Introduction to Dileptons and inMedium Vector Mesons

1
Introduction to Dileptons and in-Medium Vector
Mesons
Ralf Rapp Cyclotron Institute Physics
Department Texas AM University College Station,
Texas USA 2 Lectures at ECT EM-Probes
Workshop Trento, 04. 06.06.05
2
1.) Introduction 1.1 Electromagnetic Probes in
Strong Interactions

• g-ray spectroscopy of atomic nuclei collective
  phenomena,
• DIS off the nucleon - parton model, PDFs
  (high q2lt 0)
• - nonpert.
  structure of nucleon JLAB
• Drell-Yan pp ? eeX (q2gt 0
  symmetry, nucl. shadowing)
• thermal emission - compact stars (GRBs?!)
• - heavy-ion
  collisions SPS, RHIC, LHC, FAIR
• g
  (q20) , ee- (q2gt0)

What is the electromagnetic spectrum of QCD
matter?

3
Creating Strong-Interaction Matter in the
Laboratory
Au Au
NN-coll.
Freeze-Out
Hadron Gas
QGP
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1.2 Objective Use Dileptons to Probe the Nature
of Strongly
Interacting Matter

• Bulk Properties
• Equation of State
• Microscopic Properties
• - Degrees of Freedom
• - Spectral Functions
• Phase Transitions
• (Pseudo-) Order Parameters

• ? (some) Key Questions Can we
• infer the temperature of the matter?
• establish in-medium modifications of r , w , f
  ? ee- ?
• extract signatures of chiral symmetry
  restoration?

5
1.3 Intro-III EoS and Hadronic Modes

• All information encoded in free energy
• EoS , ,
  
• correlation functions

hadronic current
? iso/scalar pp pairs!
? dileptons, photons!
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1.4.1 Schematic Dilepton Spectrum in HICs

• Characteristic regimes in invariant ee- mass,
  M2(pe pe- )2
• Drell-Yan power law Mn
  ? high mass
• thermal exp(-M/T) - QGP (highest T) ?
  intermediate mass
• - HG
  (moderate T) ? low mass

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1.4.2 Dilepton Data at CERN-SPS
Low Mass CERES/NA45
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Outline
2. Thermal Electromagnetic Emission Rates -
Vacuum Quarks vs. Hadrons, Vector Mesons 3.
Chiral Symmetry in QCD - Spontaneous Breaking,
Hadronic Spectrum, Restoration 4. (Light) Vector
Mesons in Medium - Hadronic Many-Body
Approach - Dropping Mass, Chiral
Restoration?! 5. QGP Emission 6. Thermal Photons
7. Dilepton Spectra in Heavy-Ion Collisions -
Space-Time Evolution Comparison to SPS and RHIC
Data 8. Summary and Conclusions
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2.) Electromagnetic Emission Rates
E.M. Correlation Function
Im ?em(M,q)
Im ?em(q0q)
also e.m susceptibility (charge fluct.) ?
?em(q00,q?0)

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

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2.2 E.M. Correlator in Vacuum s(ee-?hadrons)
e e-
p - p
r I 1
r
2p 4p ...
pp
e e-
h1 h2
r w f
KK
q q
_
qq

_
s sdual(1.5GeV)2 pQCD
continuum s lt sdual Vector-Meson
Dominance
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2.3 The Role of Light Vector Mesons in HICs
Contribution to invariant mass-spectrum

• Gee keV Gtot MeV (Nee
  )thermal (Nee )cocktail ratio
• r (770) 6.7 150 (1.3fm/c)
  1 0.13 7.7
• w(782) 0.6 8.6 (23fm/c)
  0.09 0.21 0.43
  
• f(1020) 1.3 4.4 (44fm/c)
  0.07 0.31 0.23

? In-medium radiation dominated by r
-meson! Connection to chiral symmetry
restoration?!
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3.) Chiral Symmetry in QCD
3.1 Chiral Symmetry and its Breaking in
Vacuum 3.2 Consequences for the Hadronic
Spectrum 3.3 Vector-Axialvector Correlation
Functions and Chiral Restoration
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3.1.1 Chiral Symmetry in QCD Vacuum
current quark masses mu md 5-10MeV
Chiral SU(2)V SU(2)A transformation Up to
O(mq ), LQCD invariant under Rewrite LQCD using
qL,R(1g5)/2 q
Invariance under isospin and handedness
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3.1.2 Spontaneous Breaking of Chiral Symmetry
-

• strong qq attraction ? Chiral Condensate
• fills QCD vacuum

cf. Superconductor ee ? 0 , Magnet M ? 0 ,

• mass generation
  , not observables!
• but hadronic excitations reflect SBCS
• massless Goldstone bosons p 0,
• (explicit breaking fp2 mp2 mq qq )
• chiral partners split DM 0.5GeV !
• vector mesons r and w

-

chiral singlet !
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3.2.2 Hadron Spectra and SBCS in Vacuum
Axial-/Vector Correlators
Constituent Quark Mass
Data lattice Bowman etal 02 Curve
Instanton Model DiakonovPetrov 85,
Shuryak
pQCD cont.
? chiral breaking q2 1 GeV2 ? quark
condensate
nvac (2Nf ) fm-3 !

• entire spectral shape matters
• Weinberg Sum Rule(s)

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3.3.1 Melting the Chiral Condensate

• Excite vacuum (hotdense matter)
• quarks percolate / liberated
• ? Deconfinement
• qq condensate melts, ciral Symm.
• chiral partners degenerate Restoration
• (p -s, r -a1, medium effects ? precursor!)

-
How?
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3.3.2 Low-Mass Dileptons Chiral Symmetry
Vacuum

• How is the degeneration realized ?
• measure vector with ee-, but axialvector?

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Upshot of Chapters 2 3
E.M. Emission Rates ? proportional to e.m.
correlator (photon selfenergy) ? vacuum
separation in perturbative (qq) -- nonpert.
(r, w, f ) at duality scale sdual
(1.5GeV)2 ? in-med radiation low-mass ? r
-meson, high-mass ? QGP Chiral Symmetry ?
spontaneously broken in the vacuum ? mass
generation! Mq qq ? 0 (low q2) ?
hadronic spectrum chiral partners split (p-s, r
- a1, ) ? excite vacuum ? condensate melts ?
chiral restoration ? chiral partners
degenerate
-
-
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4.) Vector Mesons in Medium
4.1 Hadronic Many-Body Theory for Vector Mesons
- r -Meson in Vacuum - r -Selfenergies and
Spectral Functions - Constraints and
Consistency Photo-Absorption, QCD Sum
Rules, Lattice QCD 4.2 Vector Meson in URHICs
HotDense Matter 4.3 Dropping r -Mass Vector
Manifestation of CS 4.4 Chiral Restoration?!
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4.1 Many-Body Approach r -Meson in Vacuum
Introduce r as gauge boson into free p r
Lagrangian ?
p p
r
r -propagator
p e.m. formfactor
pp scattering phase shift
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4.1.2 r -Selfenergies in Hot Dense Matter
modifications due to interactions with
hadrons from heat bath ? In-Medium r -Propagator
r
Dr (M,qmB,T)M2-mr2-Sr pp-Sr B-Sr M -1
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(2) Direct r -Hadron Interactions r h ? R
R
r
h
(i) Meson Gas (h p, K, r)
p
G
e.g. r p ? w(770) , a1(1260) ? r p
fix coupling G via decay width
G(a1?rp)
a1
r
Generic features real parts cancel,
imaginary parts add
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4.1.3 Constraints I Nuclear Photo-Absorption
total nuclear g-absorption
in-medium r spectral cross section
function at photon
point
D,N,D
N-1
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Light-like r -Spectral Function, Dr(q0q), and
Nuclear Photo-Absorption
On the Nucleon
On Nuclei

• 2.3. resonance melt (parameter)
• (selfconsistent N(1520)?Nr)

• fixes coupling constants and
• formfactor cutoffs for rNB

Post,Mosel etal 98
Urban,Buballa,RRWambach 98
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4.1.4 r(770) Spectral Function in Nuclear Matter
In-med p-cloud r -N?B resonances
r -N?B resonances (low-density approx)
In-med p-cloud r -N ? N(1520)
Urban etal 98
Post etal 02
Cabrera etal 02
rN0.5r0
rNr0
rNr0
p N ?r N PWA
Constraints g N , g A

• Consensus strong broadening slight upward
  mass-shift
• Constraints from (vacuum) data important
  quantitatively

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4.1.5 QCD Sum Rules r(770) in Nuclear Matter
General idea dispersion relation for
correlation function
Shifman,Vainshtein Zakharov 79

• lhs operator product expansion
• for large spacelike Q2

• rhs model spectral function
• at timelike sgt0
• Resonance
• pQCD continuum

Nonpert. Wilson coeffs (condensates)
r -Meson
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QCD Sum Rule Results r(770) in Nuclear Matter
Leupold etal 98
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4.2 Vector-Meson Spectral Functions in
High-Energy Heavy-Ion Collisions Hot and Dense
Matter
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4.2.1 r -Meson Spectral Functions at SPS
HotDense Matter
Hot Meson Gas
RRWambach 99
RRGale 99

• r -meson melts in hot and dense matter
• baryon density rB more important than
  temperature
• reasonable agreement between models

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4.2.2 Light Vector Mesons at RHIC

• baryon effects important even at rB,tot 0
• sensitive to rBtot rB rB (r-N and r-N
  interactions identical)
• w also melts, f more robust ? OZI

-
-
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4.2.3 Lattice Studies of Medium Effects
Laermann, Karsch 04
calculated on lattice
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4.2.4 Comparison of Hadronic Models to LGT
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4.3 Scenarios for Dropping r -Meson Mass
(1) Naïve Quark Model mr 2Mq ? 0 at chiral
restoration
(problem kinetic energy of bound state)
(2) Scale Invariance of LQCD implement into
effective Lhad ? universal scaling law


Brown, Rho 91
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4.4 Dilepton Rates and Chiral Restoration
dRee /dM2 f B Im Pem
Braaten,PisarskiYuan 90

• Hard-Thermal-Loop result
• much enhanced over Born rate
• matching of HG and QGP
• automatic!
• Quark-Hadron Duality
• at low mass ?!
• Degenerate axialvector
• correlator?

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4.4.2 Current Status of a1(1260)
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5.) Dilepton Emission from the QGP
5.1 Pertubative vs. Lattice QCD 5.2
Emission from Resonances
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5.1 Perturbative vs. Lattice QCD
But small M ? resummations finite-T perturbation
theory (HTL)
Baseline
Braaten,PisarskiYuan 91
Im

collinear enhancement Dq,g(t-mD2)-1 1/as
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5.2 QGP Dileptons from Bound States ?
based on finite-T lattice potentials approach
to zero-binding line ? stable-mass r
-resonance
ShuryakZahed 04
Casalderrey Shuryak 04

• double-peak structure due to zero-binding line
  mixed phase
• factor 1.5-2 enhancement at M1.5GeV depends on
  quark width

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6.) Thermal Photon Emission Rates
Quark-Gluon Plasma
Naïve LO q q (g) ? g (q) ?
But other contributions in O(as) collinear
enhanced Dg(t-mD2)-11/as
Bremsstrahlung Pair-ann.scatt.
ladder resummation (LPM)
Aurenche etal 00, Arnold,MooreYaffe 01
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7.) Dilepton Spectra in Relativistic Heavy-Ion
Collisions
7.1 Space-Time Evolution of URHICs -
Formation and Freezeouts - Trajectories in
the QCD Phase Diagram 7.2 Comparison to Data
- Dileptons at SPS (vs 17, 8 GeV) -
Photons at SPS (vs 17 GeV) - RHIC (vs
200 GeV)
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7.1.1 Hadron Production in Heavy-Ion Collisions
? well described by hadron gas in
thermalchemical equilibrium
Braun-Munzinger etal 03

• SPS / RHIC chemical freezeout close to phase
  boundary
• ? need to construct evolution
• before up to earliest formation time t0 ? T0
  gt Tchem
• after down to thermal freezeout tf ?
  Tfo lt Tchem

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7.1.2 Trajectories in the Phase Diagram

• Basic assumption entropy (baryon-number)
  conservation
• ? fixes T(mB) in the phase diagram
• Time scale hydrodynamics, e.g. VFB(t)(z0vzt
  ) p (R-0 0.5a-t2)2

Caveat conserve hadron ratios after chem.
f.o. ? chemical potentials for p , K, N,
mp,K,N gt 0 for T lt Tchem
mN GeV t fm/c
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7.2.1 Low-Mass Dileptons at SPS
Top SPS Energy

• QGP contribution small
• medium effects!
• drop. mass or broadening?!

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7.2.2 Intermediate-Mass Dileptons at SPS NA50
e.m. corr. continuum-like Im ?em M2 (1 as/p
)
QGP HG!
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7.2.3 Photon Spectra at the SPS WA98
Hydrodynamics QGP HG
Huovinen,RuuskanenRäsänen 02

• T0260MeV, QGP-dominated
• still true if pp?gX included

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7.3 Dilepton Spectrum at RHIC
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8.) Conclusions

• Thermal E.M. Radiation from QCD matter
• - Low-mass dileptons in-med r (w, f) ? Chiral
  Restoration!?
• - Intermediate mass qq annihilation ?
  QGP Radiation!?
• - similar for photons but M0

-

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

• phenomenology for URHICs so far promising
• - importance of model constraints
• - precision datatheory needed for definite
  conclusions
• much excitement ahead PHENIX, NA60, CERES,
  HADES,
• ALICE,
  and theory!