Transcript QGP Diagnosis

Chiral Symmetry Restoration
in Heavy-Ion Collisions
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
High Energy/Nuclear Physics Seminar
Rice University (Houston, TX), 06.11.12
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
1.2 EM Spectral Function + Fate of Resonances
2
- em
3 2
dN ee
B

f
( q0 ,T ) Im Πem(M,q;mB,T)
4
4
d xd q  M
• Electromagnetic spectral function
- √s < 2 GeV : non-perturbative
- √s > 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?
Im Pem(M) in Vacuum
e+e- → hadrons
√s = M
-
≈ -qq / qq
1.3 Phase Transition(s) in Lattice QCD
“Tcchiral ”~150MeV
“Tcconf ” ~170MeV
[Fodor
et al ’10]
• different “transition” temperatures?!
• smooth transitions (smooth e+e- rate!)
• chiral restoration in “hadronic phase”?!
(low-mass dileptons!)
• hadron resonance gas approx.
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
2.1 Nonperturbative QCD
2
1
ˆ

L QCD  q ( i  gA - mq ) q - Gam
4
well tested at high energies, Q2 >2GeV2:
• perturbation theory (s = g2/4π << 1)
• degrees of freedom = quarks + gluons
(mu,d ≈ 5MeV)
• 3 charges (r,g,b), rich of symmetries
Q2 ≤ 2GeV2 → transition to “strong” QCD:
• effective d.o.f. = hadrons (Confinement)
• massive “constituent quarks”
mq* ≈ 350
(Chiral Symmetry
_ MeV ≈ ⅓ Mp
~ ‹0|qq|0› condensate!
Breaking)
↕ ⅔ fm
2.2 Chiral Symmetry + QCD Vacuum
LQCD( mu ,d  0 )
: flavor + “chiral” (left/right) invariant
“Higgs” Mechanism in Strong Interactions:
q
L
• qq attraction  condensate fills QCD vacuum!
qR
0 | q q | 0  0 | qLqR  qRqL | 0  -5 fm -3
Spontaneous Chiral Symmetry Breaking
q- L
q-
R
Profound Consequences:
• effective quark mass:
↔ mass generation!
m*q  0 | q q | 0
• near-massless Goldstone bosons 0,±
• “chiral partners” split: DM ≈ 0.5GeV
JP=0±
1±
1/2±
2.3 Mass Gap and Chiral Partners
Constituent Quark Mass
Axial-/Vector Correlators
“Data”: lattice [Bowman et al ‘02]
Theory: Instanton Model
[Diakonov+Petrov; Shuryak ‘85]
pQCD
cont.
●
Chiral breaking: |q2| ≤ 2 GeV2
• Spectral shape matters for
chiral symmetry breaking!
2.4 Chiral (Weinberg) Sum Rules
• Quantify chiral symmetry breaking via observable spectral functions
• Vector (r) - Axialvector (a1) spectral splitting
In  -  ds s n (Im P V - Im P A )

[Weinberg ’67, Das et al ’67]
t→(2n)
I - 2  1 f2r2 - FA ,
I -1  fπ2 ,
3
I0  -2mq 0 | q q | 0 , I1  c αs 0 | (q q)2 | 0
[ALEPH ‘98,
OPAL ‘99]
t→(2n+1)
pQCD
pQCD
• Key features of updated “fit”: [Hohler+RR ‘12]
r + a1 resonance, excited states (r’+ a1’), universal continuum (pQCD!)
2.4.2 Evaluation of Chiral Sum Rules in Vacuum
• pion decay
constants
I - 2  1 f2r2 - FA
3
• chiral quark
condensates
I0  -2mq 0 | q q | 0
I -1  fπ2
I1  c αs 0 | (q q)2 | 0
• vector-axialvector splitting (one of the) cleanest observable of
spontaneous chiral symmetry breaking
• promising (best?) starting point to search for chiral restoration
2.5 QCD Sum Rules: r and a1 in Vacuum
• dispersion relation:

2
Im
P
(
s
)
Π
(
Q
)
ds


 s Q2  s  Q2
0
• lhs: hadronic spectral fct.
[Shifman,Vainshtein+Zakharov ’79]
• rhs: operator product expansion
• 4-quark + gluon condensate dominant
vector
axialvector
●
typically 0.5%
deviation
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
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,q;mB ,T) = [M 2 - mr2 - Sr - SrB - SrM ] -1
Selfenergies: Sr =
r
S
S
SrB,rM =
r
>
B*,a1,K1...
>
r-Propagator:
N,,K…
Constraints: decays: B,M→ rN, r, ... ; scattering: N → rN, gA, …
SPS
RHIC/LHC
r B /r 0
0
0.1
0.7
2.6
3.2 QCD Sum Rules at Finite Temperature
[Hatsuda+Lee’91, Asakawa+Ko ’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]
-  / qq
- 0
qq
3.3 Chiral Condensate + r-Meson Broadening
effective hadronic theory
• Sh = mq h|qq|h
> 0 contains quark core + pion cloud
+
Shcloud
~
+
>
S
>
=
Shcore
S
• matches spectral medium effects: resonances + pion cloud
• resonances + chiral mixing drive r-SF toward chiral restoration
3.4 Vector Correlator in Thermal Lattice QCD

• Euclidean Correlation fct. P em (t ,q ;T )   dq0 rem ( q0 ,q ;T ) cosh [ q0(t - 1 / 2T )]
0
Lattice (quenched)
[Ding et al ‘10]
2
sinh [ q0 / 2T ]
Hadronic Many-Body
[RR ‘02]
GV (t ,T )
GVfree(t ,T )
• “Parton-Hadron Duality” of lattice and in-medium hadronic?!
-Im Pem /(C T q0)
3.4.2 Back to Spectral Function
• suggests approach to chiral restoration + deconfinement
3.5 Dilepton Rates: Hadronic - Lattice - Perturbative
dRee /dM2 ~ ∫d3q f B(q0;T) Im PV
[qq→ee]
[HTL]
• Hadronic, pert. + lattice QCD
tend to “degenerate” toward ~Tc
• Quark-Hadron Duality at all M ?!
( degenerate axialvector SF!)
dRee/d4q 1.4Tc (quenched)
q=0
[Ding et al ’10]
[RR,Wambach et al ’99]
3.6 Summary: Criteria for Chiral Restoration
• Vector (r) – Axialvector (a1) degenerate
In  -  ds s n (Im P V - Im P A )

[Weinberg ’67,
Das et al ’67]
I-1  fπ2 , I0  0 , I1  c αs (q q)2
• QCD sum rules:
medium modifications ↔ vanishing of condensates
• Thermal lattice-QCD
• Approach to perturbative rate (QGP)
pQCD
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
4.1 Pioneering e+e- Measurements at SPS: CERES
t
therm
fo
3 dRtherm
dN mm
M
d
q
mm
• Evolve rates over fireball expansion:
  dt VFB (t ) 
4
dM
q0
d
q
t0
Pb-Au(17.3GeV)
Pb-Au(8.8GeV)
Excess Spectra
• 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?!)
4.2 Increasing Precision: NA60 “Spectrometer”
Acc.-corrected m+m- Excess Spectra
In-In(158AGeV)
[NA60 ‘09]
Mmm [GeV]
[van Hees+RR ’08]
• invariant-mass spectrum directly
reflects thermal emission rate!
Thermal mm- Emission Rates
4.3 Dilepton Thermometer: Slope Parameters
Invariant Rate vs. M-Spectra
cont.
r
Transverse-Momentum Spectra
Tc=160MeV
Tc=190MeV
• 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
4.4 Sensitivity to Spectral Function
In-Medium r-Meson Width
Mmm [GeV]
• avg. Gr (T~150MeV) ~ 370 MeV  Gr (T~Tc) ≈ 600 MeV → mr
• driven by baryons
4.5 Low-Mass Dileptons: Chronometer
In-In Nch>30
• first “explicit” measurement of interacting-fireball lifetime:
tFB ≈ (7±1) fm/c
4.6 Low-Mass e+e- Excitation Function at RHIC
PHENIX
STAR
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
4.7 Direct Photons at RHIC
Spectra
Elliptic Flow
← excess radiation
• Teffexcess = (220±25) MeV
• QGP radiation?
• radial flow?
• v2g,dir comparable to pions!
• under-predicted by ealry QGP
emission [Holopainen et al ’11,…]
4.7.2 Thermal Photon Spectra + v2
thermal
+ prim. g
[van Hees,Gale+RR ’11]
• hadronic emission close to Tpc essential (continuous rate!)
• flow blue-shift: Teff ~ T √(1+b)/(1-b)
e.g. b=0.3: T ~ 220/1.35~ 160 MeV
• small slope + large v2 suggest main emission around Tpc
• confirmed with hydro evolution
[He at al in prep.]
5.) Conclusions
• r-meson gradually melts into QGP continuum radiation
• Mechanisms underlying r-melting ( 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 Tpc~150MeV (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)
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 Tc=160-190MeV
4.4 Low-Mass e+e- at RHIC: PHENIX vs. STAR
• “large” enhancement not accounted
for by theory
• cannot be filled by QGP radiation…
• (very) low-mass region
overpredicted… (SPS?!)
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 T~150-200MeV (true T, no blue shift!)
3.3 Axialvector in Medium: Dynamical a1(1260)

Vacuum:
In
Medium:
r

r
+
S
Sr
+
+
...
S
S
Sr
Sr
a1
= resonance
+ ...
[Cabrera,Jido,
Roca+RR ’09]
• in-medium  + r propagators
• broadening of -r scatt. Amplitude
• pion decay constant in medium:
4.5.2 Revisit Ingredients
Emission Rates
• Hadron - QGP continuity!
[Turbide et al ’04]
Fireball Evolution
• multi-strange hadrons at “Tc”
• v2bulk fully built up at hadronization
• chemical potentials for , K, …
[van Hees et al ’11]
5.1 Thermal Dileptons at LHC
• charm comparable, accurate (in-medium) measurement critical
• low-mass spectral shape in chiral restoration window
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”
(T=125-180MeV)
• enrich with (low-) pt cuts
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 r’s → minimum (opposite to SPS!)
• expect to be more pronounced at LHC
5.4 Elliptic Flow Diagnostics (RHIC)
• maximum structure due to late r decays
2.3.2 NA60 Mass Spectra: pt Dependence
Mmm [GeV]
• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …
2.2 EM Probes at SPS
• all calculated with the same e.m. spectral function!
•thermal source: Ti≈210MeV, HG-dominated, r-meson melting!
4.1.2 Mass-Temperature Emission Correlation
• generic space-time argument:
dN ee
Im P em - M / T
3 3 dN ee
3/ 2
M

d
xd
q

V
(
T
)
e
(
MT
)
FB
dMd t
q0 
M
d 4 xd 4q


dN ee
 ImP em (M, T) e- M / T T -5.5
dM dT
Tmax ≈ M / 5.5
(for Im Pem =const)
• thermal photons:
Tmax ≈ (q0/5) * (T/Teff)2
→ reduced by flow blue-shift!
Teff ~ T * √(1+b)/(1-b)
4.7.2 Light Vector Mesons at RHIC + LHC
• baryon effects important even at rB,tot= 0 :
sensitive to rBtot= rB + r-B (r-N and r-N interactions identical)
• w also melts, f more robust ↔ OZI
3.2 Dimuon pt-Spectra and Slopes: Barometer
pions: Tch=175MeV
a┴ =0.085/fm
• modify fireball evolution:
e.g. a┴ = 0.085/fm → 0.1/fm
• both large and small Tc compatible
with excess dilepton slopes
pions: Tch=160MeV
a┴ =0.1/fm
2.3.2 Acceptance-Corrected NA60 Spectra
Mmm [GeV]
Mmm [GeV]
• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …
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)? [Bjorken et al ’93, Rajagopal+Wilczek ’93]
[Z.Huang+X.N.Wang ’96
- “baked Alaska” ↔ small T
Kluger,Koch,Randrup ‘98]
- rapid quench+large domains ↔ central A-A
- therm + DCC → e+ e- ↔ M~0.3GeV, small pt
• Lumps of self-bound pion liquid?
• Challenge: consistency with hadronic data, NA60 spectra!
4.1 Nuclear Photoproduction: r Meson in Cold Matter
g + A → e+e- X
e+
g
r
• extracted
“in-med” r-width
Gr ≈ 220 MeV
Eg≈1.5-3 GeV
e-
[CLAS+GiBUU ‘08]
• Microscopic Approach:
product. amplitude
g
+
in-med. r spectral fct.
r
Fe - Ti
full calculation
fix density 0.4r0
N
[Riek et al ’08, ‘10]
M [GeV]
• r-broadening reduced at high 3-momentum; need low momentum cut!
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!)
2.3.6 Hydrodynamics vs. Fireball Expansion
• very good agreement
between original
hydro [Dusling/Zahed]
and fireball [Hees/Rapp]
2.1 Thermal Electromagnetic Emission
EM Current-Current Correlation Function:
m
m
Πem
( q )  -i  d 4 x eiqx  ( x0 )  [ jem
( x ), jem( 0 )]T
Thermal Dilepton and Photon Production Rates:
e+
e-
γ
Low Mass:
2
dRee
- em
B

f
( T ) Im Πem(M,q)
4
3 2
d q
 M
dRg
- em B
q0 3 
f ( T ) Im Πem(q0=q)
2
d q

ImPem ~ [ImDr + ImDw /10 + ImDf /5]
r -meson
dominated