Transcript QGP Diagnosis - INFN - Istituto Nazionale di Fisica Nucleare

Dileptons and Medium Effects
in Heavy-Ion Collisions
Ralf Rapp
Cyclotron Institute
+ Physics Department
Texas A&M University
College Station, USA
Perspectives in Hadronic Physics Conference 2006
ICTP Trieste, 24.05.06
Introduction: EM-Probes -- Basic Questions
QCD Phase Diagram
Chiral Condensate
‹qq›
Spectral Functions
cm
[Bielefeld]
T=1.4Tc
[Tokyo]
1.0
T/Tc
Thermalization  study the phase diagram:
• (highest) temperature of the matter
• chiral symmetry restoration (mass generation!)
• in-medium spectral properties below + above Tc
Inevitable consequences of QGP, link to lattice QCD
Outline
2.) Electromagnetic Emission and Chiral Symmetry


EM Thermal Rates
Axial-/Vector Correlators and Chiral Sum Rules
3.) Medium Effects and Thermal Dileptons



Vector Mesons in Medium: Hadronic Many-Body Theory
Experimental and Theoretical Constraints
Dilepton Rates: Hadronic vs. QGP
4.) Dileptons at SPS


CERES and NA60 Data
Interpretation + Open Issues
5.) Conclusions
2.) EM Emission Rates and Chiral Symmetry
E.M. Correlation Function:
γ
T
2
dN ee
B



f
( q0 ,T ) Im Πem(M,q;B,T)
4
4
3 2
d xd q  M
q0
dN
  f B ( q ,T ) Im Π (q =q;  ,T)

0
em 0
B
4
3
2
d xd q 
Radiation Sources:
• Quark-Gluon Plasma:
qq- → e+e , …
_
e+
e-


Πem
( q )  i  d 4 x eiqx jem
( x ) jem( 0 )
q
e+
q
e
• Hot + Dense Hadron Gas:
 +  → e+e , …

+
r
Relevance:
high mass + temp.
M > 1.5GeV, T >Tc
e+
e-
M ≤ 1 GeV
T ≤ Tc
2.2 Chiral Symmetry Breaking and Restoration
Splitting of “chiral partners” r - a1(1260)  Chiral Symmetry Breaking
Axial-/Vector in Vacuum
at Tc:
Chiral
Restoration
pQCD
cont.
• Low-Mass Dilepton Rate:
2
dN ee
B



f
( T ) ImPem ~ [ImDr+ImDw /10+ImDf /5]
4 4
3 2
d xd q  M
• Axialvector Channel:
r -meson
dominated!
± invariant mass-spectra ~ Im Da1(M) ?!
2.3 Chiral Sum Rules and the a1(1260)
• Energy-weighted moments of difference vector – axialvector:
I0    ds2 (Im P V  Im P A )  1 f2 r2  FA
3
s
[Das etal ’67]
s0
I1( s0 )    ds (Im P V  Im P A )  f2
s
0
s0
[Weinberg ’67]
I2( s0 )    ds (Im P V  Im P A )  0

0
I3   
s ds
(Im P V  Im P A )  c s ( q q )2

• explicit link:
V  A spectral fcts. (models) ↔ order parameters (lattice QCD)
• extended to finite temperature [Kapusta+ Shuryak ‘93]
3.1 Medium Effects I: Hadronic Many-Body Theory
[Chanfray etal, Herrmann etal, RR etal, Weise etal, Post etal, Eletsky etal, Oset etal, …]
Dr (M,q;B ,T) = [M 2- mr2 –Sr –SrB -SrM ] -1
r-Selfenergies: Sr =
Constraints:
- vacuum decays:
B,M→ rN, r
- scattering data:
N , A ,
N→rN
r
S
S
Nucleon
r
SrB,M =
>
B*,a1,K1...
>
r-Propagator:
N,,K…
Nuclei
rN=0.8r0
rN → 0
-ex
 absA ( q0 ) / A  Im Dr ( q0  q )
N
A
[Urban et al. ’98]
3.1.2 r(770) Spectral Function in Nuclear Matter
In-med -cloud +
Relativist. r -N → B*
r -N → B* resonances (low-density approx)
[Urban
etal ’98]
[Post
etal ’02]
rN=r0
Constraints:  N ,  A
In-med -cloud +
r -N → N(1520)
[Cabrera
etal ’02]
rN=0.5r0
rN=r0
 N →r N PWA
• good agreement: strong broadening + small mass-shift up
• constraints from (vacuum) data important quantitatively
3.1.3 QCD Sum Rules + r(770) in Nuclear Matter
dispersion relation
for correlator:

Im P  ( s )
Π ( Q 2 ) / Q 2   ds
s Q2 + s
0
• lhs: OPE (spacelike Q2):
2

2  G 2  

Q
s
P r   12 ( 1 +  s ) ln  2  + 
4
3
8 

Q
 
 4-quark
 s ( q q )2
C
+ ... condensate!
6
Q

0.2% 1%
[Leupold ’98,
Ruppert etal ’05]
[Shifman,Vainshtein
+Zakharov ’79]
• rhs: hadronic model (s>0):
Im P r ( s ) 
mr4
gr2
Im Dr ( s ) 
s ( 1 +  s ) ( s  s )
0
8

3.1.4 r-Meson Spectral Functions at SPS
Hot+Dense Matter
Model
Comparison
Hot
Meson
Gas
rB /r0
0
0.1
0.7
2.6
[Eletsky etal
’01]
[RR+Wambach
’99]
[RR+Wambach ’99]
• r-meson “melts” in hot and dense matter
• baryon density rB more important than temperature
• reasonable agreement between models
[RR+Gale ’99]
3.2 Dilepton Emission Rate: Hadron Gas vs. QGP
dRee c  2 d 3q B
 2
f ( T ) Im P em( M ,q )
2
q0
dM
M
[qq→ee]
[qq- + HTL]
[Braaten,Pisarski+Yuan ’90]
• Hard-Thermal-Loop QGP rate
enhanced over Born rate
• “matching” of HG and QGP
in vicinity of Tc
• “Quark-Hadron Duality” ?!
4.) Dilepton Spectra in Heavy-Ion Collisions
Thermal
Emission:
therm
dN ee
dM
t fo
therm
Md 3q dRee
  dt VFB (t ) 
( M ,q ;T ,i ) Acc
4
q0
d q
t
0
Pb-Pb Collisions: Trajectories in the Phase Diagram
N [GeV]
t [fm/c]
• based on entropy (+baryon-number) conservation
• volume expansion: VFB(t )= (z0+vzt )  (R┴+ 0.5a┴t 2)2
4.1 Pb-Au Collisions at SPS: CERES/NA45
• QGP contribution small
• medium effects on r-meson!
• dropping mass or broadening?!
4.2 In-In at SPS: Dimuons from NA60
[Damjanovic et al. PRL
• excellent mass resolution and statistics
• for the first time, dilepton excess spectra could be extracted!
• quantitative theory?
’06]
4.2.2 In-In at SPS: Theory vs. NA60
• predictions based r-spectral function of [RR+Wambach ’99]
• uncertainty in fireball lifetime (±25% norm.); or: infer tFB≈7fm/c !
• relative strength of thermal sources fix
• good agreement with r melting, including pt dependence
[van Hees
+RR ‘06]
4.2.3 Intermediate-Mass Region
• “4“ states dominate in 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”: [Eletsky+Ioffe ‘90]
P V ( q )  ( 1   )P V0 ( q ) +  P A0 ( q )
with  ( Tc )  1
2
[van Hees+RR ‘06]
2
4
4.2.4 NA60 Data: Other r-Spectral Functions
• switch off medium modifications
• T-, rB- dependence of bare parameters: dropping mass
• free spectral function ruled out
• meson gas insufficient either
[Brown+Rho ’91,
Hatsuda+Lee ‘92]
• dropping mass as used for CERES
disfavored (free r decays?)
4.2.5 (Some) Open Issues
• Heavy-Ion Collisions [NA60]
- centrality dependence, free r’s (surface vs. volume)
- sensitivity to fireball evolution
- quantitative w and f
- thermal radiation at intermediate mass (M=1.5-3 GeV)
- chiral restoration: ▪ “duality” (hadron liquid → sQGP)
▪ chiral sum rules
▪ chiral mixing in the M=1-1.5GeV region
• Cold Nuclei
[CB/TAPS, KEK-E325]
- dropping w-mass + broadening
- dropping r-mass without broadening ?!
5.) Conclusions
• Strong medium effects in l+l  spectra
• new level of precision in NA60 → model discrimination
• r-melting at Tc, no apparent mass shift
• alternative models? (quality control)
• Chiral Restoration:
- direct (exp.): measure axialvector
- indirect (theo.): (1) effective model (constraints)
(2) chiral sum rules (V-A moments) vs. lQCD
(3) compatibility with dilepton/photon data
• HADES, RHIC, LHC, SPS-09, CBM, …, elementary reactions
In-medium V-meson spectroscopy has begun …
3.3 Medium Effects II: Dropping Mass
Scale Invariance of LQCD → bare parameters change!?
q q1T/ n
/n
q q1vac
 f /
*
f  m*N
m N  mr mr
• density dependence:
[Hatsuda+
QCD sum rules: C ≈ 0.15 Lee ‘92]
• temperature dependence: 
quark condensate from chiral
perturbation theory: qq T   T 2 
qq
vac
 1    
  Tc  
• vector dominance coupling:
Im P r 
( m*r )4
gr2
Im Dr ( m*r )
(gauge invariance!)
*
2 
  
 1   T  
  Tc  
1
3
[Pelaez ‘03]
[Brown+Rho
’91, ‘02]
rB 

1  C r0 
3.) Medium Effects and Thermal Dileptons
3.1 Lattice QCD (QGP)
Dilepton Rate ~ ImP(w,q=0)/w2
EM Correlator ImP(w,q)/w2
T=1.5Tc
[Bielefeld Group ’02, ‘05]
• lQCD << pQCD at low mass (finite volume?)
• currently no thermal photons from lQCD
• vanishing electric conductivity!? but: [Gavai ’04]
3.4 In-Medium IV:
Vector Manifestation of Chiral Symmetry
• Hidden Local Symmetry: r-meson introduced as gauge boson,
“Higgs” mechanism generates r-mass
• Vacuum: rL↔, good phenomenology (loop exp. O(p/c , mr /c , g))
• In-Medium: T-dep. mr(0), gr matched to OPE (spacelike), match<c ,
Renormalization Group running → on-shell
[Harada,
 - dropping r-mass → 0 (RG fixed point at Tc) , Yamawaki etal, ‘01]
- violation of vector dominance: a = 2 → 1



~(a-2)
~a
e.m. spectral function? matching HG-QGP: massless mesons?
4.2 Recent Advances at SPS: Power of Precision
NA60 Data vs. Model Predictions
drop. mass (norm.)
[RR+Wambach ’99; RR’03]
drop. mass (norm.)
drop. mass (norm.)
• r-meson “melting” supported (baryons!)
• dropping mass (as used to explain CERES data) ruled out
• open issues:
(1) M > 0.9GeV (4→+ !?)
(2) normalization: 0.6 (pt <0.5GeV), 0.8 (all pt ), ~2 (pt >1GeV)
(3) other models (vector manifestation, chiral virial approach, …)
4.2.2 Modified Fireball and Absolute Normalization
• r-spectral function unchanged since [RR+Wambach ’99]
• expanding fireball, fixed S (↔Nch): VFB(t)=(z0+vzt )  (R┴0+ 0.5a┴t 2)2
Increase a┴  reduced lifetime (t =9→6fm/c), increased v┴=0.4→0.5c
[van Hees+
RR in prep.]
[courtesy
S.Damjanovic]
• reasonable agreement with absolute normalization, but …
• too little yield at high pt; “free r”? w? check central …
Revival Attempts for Dropping r-Mass
Fireball Evolution
E.g., [Skokov+Toneev ‘05]
>1GeVfm-3 ≈ c
for Dt=8 fm/c?!
Bjorken
regime:
tFB=0.5 fm/c?!
• Not compatible with gauge
invariance (no mr* in VDM)
• acceptance?
M ≥ 1GeV in NA60
[H. van Hess + RR, in prep.]
• combination of 4- + QGP + charm?!
• (beware: schematic acceptance)
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.
[Turbide,RR+Gale’04]
WA98 “Low-qt Anomaly”
• addt’l meson-Bremsstrahlung
→  K→K
[Liu+
substantial at low qt
RR’05]
5.1.2 Thermal Photons II: RHIC
• thermal radiation qt<3GeV ?!
• QGP window 1.5<qt<3GeV ?!
• also:  -radiation off jets
• shrinks QGP window qt<2GeV ?!
[Gale,Fries,Turbide,Srivastava ’04]
5.3.1 RHIC: Vector Mesons in Medium
Hadronic
Many-Body
Theory
Dilepton
Emission Rates
[qq→ee]
[qq+O(
s)]
HGeven
≈ in-med
• baryon effects in-med
important
at rB,netQGP
=0 : !
sensitive to rB,tot
=rB+rB- , most pronounced
Quark-Hadron
Duality ?! at low M
• f more robust ↔ OZI
5.3.2 Dileptons II: RHIC
[R. Averbeck,
PHENIX]
[RR ’01]
• low mass: thermal! (mostly in-medium r)
• connection to Chiral Restoration: a1 (1260)→  , 3
• int. mass: QGP (resonances?) vs. cc- → e+e-X (softening?)