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Light and Heavy Hadrons in Medium
Ralf Rapp
Cyclotron Inst. and Physics Dept.
Texas A&M University College Station, USA
Frankfurt am Main, 25.06.04
1.Introduction: Towards the Phase Transition
note: high-density CFL phase (CSC) characterized by “hadronic” excitations (“”, “”, …)
0 0.05 0.3 0.75 [GeVfm-3] 120 150-160 175 T [MeV] ½ 20 50 hadron
PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD
• Description of Chiral Symmetry Restoration / Decofinement requires nonperturbative approaches• Mean-field models (lin. -model, NJL) capture many aspects, but incomplete (limited d.o.f., only mass effects,…)
1. Introduction
2. Hadrons below Tc 2.1 Light Hadrons: Vacuum
2.2 Hadronic Many-Body Approach: u,d Sector - Mesons: 0± (-), 1± (-a1) , Baryons: - Consistency and Constraints (Nuclei, Lattice, …) - Towards a Chiral + Resonance Scheme - URHIC’s
2.3 Charmed Mesons
3. “Hadrons” at and above Tc
3.1 Continuity ?! 3.2 Heavy Quarks: Charmonium Regeneration 3.3 Light Quarks: Generalization of Coalescence
4. Conclusions
Outline
2.1 Light Hadrons: Vacuum
Tiqx jxjexdiq )0()()( 4
Correlation Function:Timelike (q2>0) : Im q0,q) → physical excitations
)Im(Im2AVs
dsf
)(Im)()(Im 22
sDg
ms
=1± (qq)
Chiral breaking: Q2 < (1.5-2 GeV)2 , J± < 5/2 (?!)
(qqq)
(ii) Light Sector in Vacuum II: Spacelike
Constituent Quark Mass
“Data”: lattice [Bowman etal ‘02]Curve: Instanton Model [Diakonov+ Petrov ’85, Shuryak]
p and d F2 Structure Functions Jlab Data
=2x/(1+√1+4M2x2/Q2) (Nachtmann Variable)
average → “Quark-Hadron Duality” [Niculescu etal. ’00]
2.2 Hadronic Many-Body Approach:
Light Sector (u,d)
2.2.1 0± Mesons: Pion and “Sigma”
2.2.2 1± : Rho and a1(1260)
2.2.3 Chiral + Resonance Scheme2.2.4 Baryons: (1232)2.2.5 Comparison to Lattice2.2.6 URHICs: E.M. Probes and Resonances
2.2.1 Pion and Sigma in MediumD=[k0
2-k2-(k0,k)]-1
>
>= +N,
N-1,-1
• finite N prevalent• “diluted” at T>0
“” → at Tc
Precursor in nuclei ?!A→()S-WaveA
URHICs: - fluct. (0,q→0) - M-spectra - (very) soft photons
(i) (770)
+>
>
B*,a1,K1...
N,,K…
Constraints:- branching ratios B,M→N, - N,Aabsorpt.,N→N- QCD sum rules
Significance of high B at low M Elab=20-40AGeV optimal?!
2.2.2 1± Mesons:
(ii) Vector Mesons at RHIC
baryon effects important even at B,tot=0 :sensitive to Btot=+B , more robust ↔ OZI -
(iii) Current Status of a1(1260)
>
> >
>
N(1520) …
,N(1900)…
a1 + + . . .
Exp: - HADES (A): a1→(+-) - URHICs (A-A) : a1→
]ImIm[1
1
1
2
4
2
42
aa
aD
g
mD
g
m
s
dsf
0 =
2.2.3 Towards a Chiral + Resonance SchemeOptions for resonance implementation:(i) generate dynamically from pion cloud [Lutz et al. ‘03, …]
(ii) genuine resonances on quark level → representations of chiral group [DeTar+Kunihiro ‘89, e.g. Jido etal ‘00, …]
N+
N(1535)-
a1 N(1520)-
N(1900)+ (1700)-
(?) (1920)+
S
P
S
S SS
P SS (a1)S
Importance of baryon spectroscopyto identify relevant decay modes!
2
3S
2
1S
2.2.4 In-Medium Baryons: (1232)
long history in nuclear physics ! ( A , A )
e.g. nuclear photoabsorption: M, up by 20MeV
little attention at finite temperature
-Propagator at finite B and T [van Hees + RR ’04]
in-medium vertex corrections incl. g’-cloud, (“induced interaction”)(1+ f - f N) thermal -gas
→N(1440), N(1520), (1600)
+ + + + ...
>
>>
> >>
>> NN-1 N-1
(i) Check: in Vacuum and in Nuclei
),(),()2(
4)( 03
3
0 qpqEGEfpd
qG NNpN
N
)(Re
)(Imtan)( 1
33 MG
MGM
232
2
),(3
2)( cmcm
NN kFkM
M
m
fM
→ ok !
(ii) (1232) in URHICs
broadening: Bose factor, →B repulsion: N-1, NN-1
not yet included: (N↔ ),( pEGmedN
2.2.5 Lattice Studies of Medium Effects
)2/sinh(
))2/1(cosh(),(Im),(
0
00
00 Tq
TqTqdqT
calculatedon lattice
more stable than below Tc?! (but: quenched)
MEM
1-
0-
extracted
[Laermann, Karsch ’04]
Comparison of Hadronic Models to LGT
)2/sinh(
))2/1(cosh(),(Im),(
0
00
00 Tq
TqTqdqT
calculate
integrate
More direct!
Proof of principle, not yet meaningful (need unquenched)
2.2.6 Observables in URHICs
(i) Lepton Pairs (ii) Photons
),(1
023
2
4Tqf
Mqd
dR Bee
Im Πem(M,q) ),( 0230 Tqf
qd
dRq B
Im Πem(q0=q)
e+
e- γ
baryon density effects!
[Turbide,Gale+RR ’03]
• consistent with dileptons• Brems with soft at low q?
(iii) Resonance Spectroscopy I: +- Spectra
MTqf
qdd
xdMd
dN vacRR
),()2(
03
3
3
Sudden Breakup Emission Rate
[Broniowski+Florkowski ’03]-mass shift ~ -50MeV small “” contribution underestimates
[Shuryak+ Brown ’03]
),(Im2
)()2(
Im0
03
3
4qMD
q
Mqf
qdd
xdMd
dNR
RR
Broadening+“”+BE not enough?!
(iv) Resonance Spectroscopy II : +p Spectra
N
Qualitatively in line with data (eV , MeV)
[courtesy P. Fachini]
(1232) at RHIC
eV±10)MeV mean-field: MeVGmM VBB 55)(
2
3
2
3 )()(
2.3 Charm(onium) below Tc
reldiss
k vsTEfkd
,,
,3
31 )(
)2(Dissociation rate
J→ DD,D*D
QCD-SR Mes-Ex
CQM pQCD
Reduced DD threshold: mD(Tc)≈-140MeV (NJL) J/ robust ’ fragile: direct ’→ DD decays
[Grandchamp+RR ’03]
3. “Hadrons” at and Above Tc
3.1 Continuity ?!3.2 Charmonium in QGP3.3 Light Hadrons in QGP
3.1 Continuity?!
Light Hadron “Masses”
[Shuryak, Zahed, Brown ’04]
However: peak in susceptibilities at Tc
↔ m→ 0
Observables ? e+e-+, fluct, , J/
qqchiral m
m
2
2
TrFyxdeconf
QQeTrLTrLLL/)(22 ,
E.M. Emission Rates
3.2 Charmonium in QGPD=[M2-m
2-]-1 , m≈const (QCD-SR, LGT)
reldiss
gqkgq vTf
kdm
,,
,3
31 )(
)2(/Im
gluo-dissociation,inefficient for m≈ 2 mc
*
“quasifree” diss.[Grandchamp+RR ’01]
)( eqNNd
dN
if c-quarks thermalize
include back-channel :
“jumps” across Tc sensitive to mc*
[Grandchamp +RR ’03]
Charmonia in URHIC’s SPS RHIC
J/ Excitation Function
3.3 Light Hadrons in QGP
• “Resonance” matter at 1-2Tc?! - EoS can be ok [Shuryak+Zahed’04]
• assess formation rates from inelastic reactions (as in charmonium case): q+q ↔ “”+X , etc.
• solve (coupled) rate equations
• accounts for energy conservation, no “sudden” approximation -formation more reliable
To be resolved:• quark masses are not “constituent”:
• role of gluons? (not really heavier than quarks…) , …
generalizescoalescence [Greco,Ko+RR, in progress]
thqq mm 0
4. 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. “”)
• Interpretations?
- many spectral properties appear to vary smoothly- connections to phase transition to be established- need nonperturbative symmetry-conserving approach, e.g. selfconsistent -derivable thermodyn. potential
Additional Slides
[PHENIX]preliminary
[PHENIX]preliminary
4.3 Charm I: Open Charm (Central A-A) (i) Yields • RHIC: -30% for =02: CGC [Tuchin], Color-Dipole [Raufeisen]
• LHC: CGC: Npart ; nonlin. DGLAP: enhanced! [Kolhinen]
(ii) pT-Spectra
dE/dx : Null Effect?! [Djordjevic]
v2(e±) : Thermalization?!
3.4 Hydro vs. Coalescence: The 2-6GeV Regime
v2: mass-dependent
But: p/(4GeV)≈0.3 [PHENIX]: 1±0.15
[Hirano,Nara]
Challenges: p/=1 + jet correlation , elliptic flow
[Fries,Hwa,Molnar]
)()(|)(|)2(
2333 bbaahh
h pfpfqqdpd
gpd
dNE
universal partonic v2(pT/n) / n soft-soft ≈ thermal ( pT » m )soft-hard: explicit thermal+jet (correlations!)
[Greco et al.]
[PHENIX] [STAR]
Direct Photons at SPS and RHIC
• large “pre-equilibrium” yield from parton cascade (no LPM)• thermal yields ~ consistent• QGP undersaturation small effect
• pQCD Cronin ~ π0
T0≈205MeV sufficient• new WA98 points: -Bremsstr. via soft ?
[Turbide etal]
• RHIC central: Ncc≈10-20,
• QCD lattice: J/’s to~2Tc
4.3 Charm II: CharmoniumRegeneration in QGP / at Tc
J/ + g c + c + X→←[PBM etal, Thews etal]
Npart
[Grandchamp]
sensitivity to mc *
-If c-quarks thermalize: )( eqNN
d
dN