Transcript Vector Probe in URHICs

Introduction to Dileptons
and in-Medium Vector Mesons
Ralf Rapp
Cyclotron Institute
+ Physics Department
Texas A&M University
College Station, Texas
USA
2 Lectures at ECT* EM-Probes Workshop
Trento, 04. + 06.06.05
1.) Introduction
1.1 Electromagnetic Probes in Strong Interactions
• g-ray spectroscopy of atomic nuclei: collective phenomena, …
• DIS off the nucleon: - parton model, PDF’s (high q2< 0)
- nonpert. structure of nucleon [JLAB]
• Drell-Yan: pp → eeX (q2> 0: d / u symmetry, nucl. shadowing)
• thermal emission: - compact stars (GRBs?!)
- heavy-ion collisions: [SPS, RHIC, LHC, FAIR]
g (q2=0) , e+e- (q2>0)
What is the electromagnetic spectrum of QCD matter?
Creating Strong-Interaction Matter in the Laboratory
e+
r
eAu + Au NN-coll.
QGP
Hadron Gas
“Freeze-Out”
Sources of Dilepton Emission:
• “primordial” (Drell-Yan) qq- annihilation: NN→e+e-X
• emission from equilibrated matter (thermal radiation)
- Quark-Gluon Plasma:
qq- → e+e- , …
- Hot+Dense Hadron Gas: p +p - → e+e- , …
_
• final-state hadron decays: p0,h → ge+e- , D,D → e+e- X , …
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      e+e- ?
• extract signatures of chiral symmetry restoration?
1.3 Intro-III: EoS and Hadronic Modes
All information encoded in free energy:  (  B ,T )  -T log Z / V
• EoS: P  -  ,   -  (   ) , s  - 

T
• correlation functions:   ( q )  -i  d 4 x e iqx  ( t ) Tr rˆ [ j ( x ), j ( 0 )] / Z
j  q  q : “hadronic” current
QCD Order Parameters and Hadronic Modes
- = ∂ / ∂mq
• condensate: ‹qq›
suscept.: cs=∂2 / ∂mq2 =s (q=0) = ls2 Ds (q=0)
~ (ms )-2
↔ iso/scalar pp pairs!
‹qq›
lattice
cs QCD
1.0
T/Tc
• p decay const: fp2= - ∫ ds/s ( Im V - Im A )
2 ImD
[Weinberg ’67,
l
r
r ↔ dileptons, photons!
Kapusta+Shuryak ’94]
1.4.1 Schematic Dilepton Spectrum in HICs
qq
Characteristic regimes in invariant e+e- 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
1.4.2 Dilepton Data at CERN-SPS
Low Mass: CERES/NA45
Intermediate Mass: NA50
Central Pb-Pb
158 AGeV
open
charm
DrellYan
(DD)
Mee [GeV]
• final-state
hadron
decays
strong excess
around
M≈0.5GeV
yieldininr
p-A collisions
• saturate
little excess
region
M [GeV]
• factor ~2 excess
• open charm? thermal? …
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
2.) Electromagnetic Emission Rates

E.M. Correlation Function: Πem( q )  -i d 4 x eiqx  jem( x ) jem( 0 )T
e+
e-
γ
2
dRee
B


f
( T ) Im Πem(M,q)
4
3 2
d q p M
dRg -  B
q0 3  2 f ( T ) Im Πem(q0=q)
dq p
= O(1)
= O(αs )
also: e.m susceptibility (charge fluct.): χ = Πem(q0=0,q→0)
In URHICs:
• source strength: dependence on T, B, p , medium effects, …
• system evolution: V(t), T(t), B(t), transverse expansion, …
• nonthermal sources: Drell-Yan, open-charm, hadron decays, …
• consistency!
2.2 E.M. Correlator in Vacuum: s(e+e-→hadrons)
e+
p-
r
p
ee+
h1
h2
q
I 1
2p+ 4p+...
pp
r + +
KK
_
…
_
e-
+
r
qq
q
Im  em ( s ) 
S ( s )
-s

2
N c  ( eq ) 1 +
+ 
12p
p


u ,d ,s
2
2
 mV 
 g  Im DV ( s )
r , , 
 V 

s ≥ sdual~(1.5GeV)2 :
pQCD continuum
s < sdual :
Vector-Meson Dominance
2.3 The Role of Light Vector Mesons in HICs
Contribution to invariant mass-spectrum:
dNV ee
V ee
3
4 dRee
  d q d x 4  NV ( M )
t
dM
M
d q
thermal emission
tFB ~ 10fm/c
after freezeout
tV ~ 1/Vtot
ee [keV] tot [MeV] (Nee )thermal (Nee )cocktail ratio
r (770)
(782)
(1020)
6.7
150 (1.3fm/c)
1
0.13
7.7
0.6
8.6 (23fm/c)
0.09
0.21
0.43
1.3
4.4 (44fm/c)
0.07
0.31
0.23
 In-medium radiation dominated by r -meson!
Connection to chiral symmetry restoration?!
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
3.1.1 Chiral Symmetry in QCD: Vacuum
2
1
/ - m̂q ) q - Ga
L QCD  q ( i/ + gA
4
current quark masses: mu ≈ md ≈ 5-10MeV
Chiral SU(2)V × SU(2)A transformation:
Up to O(mq ), LQCD invariant under

 
q  RV ( V ) q  exp( - iV  t / 2 ) q

 
q  RA (  A ) q  exp( - ig 5  A  t / 2 ) q
Rewrite LQCD using qL,R=(1±g5)/2 q :
1 2
 uL 
 uR 
LQCD  ( uL , d L ) iD
/   + ( uR , d R ) iD
/   + O ( mq ) - Ga
4
 dL 
 dR 


Invariance
under
q L ,R  exp( - i L ,R  t / 2 ) q L ,R
isospin and “handedness”
3.1.2 Spontaneous Breaking of Chiral Symmetry
-
• strong qq attraction  Chiral Condensate
fills QCD vacuum: q q  qLqR + qRqL  0
[cf. Superconductor: ‹ee›≠ 0 , Magnet ‹M› ≠ 0 , … ]
qL
qR
q- R
q- L
• mass generation q q  2M*  -4G q q , not observables!
but: hadronic excitations reflect SBCS:
• “massless” Goldstone bosons
p 0,±
- )
(explicit breaking: fp2 mp2= mq ‹qq›
• “chiral partners” split: M ≈ 0.5GeV !
• vector mesons r and :

 


1
RA(  ) ri 
( RAq )g t i ( RAq )  ri + (   a1 )i
2

RA(  )      chiral singlet !

JP=0±
1±
1/2±
3.2.2 Hadron Spectra and SBCS in Vacuum
Constituent Quark Mass
Axial-/Vector Correlators
“Data”: lattice [Bowman etal ‘02]
Curve: Instanton Model
[Diakonov+Petrov ’85, Shuryak]
pQCD
cont.
●
|q2|
chiral breaking:
● quark condensate:
≤1
0 | q q | 0  ( -250MeV )3
nvac≈ (2Nf ) fm-3 !
GeV2
Im  AI 1 
ma41
ga21
Im Da1 ( s ) - s fp2p  ( s - mp2 )
• entire spectral shape matters
• Weinberg Sum Rule(s)
fp2  -  ds (Im  VI 1 - Im  AI 1 )
ps
3.3.1 “Melting” the Chiral Condensate
Excite vacuum (hot+dense matter)
• quarks “percolate” / liberated
 Deconfinement
‹qq›
- condensate “melts”, ciral Symm.
• ‹qq›
chiral partners degenerate Restoration
(p -s, r -a1, … medium effects → precursor!)
How?
lattice
cm QCD
1.0
T/Tc
cPT
many-body
degrees of freedom?
QGP
(2 ↔ 2)
(3-body,...)
(resonances?)
consistent
extrapolate
pQCD
0
0.05
120, 0.5r0
0.3
150-160, 2r0
0.75
175, 5r0
[GeVfm-3]
T[MeV], rhad
3.3.2 Low-Mass Dileptons + Chiral Symmetry
At Tc: Chiral Restoration
Vacuum
• How is the degeneration realized ?
• “measure” vector with e+e-, but axialvector?
Upshot of Chapters 2 + 3
E.M. Emission Rates:
●
proportional to e.m. correlator (photon selfenergy)
- -- nonpert. (r, ,  )
vacuum: separation in perturbative (qq)
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!
- ≠ 0 (low q2)
Mq* ~ ‹qq›
● hadronic spectrum: chiral partners split (p-s, r -a1, …)
● excite vacuum → condensate melts → chiral restoration
→ chiral partners degenerate
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: Hot+Dense Matter
4.3 Dropping r -Mass; Vector Manifestation of CS
4.4 Chiral Restoration?!
4.1 Many-Body Approach: r -Meson in Vacuum
Introduce r as gauge boson into free p +r Lagrangian 
p







int
r
Lpr
 g r  ( p   p ) - 1 g 2r  r  p  p
p
2
4
4
 2
2


2 
d
k
d
k D (k )

r (q )  g 
D
(
k
)

D
(
k
+
q
)

+
2
g
g
q

p
 4 p
4 p
 r 0
( 2p )
r -propagator: Dr ( M )  [ M
p e.m. formfactor
| Fp ( M ) |2  ( mr( 0 ) )4 | Dr ( M ) |2
pp scattering phase shift
-1
Im Dr ( M ) 

pp ( M )  tan 
 Re Dr ( M ) 
( 2p )
-1
- ( mr( 0 ) )2 -  rpp ( M
)]
|Fp|2
pp
2
Ar 
- 2ImDr
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,q;B,T)=[M2-mr2-rpp-r B-r M ]-1
(1) Medium Modifications of Pion Cloud
[Chanfray etal, Herrmann etal,
RR etal, Weise etal, Oset etal, …]
2
 rpp   Dpmed vrpp
Dpmed (1 + 2 f p ) +  Dpmed vrrpp (1 + f p )
 rpp 
r
p
p
p
+
In-med p-prop. Dp= [k02-k2-p(k0 ,k)]-1
→ mostly affected by (anti-) baryons
(2) Direct r -Hadron Interactions: r + h → R
 r hR   d k 3 DR ( k + q ) vr2 hR [ f h( k )  f R (  R )]
( 2p )
(i) Meson Gas (h = p, K, r)
e.g. r + p → (770) , a1(1260) → r + p
fix coupling G via decay width (a1→rp)
Generic features: real parts cancel,
imaginary parts add
r
a1
G
>
R
>
3
h
p
r
Decay Phase Space
(ii) r -Baryon Interactions (h = N, , …)
(1700)
• S-wave: r + N → N(1520), (1700) → r + N , etc.
• Coupling constant → free decay:
 B rN  C f r2BN
mB - m N
2
2 2
M
dM
A
(
M
)
q
Q
F
(
q
)
r
cm

2mp
N(1520)
e.g.: (N(1520)→Nr) ≈ 25MeV,
((1700)→Nr) ≈ 130MeV
4.1.3 Constraints I: Nuclear Photo-Absorption
total nuclear g-absorption
cross section
in-medium r –spectral
function at photon point
4
s gabs
(
q
)
m
A
0
r
med
4
p

4
p

Im  em( q0  q )  Im
D
( M  0,q )
r
2
A
q0 r N
q0 r N g
r
>
r
>
N-1
,N*,*
g N → B*
direct resonance!
p
p
g N → p N,
meson exchange!
Light-like r -Spectral Function, Dr(q0=q),
and Nuclear Photo-Absorption
On the Nucleon
On Nuclei
gN
gA
p-ex
• fixes coupling constants and
formfactor cutoffs for rNB
• 2.+3. resonance melt (parameter)
(selfconsistent N(1520)→Nr)
[Urban,Buballa,RR+Wambach ’98]
[Post,Mosel etal ’98]
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)
[Urban
etal ’98]
[Post
etal ’02]
rN=r0
Constraints: g N , g A
In-med p-cloud +
r -N → N(1520)
[Cabrera
etal ’02]
rN=0.5r0
rN=r0
p N →r N PWA
• Consensus: strong broadening + slight upward mass-shift
• Constraints from (vacuum) data important quantitatively
4.1.5 QCD Sum Rules + r(770) in Nuclear Matter
General idea:
[Shifman,Vainshtein
+Zakharov ’79]
dispersion relation for correlation function

Im   ( s )
2
2
2
ds
Π ( Q  -q ) / Q  
s Q2 + s
0
• lhs: operator product expansion • rhs: model spectral function
for large spacelike Q2:
at timelike s>0:
Π ( q2 )  -i  d 4 x e iqx  j ( x ) j ( 0 )T
Resonance +
cn
pQCD continuum
Nonpert.
  2n Wilson
coeffs
Q
n
(condensates)
r -Meson:
2

2  G 2 p 

Q
s
 r  - 12 (1 +  s ) ln  2  + p
4
3
8p 

Q
 

4-quark
 s ( q q )2
-C
+ ... condensate!
6
Q

Im  r ( s ) 
mr4
gr2
Im Dr ( s ) -
s (1 +  s ) ( s - s
)
dual
8p
p
QCD Sum Rule Results: r(770) in Nuclear Matter
[Leupold etal ’98]
Comparison
to hadronic
Vacuum:
- 2> = k <qq>
- 2
<(qq)
many-body
models
- 2> decreases
Nuclear Matter: <(qq)
 softening of r -propagator
0.2%
1%
• roughly consistent
• sensitive to detailed shape
• decreasing mass or
increasing width
4.2 Vector-Meson Spectral Functions in
High-Energy Heavy-Ion Collisions:
Hot and Dense Matter
4.2.1 r -Meson Spectral Functions at SPS
Hot+Dense Matter
Model
Comparison
Hot
Meson
Gas
rB/r0
0
0.1
0.7
2.6
[RR+Wambach ’99]
[Eletsky etal
’01]
[RR+Wambach
’99]
[RR+Gale ’99]
• r -meson “melts” in hot and dense matter
• baryon density rB more important than temperature
• reasonable agreement between models
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)
•  also melts,  more robust ↔ OZI
4.2.3 Lattice Studies of Medium Effects

calculated
on lattice
[Laermann,
Karsch ’04]
cosh( q0 (t - 1 / 2T ))
 (t , T )   dq0 Im  (q0 , T )
sinh( q0 / 2T )
0
extracted
1-
MEM
0-
4.2.4 Comparison of Hadronic Models to LGT

cosh( q0 (t - 1 / 2T ))
 (t , T )   dq0 Im  (q0 , T )
sinh( q0 / 2T )
0
calculate
integrate
More direct!
Proof of principle, not yet meaningful (need unquenched)
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
/3
 universal scaling law q q1T/ 3 q q1vac
 m*N m N  m*r mr [Brown+,
Rho ’91]
(3) Vector Manfestation of Chiral Symmetry [Harada+Yamawaki, ’01]
(a) Vacuum: effective Lpr with rL≡p (“VM”)
(b) Finite Temperature:
thermal p- and r -loop expansion → fp(T) , mr(T)
QCD-matching requires “intrinsic” T-dependence of bare mr(0), gr
 dropping r -mass
4.4 Dilepton Rates and Chiral Restoration
dRee /dM2 ~ f B Im em
[qq→ee]
[qq+O(
s)-HTL] [Braaten,Pisarski+Yuan ’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?
4.4.2 Current Status of a1(1260)
r
+
>
+
N(1520)…
Exp: - HADES (pA): a1→(p+p-)p
- URHICs (A-A) : a1→ pg
>
...
>
p
p
>
a1
,N(1900)…
4
4
m
m
ds
a1
r
2
fp  - 
( 2 Im Dr - 2 Im Da1 )
p s gr
ga
1
5.) Dilepton Emission from the QGP
5.1 Pertubative vs. Lattice QCD
5.2 Emission from “Resonances”
5.1 Perturbative vs. Lattice QCD
q
_
e+
q
e-
Baseline:
Im
[
q
q
]=
But: small M → resummations
finite-T perturbation theory (HTL)
[Braaten,Pisarski+Yuan ‘91]
+
+
+…
collinear enhancement:
Dq,g=(t-mD2)-1 ~ 1/αs
• large enhancement at low M
• not shared by lattice calculations:
threshold + resonance structures
[Bielefeld
(photon rate?!)
Group ‘02]
5.2 QGP Dileptons from Bound States
[Shuryak+Zahed ‘04]
→ based on finite-T lattice potentials
approach to “zero-binding line”  ~ stable-mass r -resonance
Dilepton Spectrum
_
ratio to pert. qq rate
[Casalderrey+
Shuryak ‘04]
Mee/mq
• double-peak structure due to zero-binding line + mixed phase
• factor 1.5-2 enhancement at M≈1.5GeV; depends on quark width
6.) Thermal Photon Emission Rates
and Dense Hadron Gas
Emission Hot
Rates
q + q (g) → g (q) + γ
Low energy: vector dominance
Quark-Gluon Plasma
“Naïve” LO:
q
 Im Πem(q0=q) ~ Im Dr (q0=q)
r
q
p
g
But: other contributions in O(αs)
collinear enhanced Dg=(t-mD2)-1~1/αs
p
High energy: meson exchange
p
Bremsstrahlung
Pair-ann.+scatt.
Total HG ≈(LPM)
in-med QGP !
+ ladder resummation
[Aurenche etal ’00, Arnold,Moore+Yaffe ’01]
γ
pa1,
r
p
to be understood…
[Kapusta,Lichard+Seibert ’91, … ,
Turbide,RR+Gale’04]
7.) Dilepton Spectra in
Relativistic Heavy-Ion Collisions
7.1 Space-Time Evolution of URHIC’s
- Formation and Freezeouts
- Trajectories in the QCD Phase Diagram
7.2 Comparison to Data
- Dileptons at SPS (√s = 17, 8 GeV)
- Photons at SPS (√s = 17 GeV)
- RHIC (√s = 200 GeV)
7.1.1 Hadron Production in Heavy-Ion Collisions
→ well described by hadron gas in n (  ,T )  d d 3k f ( E ; ,T )
i
k B
3
thermal+chemical equilibrium: i B
( 2p )
[Braun-Munzinger etal ‘03]
SPS / RHIC: “chemical freezeout” close to phase boundary
 need to construct “evolution”
• before: up to earliest “formation” time t0 ↔ T0 > Tchem
• after: down to thermal freezeout
tf ↔ Tfo < Tchem
7.1.2 Trajectories in the Phase Diagram
• Basic assumption: entropy (+baryon-number) conservation
 fixes T(B) in the phase diagram
• Time scale: hydrodynamics, e.g. VFB(t)=(z0+vzt ) p (R┴0+ 0.5a┴t2)2
Caveat: conserve hadron
ratios after chem. f.o.
 chemical potentials
for p , K, N,…:
p,K,N > 0 for T < Tchem
N [GeV]
t [fm/c]
Thermal Dilepton Emission Spectrum
therm
dN ee
dM
t fo
therm
Md 3q dN ee
N
p Acc


  dt VFB (t ) 
(
M
,
q
;
T
,

)
exp
(

/
T
)
i
p
4
4
q0 d xd q
t
0
7.2.1 Low-Mass Dileptons at SPS
Top SPS Energy
• QGP contribution small
• medium effects!
• drop. mass or broadening?!
Lower SPS Energy
• enhancement increases!
• confirms importance of
baryonic effects (predicted)
7.2.2 Intermediate-Mass Dileptons at SPS: NA50
e.m. corr. continuum-like: Im Πem~ M2 (1 + s/p +…) QGP + HG!
Thermal Fireball (chem-off-eq)
Ti≈210MeV , HG-dominated
[RR+Shuryak ’99]
Hydrodynamics (chem-eq)
Ti≈300MeV, more QGP contr.
[Kvasnikowa,Gale+Srivastava ’02]
7.2.3 Photon Spectra at the SPS: WA98
Hydrodynamics: QGP + HG
[Huovinen,Ruuskanen+Räsänen ’02]
• T0≈260MeV, QGP-dominated
• still true if pp→gX included
Expanding Fireball + pQCD
[Turbide,RR+Gale’04]
• pQCD+Cronin at qt >1.5GeV
 T0=205MeV suff., HG dom.
7.3 Dilepton Spectrum at RHIC
MinBias Au-Au (200AGeV
[R. Averbeck,
PHENIX]
[RR ’01]
thermal
• low mass: thermal dominant
• int. mass: cc
e+X , rescatt.?
e-X
run-4 results
eagerly awaited …
8.) Conclusions
• Thermal E.M. Radiation from QCD matter
- Low-mass dileptons: in-med r (, ) ↔ Chiral Restoration!?
- Intermediate mass: qq- annihilation ↔ QGP Radiation!?
- similar for photons but M=0
• 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 data+theory needed for definite conclusions
• much excitement ahead: PHENIX, NA60, CERES, HADES,
ALICE, …
and theory!