Transcript Light and Heavy Hadrons in Medium - uni

Light and Heavy Hadronic Modes
in Medium
Ralf Rapp
Cyclotron Institute
+ Physics Department
Texas A&M University
College Station, USA
Universität Bielefeld, 11.01.05
1. Motivation: Relativistic Heavy-Ion Collisions
J/y
Au + Au
QGP ?!
e+
e-
r
g
Hadron Gas
Signatures of the QGP?
• Suppression of J/y-Mesons
• Decays of r-Mesons
• Photons
…
“Freeze-Out”
Au + Au → X
1.2 Current Status: Towards QGP Discovery
• So far: RHIC observables
↔ bulk properties of the produced matter:
- energy density e≈20GeVfm-3 ↔ jet quenching (high-pt)
- thermalization + EoS
↔ hydrodynamics (v0,v2)
- partonic degrees of freedom ↔ coalescence (p/p, v2-scal)
• Future: need to understand
microscopic properties (phase transition, “QGP” !?):
- Deconfinement
↔ quarkonia (J/y, , …)
- Chiral Symmetry Restoration ↔ dileptons
( - temperature
↔ photons )
Outline
1. Introduction
2. Vacuum: Chiral Symmetry (Breaking)
3. (Light) Hadrons below Tc
3.1 Mesons: 0± (p-s), 1± (r-a1) , Baryons: N, D(1232)
3.2 Towards Chiral + Resonance Scheme
3.3 URHICs: Dileptons + Photons
4. Heavy-Quark Modes
4.1 Charmed Hadrons below Tc
4.2 Heavy-Quark Equilibration
4.3 Quarkonia in the QGP
4.4 URHICs: Suppression vs. Regeneration
5. Conclusions
2.) Chiral Symmetry in QCD: Vacuum
1 2
SU(2)L× SU(2)R
ˆ q ) q  Ga
 m
LQCD  q ( i  gA
invariant (mu,d≈0)
4
qR
Spontaneous Breaking: strong qq- attraction qL
 Bose Condensate q q  q Lq R  q R q L  0
fills QCD vacuum! [cf. Superconductor: ‹ee›≠0
q- L
q- R
Magnet ‹M›≠0 , … ]
Profound Consequences:
• energy gap: Dq q  2m*q  q q
↔ mass generation!
• massless Goldstone bosons
p0,±
• “chiral partners” split, DM≈0.5GeV:
JP=0±
1±
1/2±
2.1 Light Hadrons: Vacuum
Correlation Function:  (q)  i  d 4 x e iqx j ( x) j (0)
T
2
Timelike (q >0) : Im (q0,q) → physical excitations
=1± (qq)
fp2
ds
   (Im V  Im  A )
ps
Im   ( s )  ( m2 / g )2 Im D ( s )
(qqq)
Chiral breaking:
Q2 < (1.5-2 GeV)2 , J± < 5/2 (?!)
2.2 “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
e[GeVfm-3]
T[MeV], rhad
3. Hadrons in Medium: Light Sector (u,d)
3.1.1
3.1.2
3.2
3.3
3.4
3.5
0± Mesons: p and “s”
1± : r(770) and a1(1260)
Chiral + Resonance Scheme
Baryons: D(1232), N
Comparison to Lattice
URHICs: E.M. Probes (and Resonances)
3.1.1 Pion and Sigma in Medium
Dp=[k02-wk2-Sp(k0,k)]-1
>
Sp =
>
N,D
N-1,D-1
+
p
Ds → Dp at Tc
Precursor in nuclei ?!
pA→(pp)S-WaveA
URHICs: - fluct. s(0,q→0)
- pp M-spectra
• rN prevalent, smeared at T>0
- (very) soft photons
3.1.2 (Axial-) Vector Mesons in Medium
(a) Hadronic Many-Body Theory
Dr(M,q:B,T)=[M2-mr2-Srpp-SrB-SrM ]-1
Propagator:
r
Sp
[Chanfray etal, Herrmann etal, RR etal, Koch etal,
Weise etal, Post etal, Eletsky etal, Oset etal, …]
2
 S rpp   Dpmed v rpp
Dpmed
Sp
>
B*,a1,K1...
>
N,p,K…
2
p
M
 S r B ,M   DM v rp
[
f

f
]
M
Constraints:
- B,M→rN,rp
- gN, gA, pN→rN
- QCDSRs, lattice
(b) Effective Field Theory [Harada, Yamawaki, Sasaki etal]
HLS with rL≡p (“VM”); vacuum: loop exp. O(p/Lc , mr/Lc , g)
In-Med.: T-dep. of bare mr(0), gr via matching to OPE, Lmatch<Lc
+ RG-running to on-shell  dropping r-mass
(i) r -Mesons 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
[RR+Gale ’99]
(ii) Vector Mesons at RHIC
e+e- Emission Rates: dRee/dM ~ f B Imem
[qq→ee]
[qq+O(
s)]
baryon effects in-med
important
at rB,net
=0! :
HGeven
≈ in-med
QGP
sensitive to rB,totQuark-Hadron
=rB+rB- , f more
robust
Duality
?! ↔ OZI
(iii) Current Status of a1(1260)
Sr
+
>
+
N(1520) …
Exp: - HADES (pA): a1→(p+p-)p
- URHICs (A-A) : a1→ pg
>
...
>
Sp
Sp
>
a1
D,N(1900)…
4
4
m
m
ds r
a1
2
fp    [ 2 Im Dr  2 Im Da1 ]
p s gr
ga
0 
1
=
3.2 Towards a Chiral + Resonance Scheme
Options for resonance implementation:
(i) generate dynamically from pion cloud [Kolomeitsev etal ‘03, …]
(ii) genuine resonances on quark level
→ representations of chiral group [DeTar+Kunihiro ‘89, Jido etal ’00, …]
e.g.
p
s
rS
p
P
pS
r
pS
a1
1
S
2
N+
pS
p
3 P
S
2
D
pS
N(1535)
rS
(a1)S
pS
N(1520)
D(1700)-(?)
N(1900)+
D(1920)+
Importance of baryon spectroscopy
to identify relevant decay modes!
3.3 In-Medium Baryons: D(1232) and N(939)
 long history in nuclear physics ! ( pA , gA )
e.g. nuclear photoabsorption: MD , GD up by 20-40MeV
 little attention at finite temperature
 D-Propagator at finite rB and T
>
in-medium
p-cloud,
(1+ f p - f N)
+
+
>
>
DN-1
>
D
Sp
NN-1
[van Hees+RR ’04]
>
vertex corrections incl. g’
(“induced interaction”)
+
+
...
>
pD→N(1440),
N(1520),
D(1600)
thermal p-gas
D in Nuclei and Heavy-Ion Collisions
D(1232)
Spectral
Fct.
at
RHIC
D in Nuclear g Absorption
Nucleon Spectral Fct. at RHIC
 broadening:
Bose factor, pD→B
 repulsion: pDN-1, pNN-1
 substantial broadening due to
resonant pN → B scattering
3.4 Lattice Studies of Medium Effects

calculated
on lattice
cosh( q0 (  1 / 2T ))
 ( , T )   dq0 Im  (q0 , T )
sinh( q0 / 2T )
0
extracted
[Laermann,
Karsch ’04]
1-
MEM
0-
Comparison of Hadronic Models to LGT

cosh( q0 (  1 / 2T ))
 ( , T )   dq0 Im  (q0 , T )
sinh( q0 / 2T )
0
calculate
integrate
More direct!
Proof of principle, not yet meaningful (need unquenched)
3.5 Observables in URHICs
(i) Dileptons
2 1 B
  3 2 f ( q0 ,T ) Im
4
d q
p M
dRee
e+
eΠem(M,q)
γ
(ii) Photons
 B
q0 3   2 f (q0 , T ) Im Πem(q0=q)
dq p
dR g
[Turbide,Gale+RR ’03]
baryon density effects!
• consistent with dileptons
• pp Brems with soft s at low q?
4. Heavy-Quark Modes
4.1
4.2
4.3
4.4
Charmed Mesons below Tc
Heavy-Quark Equilibration
Charmonium in QGP
URHICs: Suppression vs. Regeneration
4.1 Charmed Mesons in Hadronic Matter
mD(T,rB) expected to decrease
(Chiral Symmetry Restoration)
Gy  y1  
d 3k
(2p )3
f p , r s pdiss
, r y v rel
[Weise etal ’01]
 reduced threshold for
p,r  Y → DD
[Grandchamp+RR ’03]
 J/y robust
 Y’ fragile: Y’→ DD decays
4.2 Heavy-Quark Thermalization in QGP ?
• Naively: 1 scatt. Q2≈ T2, (pt,therm)2≈ mcT  Nscatt≈(pt,therm/Q)2 ≈5
• more quantitative: Boltzmann Eq.
[Svetitsky ’88]

 f 
f ( p, t )   
  d 3k [ w ( p  k ) f ( p  k )  w ( p, k ) f ( p)]
t
 t  coll
f
( pf )
2 f

g
D 2
t
p
p
gp   d k w(k , p) k
3
1-D Fokker Planck Eq.
scatt. rate
2
1 3
D   d k w (k , p) k diff. const.
2

1
E p /T
[ p p0 ( t )]2 / 2s 2
f ( p, t ) 
e
e
2p s
D
s (t ) 2  (1  e 2gt )
g
e.g.: pQCD Xsections, T=500MeV, s=0.6(0.3)
 g=0.25 (0.06) fm-1 ↔ 4-15fm/c
(very) slow!
Resonance cross section
c + q → “D” → c + q ?!
4.2.1 Resonant Open-Charm Rescattering
_
_
c + q → “D” → c + q
• effective model with pseudo/scalar
+ axial/vector “D-mesons”
L Dcq
( 1  v )
 GD q
G f D c  h.c.
2
G  1, g 5 , g  , g 5g 
• chirally symmetric for light quarks
• heavy-quark symmetry
 j conserved to LO(1/mc)
• parameters: mD(0), GD
[van Hees+RR ’04]
“Light”-Quark Resonances
1.4Tc
[Asakawa+
Hatsuda ’03]
4.2.2 Heavy-Quark Thermalization Times in QGP
[van Hees+RR ’04]
Charm Quarks
Bottom vs. Charm
pQCD
“D”
• resonance scatt. isotropic
• secondary open-charm ?!
[50% for 3  s ( gg  c c ) ]
• bottom quarks “barely”
thermalize at RHIC
4.2.3 Single-e± Spectra at RHIC: D → e+X
pt-Spectra: p-p vs Hydro
Ellitpic Flow + Coalescence
[Batsouli etal. ’02]
D
B
PHENIX
130AGeV
jetquench
[Djordjevic
etal ’04]
e±
practically indistinguishable
does charm equilibrate?
_
etal ’95,
• dynamical origin of resonances? cc production? [Müller
Molnar’04]
• onset of pQCD regime: pt>5-6GeV ? open bottom?
4.2 Charmonium in QGP
[Datta etal
’03]
• Lattice: hc, J/y survive up to ~2Tc
• mass my ≈ const ~ 2mc*
• width: Gy  y1  
d 3k
(2p )3
f q, g (T ) s qdiss
, g y v rel
gluo-dissociation
Cross Sections
[Bhanot+Peskin ‘84]
“quasifree” diss.
[Grandchamp+RR ‘01]
Dissociation Times
4.3.1 Charmonium Regeneration vs. Suppression
etal ’01,
• statistical coalescence at Tc: chem.+therm. equil. [PBM
Gorenstein etal ’02, …]
• charmonia above Tc
 formation in QGP: detailed balance!
[Thews etal ’01, Ko etal ’02 …
→ c + c- + X
J/y + g ←
for thermalized c-quarks:
dNy
d
  Gy ( Ny  Nyeq )
“jumps” at Tc
sensitive to N cc , mc*
rather direct link to lattice QCD!
Equilibration close to Tc ?!
Grandchamp+RR ’02]
SPS
4.3.2 Charmonium in A-A
[Grandchamp
+RR ’03]
RHIC
J/y Excitation Function
• QGP regeneration dominant
• sensitive to:
mc* , open-charm degeneracy,
(Ncc)2 ↔ rapidity, √s, A
4.3.3 Upsilon in A-A
[Lumpkins, Grandchamp, van Hees, Sun +RR ’05]
RHIC
LHC
• bottomonium suppression as unique QGP signature ?!
• caveat:  equil. number (very) sensitive to (mb)*, therm
5. Conclusions
• Hadronic Many-Body Theory can provide:
- valuable insights into hadron properties in medium
- understanding of observables in nuclear reactions
• The physics is often in the width (exception: e.g. “s”)
• Interpretations?
- many spectral properties appear to vary smoothly
- connections to phase transition to be established
- need nonperturbative symmetry-conserving approach,
e.g. selfconsistent F-derivable thermodyn. potential
Additional Slides
(iii) Resonance Spectroscopy I: p+p- Spectra
Sudden Breakup
Emission Rate
vac
 pp
d R d 3q R

f (q0 , T )

3
3
M
d xdM p (2p )
dNpp
dR
d 3q R
2M

Im
S
f
(
q
)
Im DR ( M , q)
pp 
0
4
3
q0
d xdM p
(2p )
dNpp
pp
[Broniowski+Florkowski ’03]
 r-mass shift ~ -50MeV
 small “s” contribution
 underestimates rp
[Shuryak+
Brown ’03]
Broadening+“s”+BE not enough?!
(iv) Resonance Spectroscopy II : p+p Spectra
D(1232) at RHIC
D(1232) Spectral Fct. at RHIC
pN
[courtesy P. Fachini]
DMD22MeV
DGD (45±15)MeV
s mean-field:
DM D(s )
Qualitatively in line with data
(DMD6 MeV , DGD65 MeV)
3 (s ) 3
 Dm r  Gs ( r B  r B  rV )  55 MeV
2
2
(ii) D(1232) in URHICs
 broadening: Bose factor, pD→B
 repulsion: pDN-1, pNN-1
not yet included: GNmed ( E , p) (pN↔D)
Direct Photons at SPS and RHIC
[Turbide etal]
• pQCD Cronin ~ π0
 T0≈205MeV sufficient
• new WA98 points:
pp-Bremsstr. via soft s ?
• large “pre-equilibrium” yield
from parton cascade (no LPM)
• thermal yields ~ consistent
• QGP undersaturation small effect
J/y Width from Lattice QCD
3.1 Continuity?!
E.M. Emission Rates
Light Hadron “Masses”
[Shuryak,
Zahed,
Brown ’04]
[RR+Wambach ’99]
However: peak in susceptibilities at Tc
 2  q q
↔ ms → 0
c chiral  2 
mq
mq
2
c deconf  L2  L , TrLx TrLy  e
 FQQ ( r ) / T
Observables ? e+e-+pg, fluct, pp, J/y,...
[Turbide,Gale+RR ’03]
3.3 Light Hadrons in QGP
• “Resonance” matter at 1-2Tc?! - EoS can be ok
• assess formation rates from inelastic reactions
 ↔ “p”+X , etc.
(as in charmonium case): q+q
• solve (coupled) rate equations
[Shuryak+Zahed’04]
generalizes
coalescence
[Greco,Ko+RR,
in progress]
• accounts for energy conservation, no “sudden” approximation
 p-formation more reliable
To be resolved:
mq  g 0 mqth
• role of gluons? (not really heavier than quarks…) , …
• quark masses are not “constituent”:
4.3 Charm II: Charmonium
• RHIC central: Ncc≈10-20,
• QCD lattice: J/y’s to ~2Tc
If c-quarks
thermalize:
dNy
d
Regeneration in QGP / at Tc
→ c- + c + X
J/y + g ←
[PBM etal,
Thews etal]
  Gy ( Ny  Nyeq )
[Grandchamp]
sensitivity to m*c
Npart
3.4 Hydro vs. Coalescence: The 2-6GeV Regime
[Hirano,Nara]
[Fries,Hwa,Molnar]
E
dN h
3
d p
 gh 
ds  p
(2p )3
v2: mass-dependent
But: p/p(4GeV)≈0.3
[PHENIX]: 1±0.15
[STAR]
[Greco et al.]
[PHENIX]
 2


 d q |y h (q ) | f a( pa ) f b ( pb )
3
 universal partonic v2(pT/n) / n
soft-soft ≈ thermal ( pT » m )
soft-hard: explicit thermal+jet (correlations!)
Challenges: p/p=1 + jet correlation , f elliptic flow