Chiral Symmetry Restoration in Heavy-Ion Collisions

1
Chiral Symmetry Restoration in Heavy-Ion
Collisions
Ralf Rapp Cyclotron Institute Dept of
Phys Astro Texas AM University College
Station, USA High Energy/Nuclear Physics
Seminar Rice University (Houston, TX), 06.11.12
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1.) Intro-I Probing Strongly Interacting Matter

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

• ? Would like to extract from Observables
• temperature transport properties
• in-medium spectral functions
• signatures of deconfinement chiral symmetry
  restoration

3
1.2 EM Spectral Function Fate of Resonances
Im Pem(M) in Vacuum
Im ?em(M,qmB,T)

• Electromagnetic spectral function
• - vs lt 2 GeV non-perturbative
• - vs gt 2 GeV perturbative (dual)
• Vector resonances prototypes
• - representative for bulk hadrons
• neither Goldstone nor heavy flavor
• Medium modifications of resonances
• - QCD phase structure
• - where in the diagram?

ee- ? hadrons
vs M
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1.3 Phase Transition(s) in Lattice QCD
Tcchiral 150MeV
Tcconf 170MeV
Fodor et al 10

• different transition temperatures?!
• smooth transitions (smooth ee- rate!)
• chiral restoration in hadronic phase?!
• (low-mass dileptons!)
• hadron resonance gas approx.

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Outline
2.) Chiral Symmetry Breaking in Vacuum ?
Higgs Mechanism, Condensates Mass Gap in QCD
? Hadron Spectrum, Chiral Partners Sum
Rules 3.) EM Spectral Function in Medium ?
Hadronic Theory ? QGP Lattice QCD 4.) EM
Probes in Heavy-Ion Collisions ? Spectro-,
Thermo-, Chrono- Baro-meter ? Excitation
Function ? Thermal Photons 5.) Conclusions
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2.1 Nonperturbative QCD

• well tested at high energies, Q2 gt 2 GeV2
• perturbation theory (as g2/4p ltlt 1)
• degrees of freedom quarks gluons
• 3 charges (r,g,b), rich of symmetries

(mu,d 5MeV)
_
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2.2 Chiral Symmetry QCD Vacuum
flavor chiral (left/right) invariant

• Higgs Mechanism in Strong Interactions
• qq attraction ? condensate fills QCD vacuum!
• Spontaneous Chiral Symmetry Breaking

-
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2.3 Mass Gap and Chiral Partners
Axial-/Vector Correlators
Constituent Quark Mass
Data lattice Bowman et al 02 Theory
Instanton Model DiakonovPetrov Shuryak 85
pQCD cont.

• Spectral shape matters for
• chiral symmetry breaking!

? Chiral breaking q2 2 GeV2
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2.4 Chiral (Weinberg) Sum Rules

• Quantify chiral symmetry breaking via observable
  spectral functions
• Vector (r) - Axialvector (a1) spectral
  splitting

Weinberg 67, Das et al 67
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2.4.2 Evaluation of Chiral Sum Rules in Vacuum

• pion decay
• constants
• chiral quark
• condensates

• vector-axialvector splitting (one of the)
  cleanest observable of
• spontaneous chiral symmetry breaking
• promising (best?) starting point to search for
  chiral restoration

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2.5 QCD Sum Rules r and a1 in Vacuum

• dispersion relation

Shifman,VainshteinZakharov 79

• lhs hadronic spectral fct.

• rhs operator product expansion

• 4-quark gluon condensate dominant

vector
axialvector

? typically 0.5

deviation
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Outline
2.) Chiral Symmetry Breaking in Vacuum ?
Higgs Mechanism, Condensates Mass Gap in QCD
? Hadron Spectrum, Chiral Partners Sum
Rules 3.) EM Spectral Function in Medium ?
Hadronic Theory ? QGP Lattice QCD 4.) EM
Probes in Heavy-Ion Collisions ? Spectro-,
Thermo-, Chrono- Baro-meter ? Excitation
Function ? Thermal Photons 5.) Conclusions
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3.1 Vector Mesons in Hadronic Matter
Chanfray et al, Herrmann et al, Asakawa et al,
RR et al, Koch et al, Klingl et al, Post et al,
Eletsky et al, Harada et al
Dr (M,qmB ,T) M 2 - mr2 - Srpp - SrB - SrM
-1
r-Propagator
B,a1,K1...
Sp
r
r
SrB,rM
Srpp
Selfenergies
N,p,K
Sp
Constraints decays B,M? rN, rp, ...
scattering pN ? rN, gA,
SPS
RHIC/LHC
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3.2 QCD Sum Rules at Finite Temperature
HatsudaLee91, AsakawaKo 93, Klingl et al
97, Leupold et al 98, Kämpfer et al 03,
Ruppert et al 05
rV/s
T GeV
Percentage Deviation

• r and r melting
• compatible with
• chiral restoration

Hohler RR 12
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3.3 Chiral Condensate r-Meson Broadening
effective hadronic theory
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3.4 Vector Correlator in Thermal Lattice QCD

• Euclidean Correlation fct.

Lattice (quenched) Ding et al 10
Hadronic Many-Body RR 02

• Parton-Hadron Duality of lattice and
  in-medium hadronic?!

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3.4.2 Back to Spectral Function
-Im Pem /(C T q0)

• suggests approach to chiral restoration
  deconfinement

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3.5 Dilepton Rates Hadronic - Lattice -
Perturbative dRee /dM2 ?d3q f B(q0T) Im PV

• Hadronic, pert. lattice QCD
• tend to degenerate toward Tc
• Quark-Hadron Duality at all M ?!
• (? degenerate axialvector SF!)

-
qq?ee
HTL
RR,Wambach et al 99
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3.6 Summary Criteria for Chiral Restoration

• Vector (r) Axialvector (a1) degenerate

Weinberg 67, Das et al 67
pQCD

• QCD sum rules
• medium modifications ? vanishing of
  condensates
• Thermal lattice-QCD
• Approach to perturbative rate (QGP)

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Outline
2.) Chiral Symmetry Breaking in Vacuum ?
Higgs Mechanism, Condensates Mass Gap in QCD
? Hadron Spectrum, Chiral Partners Sum
Rules 3.) EM Spectral Function in Medium ?
Hadronic Theory ? QGP Lattice QCD 4.) EM
Probes in Heavy-Ion Collisions ? Spectro-,
Thermo-, Baro- Chrono-meter ? Excitation
Function ? Thermal Photons 5.) Conclusions
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4.1 Pioneering ee- Measurements at SPS CERES

• Evolve rates over fireball expansion

Excess Spectra
Pb-Au(17.3GeV)
Pb-Au(8.8GeV)

• first quantitative measurement of excess yield
  and shape
• consistent with a melting of the r resonance
  around Tpc
• indications for larger effects at lower beam
  energy baryons!
• hints for large very-low mass excess (photons!
  conductivity?!)

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4.2 Increasing Precision NA60 Spectrometer
Acc.-corrected mm- Excess Spectra

In-In(158AGeV)
NA60 09
Mmm GeV
van HeesRR 08

• invariant-mass spectrum directly
• reflects thermal emission rate!

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4.3 Dilepton Thermometer Slope Parameters
Invariant Rate vs. M-Spectra
Transverse-Momentum Spectra
cont.
Tc160MeV Tc190MeV
r

• Low mass radiation from around T Tpcc
  150MeV
• Intermediate mass T 170 MeV and above
• Consistent with pT slopes incl. flow Teff T
  M (bflow)2

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4.4 Sensitivity to Spectral Function
In-Medium r-Meson Width

• avg. Gr (T150MeV) 370 MeV ? Gr (TTc)
  600 MeV ? mr
• driven by baryons

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4.5 Low-Mass Dileptons Chronometer
In-In Nchgt30

• first explicit measurement of
  interacting-fireball lifetime
• tFB (71) fm/c

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4.6 Low-Mass ee- Excitation Function at RHIC
STAR
PHENIX
QM12

• tension between PHENIX and STAR (central Au-Au)
• no apparent change of the emission source (?)
• consistent with universal medium effect around
  Tpc
• partition hadronic/QGP depends on EoS, total
  yield invariant

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4.7 Direct Photons at RHIC
Spectra
Elliptic Flow
? excess radiation

• Teffexcess (22025) MeV
• QGP radiation?
• radial flow?

• v2g,dir comparable to pions!
• under-predicted by ealry QGP
• emission

Holopainen et al 11,
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4.7.2 Thermal Photon Spectra v2
thermal prim. g

van Hees,GaleRR 11

• hadronic emission close to Tpc essential
  (continuous rate!)
• flow blue-shift Teff T v(1b)/(1-b)
• e.g. b0.3 T 220/1.35 160 MeV
• small slope large v2 suggest main emission
  around Tpc
• confirmed with hydro evolution

He at al in prep.
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5.) Conclusions

• r-meson gradually melts into QGP continuum
  radiation
• Mechanisms underlying r-melting (p cloud
  resonances) find
• counterparts in hadronic S-terms, which restore
  chiral symmetry
• Quantitative studies relating r-SF to chiral
  order parameters with
• QCD and Weinberg-type sum rules ongoing
• Low-mass dilepton spectra in URHICs point at
  universal source,
• with avg. emission temperatures around
  Tpc150MeV (slopes, v2)
• Future precise characterization of EM emission
  source at
• RHIC/LHC CBM/NICA/SIS holds rich info on QCD
  phase
• diagram (spectral shape disp. rel., source
  collectivity lifetime)

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4.3 Dimuon pt-Spectra and Slopes Barometer
Effective Slopes Teff

• theo. slopes originally too soft
• increase fireball acceleration,
• e.g. a- 0.085/fm ? 0.1/fm
• insensitive to Tc160-190MeV

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4.4 Low-Mass ee- at RHIC PHENIX vs. STAR

• large enhancement not accounted
• for by theory
• cannot be filled by QGP radiation

• (very) low-mass region
• overpredicted (SPS?!)

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4.1.2 Sensitivity of NA60 to Spectral Function
Emp. scatt. ampl. T-r approximation Hadronic
many-body Chiral virial expansion
Thermometer
CERN Courier Nov. 2009

• Significant differences in low-mass region
• Overall slope T150-200MeV (true T, no blue
  shift!)

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3.3 Axialvector in Medium Dynamical a1(1260)
p

a1 resonance
. . .
Vacuum
r

In Medium
. . .
Cabrera,Jido, RocaRR 09
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4.5.2 Revisit Ingredients
Emission Rates
Fireball Evolution

• multi-strange hadrons at Tc
• v2bulk fully built up at hadronization
• chemical potentials for p, K,

• Hadron - QGP continuity!

Turbide et al 04
van Hees et al 11
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5.1 Thermal Dileptons at LHC

• charm comparable, accurate (in-medium)
  measurement critical
• low-mass spectral shape in chiral restoration
  window

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5.2 Chiral Restoration Window at LHC

• low-mass spectral shape in chiral restoration
  window
• 60 of thermal low-mass yield in chiral
  transition region
• 
  (T125-180MeV)
• enrich with (low-) pt cuts

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5.3 QGP Barometer Blue Shift vs. Temperature
RHIC
SPS

• QGP-flow driven increase of Teff T M
  (bflow)2 at RHIC
• temperature overcomes flowing late rs ?
  minimum (opposite to SPS!)
• expect to be more pronounced at LHC

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5.4 Elliptic Flow Diagnostics (RHIC)

• maximum structure due to late r decays

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2.3.2 NA60 Mass Spectra pt Dependence
Mmm GeV

• more involved at pTgt1.5GeV Drell-Yan,
  primordial/freezeout r ,

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2.2 EM Probes at SPS

• all calculated with the same e.m. spectral
  function!
• thermal source Ti210MeV, HG-dominated, r-meson
  melting!

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4.1.2 Mass-Temperature Emission Correlation

• generic space-time argument
• ?
• Tmax M / 5.5
• (for Im Pem const)

• thermal photons
• Tmax (q0/5) (T/Teff)2
• ? reduced by flow blue-shift!
• Teff T v(1b)/(1-b)

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4.7.2 Light Vector Mesons at RHIC LHC

• 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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3.2 Dimuon pt-Spectra and Slopes Barometer
pions Tch175MeV a- 0.085/fm
pions Tch160MeV a- 0.1/fm

• modify fireball evolution
• e.g. a- 0.085/fm ? 0.1/fm
• both large and small Tc compatible
• with excess dilepton slopes

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2.3.2 Acceptance-Corrected NA60 Spectra
Mmm GeV
Mmm GeV

• more involved at pTgt1.5GeV Drell-Yan,
  primordial/freezeout r ,

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4.4.3 Origin of the Low-Mass Excess in PHENIX?

• QGP radiation insufficient
• space-time , lattice QGP rate
• resum. pert. rates too small

• must be of long-lived hadronic origin
• Disoriented Chiral Condensate (DCC)?
• Lumps of self-bound pion liquid?
• Challenge consistency with hadronic data, NA60
  spectra!

Bjorken et al 93, RajagopalWilczek 93
- baked Alaska ? small T - rapid
quenchlarge domains ? central A-A - ptherm
pDCC ? e e- ? M0.3GeV, small pt
Z.HuangX.N.Wang 96 Kluger,Koch,Randrup 98
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4.1 Nuclear Photoproduction r Meson in Cold
Matter
g A ? ee- X

• extracted
• in-med r-width
• Gr 220 MeV

e e-
Eg1.5-3 GeV
g
r
CLASGiBUU 08

• r-broadening reduced at high 3-momentum need
  low momentum cut!

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1.2 Intro-II EoS and Particle Content

• Hadron Resonance Gas until close to Tc
• - but far from non-interacting
• short-lived resonances R
• a b ? R ? a b , tR 1 fm/c
• Parton Quasi-Particles shortly above Tc
• - but large interaction measure I(T) e -3P

? both phases strongly coupled (hydro!)
- large interaction rates ? large collisional
widths - resonance broadening ? melting ?
quarks - broad parton quasi-particles -
Feshbach resonances around Tc (coalescence!)

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2.3.6 Hydrodynamics vs. Fireball Expansion

• very good agreement
• between original
• hydro Dusling/Zahed
• and fireball Hees/Rapp

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2.1 Thermal Electromagnetic Emission
EM Current-Current Correlation Function
Thermal Dilepton and Photon Production Rates
Im ?em(M,q)
Im ?em(q0q)
r -meson dominated
ImPem ImDr ImDw /10 ImDf /5
Low Mass