Transcript r Mesons in Medium at RHIC + JLab Ralf Rapp Cyclotron Institute + Dept.

r Mesons in Medium at RHIC + JLab
Ralf Rapp
Cyclotron Institute +
Dept. of Physics & Astronomy
Texas A&M University
College Station, USA
Theory Center Seminar
Jefferson Lab (Newport News, VA), 28.03.11
1.) Introduction: QCD Hadron and Phase Structure
• Electromagn. spectral function
- √s ≤ 1 GeV : non-perturbative
- √s ≥ 2 GeV : pertubative (“dual”)
• Disappearance of resonances
↔ phase structure changes:
- hadron gas → Quark-Gluon Plasma
- realization of transition?
• Thermal e+e- emission rate from
hot/dense matter (lem >> Rnucleus )
2
dN ee
- em
B

f
( q0 ,T ) Im Πem(M,q;mB,T)
4
4
3 2
d xd q  M
• Temperature? Degrees of freedom?
• Deconfinement? Chiral Restoration?
e+e- → hadrons
√s=M
1.2 Intro-II: Low-Mass Dileptons at CERN-SPS
CERES/NA45 [2000]
NA60 [2005]
mee [GeV]
• strong excess around M ≈ 0.5GeV (and M > 1GeV)
• little excess in r/w and f region
Outline
1.) Introduction
2.) Resonances + Chiral Symmetry
 Spontaneous Chiral Symmetry Breaking + Chiral Partners
3.) r Meson in Medium
 Hadronic Lagrangian + Empirical Constraints
 Many-Body Theory + Spectral Functions
4.) Dilepton Spectra in Heavy-Ion Collisions
 Thermal Emission Rates, Lattice QCD
 Phenomenology in URHICs
5.) Dilepton Spectra in Nuclear Photo-Production
 Elementary Amplitude, CLAS Phenomenology
6.) Conclusions
2.1 Chiral Symmetry Breaking + Hadron Spectrum
Condensates fill QCD vacuum: 0 | q q | 0  0 | qLqR  qRqL | 0  5 fm -3
Quark Level: Const. Mass
Observables: Hadron Spectrum
M [GeV]
“Data”: lattice [Bowman et al ‘02]
Theory: Instanton Model
[Diakonov+Petrov; Shuryak ‘85]
• Mq* ~ ‹0|qq|0›
• chiral breaking: |q2| ≤ 1 GeV 2
D(1700)
N(1520)
D(1232)
JP=0±
1±
1/2±
3/2±
• energy gap
• massless Goldstone mode
• “chiral partners” split (½ GeV)
2.2 Q2-Dependence of Chiral Breaking
Axial-/Vector Mesons
F2-Structure Function (spacelike)
JLAB
Data
p
pQCD
cont.
d
• Weinberg Sum Rule(s)
f2  -  ds (Im  VI 1 - Im  AI 1 )
s
• spectral distributions!
x≈x
• average → Quark-Hadron Duality
• lower onset-Q2 in nuclei?
[Niculescu et al ’00]
Outline
1.) Introduction
2.) Resonances + Chiral Symmetry
 Spontaneous Chiral Symmetry Breaking + Chiral Partners
3.) r Meson in Medium
 Hadronic Lagrangian + Empirical Constraints
 Many-Body Theory + Spectral Functions
4.) Dilepton Spectra in Heavy-Ion Collisions
 Thermal Emission Rates, Lattice QCD
 Phenomenology in URHICs
5.) Dilepton Spectra in Nuclear Photo-Production
 Elementary Amplitude, CLAS Phenomenology
6.) Conclusions
3.1 r-Meson in Vacuum and Hot/Dense Matter
• Vacuum: chiral  r Lagrangian  Sr 
→ P-wave  phase shift,  el.-mag. formfactor

r

+
• Hadronic Matter: effective Lagrangian for interactions with heat bath
 In-Medium r -Propagator
r
Dr (M,q;mB,T) = [M2 - mr2 -Sr - Sr B -Sr M ]-1
Sr =
[Chanfray et al, Herrmann et al,
Urban et al, Weise et al, Oset et al, …]
• r-Hadron Scattering
[Haglin, Friman et al,
RR et al, Post et al, …]
SrB,M =
+
S
r
>
R=D, N(1520), a1, K1 ...
>
• Pion Cloud
S
S
r
h=N, , K …
• constrain effective vertices: R→ r h, scattering data (N→rN, gN/A)
3.2 Scattering Processes from r Spectral Function
↔ Cuts (imag. parts) of Selfenergy Diagrams:

N-1


r
>
B
N
S
r
D
N-1
r
resonance
excitation
gN→D→N
meson-exchange
scattering
g N →  N,  D
meson-exchange
current
g NN →NN, ND
3.3 Constraints from Nuclear Photo-Absorption
g-absorption cross section
in-medium r spectral function
 gabs
A ( q0 )
 - 4  Im  em ( q0  q )  Im Drmed ( M  0,q )
A
q0 r N
Nucleon
[Urban,Buballa,
RR+Wambach ’98]
Nuclei
gN
gA
-ex
• quantitative determination of
interaction vertex parameters
• melting of 2.+3. resonances
3.4 r Spectral Function in Nuclear Matter
In-med. -cloud +
rN→B* resonances
[Urban
et al ’98]
rN→B* resonances
(low-density approx.)
In-med -cloud +
rN → N(1520)
[Post
et al ’02]
rN=r0
Constraints: g N , g A
 N →r N PWA
• strong broadening + small upward mass-shift
• empirical constraints important quantitatively
[Cabrera
et al ’02]
rN=0.5r0
rN=r0
3.5 r Spectral Function in Heavy-Ion Collisions
Hot+Dense Matter
Hot Meson Gas
rB /r0
0
0.1
0.7
2.6
[RR+Wambach ’99]
• r-meson “melts” in hot /dense matter
• medium effects dominated by baryons
[RR+Gale ’99]
Outline
1.) Introduction
2.) Resonances + Chiral Symmetry
 Spontaneous Chiral Symmetry Breaking + Chiral Partners
3.) r Meson in Medium
 Hadronic Lagrangian + Empirical Constraints
 Many-Body Theory + Spectral Functions
4.) Dilepton Spectra in Heavy-Ion Collisions
 Thermal Emission Rates, Lattice QCD
 Phenomenology in URHICs
5.) Dilepton Spectra in Nuclear Photo-Production
 Elementary Amplitude, CLAS Phenomenology
6.) Conclusions
4.1 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:   - → e+e- , …
_
• final-state hadron decays: 0,h → ge+e- , D D → e+e- X , …
4.2 Thermal Dilepton Emission
g*
e+
e-
Rate:
2
dN ee
- em
B

f
( q0 ,T ) Im Πem(M,q;mB,T)
4
4
3 2
d xd q  M
ee→had / ee→mm ~ Im em(M) / M2
e+
e-
r


M ≤ 1 GeV: non-perturbative
√s=M
Imem ~ [Im Dr + Im Dw /10 + Im Df /5]
“Hadronic Spectrometer” (T ≤ Tc)
e+
q-
e-
q
M > 1.5 GeV: perturbative
Im em ~ Nc ∑(eq)2
“QGP Thermometer” (T > Tc)
4.2.2 Dilepton Rates: Hadronic vs. QGP
dRee /dM2 ~ ∫d3q f B(q0;T) Im em
[qq→ee]
[HTL]
• Hadronic and QGP rates tend to
“degenerate” toward ~Tc
F2-Structure Function
• Quark-Hadron Duality at all M ?!
( degenerate
JLAB
Data
axialvector
SF!)
p
d
[RR,Wambach et al ’99]
x
4.3 Lattice-QCD Dilepton Rate
[Kaczmarek et al ’10]
dRee/d4q
q=0
1.4Tc (quenched)
• low-mass enhancement in lattice rate!
• similar to hard-thermal-loop resummed perturbation theory
[Braaten,Pisarski+Yuan ‘90]
4.3.2 Euclidean Correlators: Lattice vs. Hadronic

• Euclidean Correlation fct. GV ( ,q ;T )   dq0 Im V ( q0 ,q ;T ) cosh [ q0( - 1 / 2T )]
0
Lattice [Kaczmarek et al ‘10]
2
sinh [ q0 / 2T ]
Hadronic Many-Body vs. Lat. [’02]
GV ( ,T )
GVfree( ,T )
• “Duality” of lattice (1.4 Tc) and hadronic many-body (“Tc”) rates?!
-Im em /(C T q0)
4.3.3 Back to Spectral Function
• corroborates approach to chiral restoration !?
4.4 Dileptons in Heavy-Ion Collisions
• Evolve rates over fireball expansion:
m+m- Spectra at CERN-SPS
therm
dN ee
2
In-In(158AGeV)
[NA60 ‘09]
Mmm [GeV]
• invariant-mass spectrum directly
reflects thermal emission rate:
[van Hees
+RR ’08]
- M<1GeV: r broadening
- M>1GeV: Tslope ~ 160-180 MeV
dM
 fo
therm
d 3q dRee
  d VFB ( ) 
2q0 d 4q

0
Thermal mm- Emission Rate
4.4.2 Conclusions from Dilepton “Excess” Spectra
• thermal source (T~120-200MeV)
• M<1GeV: in-medium r meson
- no significant mass shift
- avg. Gr (T~150MeV) ~ 350-400 MeV
 Gr (T~Tc) ≈ 600 MeV → mr
- driven by baryons
• M>1GeV: radiation around Tc
• fireball lifetime “measurement”:
FB ~ (6.5±1) fm/c (semicentral In-In)
• approach seems to fail at RHIC
[van Hees+RR ‘06, Dusling et al ’06,
Ruppert et al ’07, Bratkovskaya et al ‘08]
Mmm [GeV]
Outline
1.) Introduction
2.) Resonances + Chiral Symmetry
 Spontaneous Chiral Symmetry Breaking + Chiral Partners
3.) r Meson in Medium
 Hadronic Lagrangian + Empirical Constraints
 Many-Body Theory + Spectral Functions
4.) Dilepton Spectra in Heavy-Ion Collisions
 Thermal Emission Rates, Lattice QCD
 Phenomenology in URHICs
5.) Dilepton Spectra in Nuclear Photo-Production
 Elementary Amplitude, CLAS Phenomenology
6.) Conclusions
5.1 Nuclear Photoproduction: r Meson in Cold Matter
g+A→
e+e-
X
e+
g
r
Eg ≈ 1.5-3 GeV
[CLAS+GiBUU ‘08]
• extracted “in-medium” r-width Gr ≈ 220 MeV - small?!
e-
5.2 Equilibrium Approach
(a) Production Amplitude: t-channel [Oh+Lee ‘04] + resonances (r spectr. fct.!)
g d → e+e- X
r
g
+ CLAS
N
g N→ rN
(b) Medium Effects:
r propagator in cold nuclear matter
- broadening much reduced with
increasing 3-momentum
d gAeeX
~  f N | Tprod |2 | Dr |2 Gg * ee
dM
Im Dr [1/MeV2]
[Riek et al ’08, ‘10]
M [GeV]
5.2.2 Application to CLAS Data
Eg ≈1.5-3 GeV, uniform production points, decay distribution with in-med Gr
Density at r Decay Point
• average qr ~ 2GeV  average rN(Fe) ~ 0.4r0
• free norm: c2 =1.08 vs. 1.55 in-med vs. vac r spectral function
• need low momentum cut + absolute cross section!
5.3 Predictions for r Photoproduction
3-Momentum Cuts
• low-momentum yield small,
but spectral broadening strong
Transparency Ratio
X.) Axialvector in Medium: Dynamical a1(1260)

Vacuum:
In
Medium:
r

r
+
S
Sr
...
+
+
S
S
Sr
Sr
a1
= resonance
+ ...
• in-medium  + r propagators
• broadening of -r scattering
amplitude
[Cabrera et al. ’10]
6.) Conclusions
• EM spectral function ↔ excitations of QCD vacuum
- ideal tool to probe hot/dense matter
• Effective hadronic Lagrangian + many-body theory:
- strong r broadening in (baryonic) medium,
suppresed at large momentum (CLAS!)
• Dileptons in heavy-ion collisions:
- spectro- /thermo-meter (CERES, NA50,NA60)
- r melting at “Tc” = 160-190 MeV
→ quark-hadron duality?! hadron liquid?!
• Sum rules + axialvector spectral function to tighten
relations to (partial) chiral restoration
• Future experiments at RHIC-2, FAIR +LHC; JLAB?!
4.2.4 Intermediate-Mass Dileptons: Thermometer
• QGP or Hadron Gas (HG) radition?
• vary critical temperature Tc in fireball evolution
qq- → mm → mm(e.g. a1 → mm-)
green: Tc=190MeV
red: Tc=175MeV (default)
blue: Tc=160MeV
• partition QGP vs. HG depends on Tc
(spectral shape robust: dilepton rate “dual” around Tc! )
• Initial temperature Ti ~ 190-220 MeV at CERN-SPS
4.4 Sum Rules and Order Parameters
• QCD-SRs

Π ( Q 2 )
ds Im   ( s )

 s Q2  s
Q2
0
2
2

2  G 2  




(
q
q
)

Q
2

s
s
1
 r ( Q )  2 ( 1   s ) ln  2  
-C
 ...
4
6
3
8 
Q
Q

 
[Hatsuda+Lee ’91, Asakawa+Ko ’92, Klingl et al ’97,
Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]
• Weinberg-SRs: moments Vector-Axialvector
In  -  ds s n (Im  V - Im  A )

[Weinberg ’67, Das et al ’67,
Kapusta+Shuryak ‘93]
I-2  1 fπ2 rπ2 - FA , I-1  fπ2 , I0  0 , I1  c αs (q q)2
3
 Promising synergy of lQCD and effective models
3.2.5 EM Probes in Central Pb-Au/Pb at SPS
Di-Electrons [CERES/NA45]
Photons [WA98]
[Turbide et al ’03,
• consistency of virtual+real photons (same em)
van Hees+RR ‘07]
• very low-mass di-electrons ↔ (low-energy) photons
[Srivastava et al ’05, Liu+RR ‘06]
3.5.2 Rho, Omega + Phi Freezeout from pt-Spectra
r
• r freezeout = fireball freezeout
• adjust w and f freezeout
contribution to fit pt-spectra
• sequential freezeout f → w → r
• consistent with mass spectra
3.5.3 Composition of Mass Spectra in qt-Bins
low qt
high qt
intermed. qt
• high qt ≥ 1.5GeV:
- medium effects reduced
- non-thermal sources take over
3.5 Dimuon pt-Spectra and Slopes
• check fireball evolution to fit slopes
of excess radiation (▼)
(thermal radiation softer by Lorentz-1/g)
• increase a┴ = 0.085/fm → 0.1/fm
(viscous effects, larger grads. in In-In …)
5.2.5 NA60 Dimuons: pt-Slopes
• in-medium radiation “harder” than
hadrons at freezeout?!
(thermal radiation softer by Lorentz-1/g)
• smaller Tch helps (larger Tfo)
• non-thermal sources (DY, …)?
• additional transverse acceleration?
• hadron spectra (pions)?
Tch=160MeV
a┴ =0.1/fm
Tch=175MeV
pions: T
=175MeV
Tch
ch=160MeV
a┴ =0.085/fm
Tch=160MeV
pions: T =160MeV
a┴ =0.085/fm ach =0.1/fm
┴
2.2 Chiral + Resonance Scheme


rS

P
S
r
S
a1
1
S
2
N+
S

3 P
S
2
D
S
N(1535)rS
(a1)S
S
N(1520)
D(1700) (?)
• add S-wave pion → chiral partner
• P-wave pion → quark spin-flip
• importance of baryon spectroscopy
N(1900)+
D(1920)+
3.1 Axial/Vector Mesons in Vacuum
Introduce r, a1 as gauge bosons into free  +r +a1 Lagrangian 


 m  1 2  m   r
int
L  g r  (    ) - g r  r  
r
m
2
m

r -propagator: Dr ( M )  [ M 2 - ( mr( 0 ) )2 - S r ( M )] -1
 EM formfactor
2
| F ( M ) |
 ( mr( 0 ) )4
2
| Dr ( M ) |
 scattering phase shift
-1
Im Dr ( M ) 

 ( M )  tan 
 Re Dr ( M ) 
|F|2

3.3 “Non-Thermal Dilepton Sources
→ relevant at M, qt ≥ 1.5 GeV (?)
• primordial qq- annihilation (Drell-Yan): NN → e+e- X
• r mesons at thermal freeze-out (“blast-wave”):
- extra Lorentz-g factor relative to thermal radiation
- qt-spectra + yield fixed by fireball model
• primordial (“hard”) r mesons:
- schematic jet-quenching
with abs fit to pions
• late _decays: 0,h → ge+e- ,
DD → e+e-X , J/y→e+e- , …
f.o. + prim. 
2.2 Electric Conductivity
 em
2 lim
2
e
 2 Im  ( q ,q  0 )
em 0
3 q0  0 q0
• pion gas (chiral pert. theory)
[Fernandez-Fraile+Gomez-Nicola ’07]
em / T ~ 0.01 for T ~ 150-200 MeV
• quenched lattice QCD [Gupta ’04]
em / T ~ 0.35 for T = (1.5-3) Tc
• soft-photon limit
q0
dNg
d 4 x d 3q
( q0  0 ) 
3T 
3 em
( 2 )
3.2.3 NA60 Excess Spectra vs. Theory
[CERN Courier
Nov. 2009]
• Thermal source does very well
• Low-mass enhancement very sensitive to medium effects
• Intermediate-mass: total agrees, decomposition varies