4

22

2

2

22

3ln1

81

3.2.5 EM Probes in Central Pb-Au/Pb at SPS

• consistency of virtual+real photons (same em)

• very low-mass di-electrons ↔ (low-energy) photons[Srivastava et al ’05, Liu+RR ‘06]

Di-Electrons [CERES/NA45] Photons [WA98]

[Turbide et al ’03,van Hees+RR ‘07]

3.5.2 Rho, Omega + Phi Freezeout from pt-Spectra

• sequential freezeout →→• consistent with mass spectra

• freezeout = fireball freezeout

• adjust and freezeout contribution to fit pt-spectra

3.5.3 Composition of Mass Spectra in qt-Bins

• high qt ≥ 1.5GeV:

- medium effects reduced - non-thermal sources take over

low qt

high qt

intermed. qt

3.5 Dimuon pt-Spectra and Slopes

• check fireball evolution to fit slopes of excess radiation (▼) (thermal radiation softer by Lorentz-1/

• increase a┴ = 0.085/fm → 0.1/fm (viscous effects, larger grads. in In-In …)

5.2.5 NA60 Dimuons: pt-Slopes

• in-medium radiation “harder” than hadrons at freezeout?! (thermal radiation softer by Lorentz-1/• smaller Tch helps (larger Tfo)

• non-thermal sources (DY, …)?• additional transverse acceleration?• hadron spectra (pions)?

Tch=175MeVTch=160MeV

Tch=160MeVa┴ =0.1/fm

Tch=160MeVa┴ =0.085/fm

pions: Tch=175MeV a┴ =0.085/fm

pions: Tch=160MeV a┴ =0.1/fm

2.2 Chiral + Resonance Scheme

N+

N(1535)-

a1 N(1520)-

N(1900)+ (1700)-

(?) (1920)+

S

P

S

S SS

P SS (a1)S

• add S-wave pion → chiral partner• P-wave pion → quark spin-flip • importance of baryon spectroscopy

2

3S

2

1S

3.1 Axial/Vector Mesons in Vacuum

Introduce a1 as gauge bosons into free + +a1 Lagrangian

2

21 g)(gintL

1202 )]M()m(M[)M(D )(

EM formfactor

scattering phase shift

2402 |)M(D|)m(|)M(F| )(

)M(DRe)M(DIm

)M(

1-tan

|F|2

-propagator:

3.3 “Non-Thermal Dilepton Sources

→ relevant at M, qt ≥ 1.5 GeV (?)

• primordial qq annihilation (Drell-Yan): NN → e+eX

• mesons at thermal freeze-out (“blast-wave”):

- extra Lorentz- factor relative to thermal radiation - qt-spectra + yield fixed by fireball model

• primordial (“hard”) mesons: - schematic jet-quenching with abs fit to pions

-

• late decays: ,→ e+e , DD → e+eX, J/→e+e , …

_ f.o. + prim.

2.2 Electric Conductivity

)q,q(Imqq

e 020lim

32

0em00

2

em

• pion gas (chiral pert. theory)

em / T ~ 0.01 for T ~ 150-200 MeV

[Fernandez-Fraile+Gomez-Nicola ’07]

• quenched lattice QCD

em / T ~ 0.35 for T = (1.5-3) Tc

[Gupta ’04]

• soft-photon limit em30340230

)(T)q(

qdxd

dNq

3.2.3 NA60 Excess Spectra vs. Theory

• Thermal source does very well • Low-mass enhancement very sensitive to medium effects• Intermediate-mass: total agrees, decomposition varies

[CERN Courier Nov. 2009]

Documents

r Mesons in Medium at RHIC + JLab