Light and Heavy Hadronic Modes in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas...
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Transcript of Light and Heavy Hadronic Modes in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas...
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
“Freeze-Out” Hadron Gas
QGP ?!
Au + Au
1. Motivation: Relativistic Heavy-Ion Collisions
Au + Au → X
e+
e-
Signatures of the QGP?
• Suppression of J/-Mesons
• Decays of -Mesons
• Photons …
J/
1.2 Current Status: Towards QGP Discovery
• So far: RHIC observables ↔ bulk properties of the produced matter:
- energy density ≈20GeVfm-3 ↔ jet quenching (high-pt) - thermalization + EoS ↔ hydrodynamics (v0,v2)
- partonic degrees of freedom ↔ coalescence (p/, v2-scal)
• Future: need to understand microscopic properties (phase transition, “QGP” !?):
- Deconfinement ↔ quarkonia (J/, , …) - Chiral Symmetry Restoration ↔ dileptons ( - temperature ↔ photons )
1. Introduction
2. Vacuum: Chiral Symmetry (Breaking)
3. (Light) Hadrons below Tc
3.1 Mesons: 0± (-), 1± (-a1) , Baryons: N, 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
Outline
2.) Chiral Symmetry in QCD: Vacuum
2
4
1aq Gq)m̂Agi(q QCDL SU(2)L× SU(2)R
invariant (mu,d≈0)
Spontaneous Breaking: strong qq attraction Bose Condensate fills QCD vacuum!
0 LRRL qqqqqq >
>
>
>qLqR
qL-qR
-[cf. Superconductor: ‹ee›≠0 Magnet ‹M›≠0 , … ]
-
Profound Consequences:• energy gap: ↔ mass generation!
• massless Goldstone bosons 0,±
• “chiral partners” split, M≈0.5GeV:
qqm*qqq 2
JP=0± 1± 1/2±
2.1 Light Hadrons: Vacuum
Tiqx jxjexdiq )0()()( 4
Correlation Function:Timelike (q2>0) : Im q0,q) → physical excitations
=1± (qq)
)Im(Im2AVs
dsf
)s(DIm)g/m()s(Im 22
Chiral breaking: Q2 < (1.5-2 GeV)2 , J± < 5/2 (?!)
(qqq)
2.2 “Melting” the Chiral Condensate
How?
Excite vacuum (hot+dense matter)
• quarks “percolate” / liberated Deconfinement • ‹qq› condensate “melts”, iral Symm. chiral partners degenerate Restoration(-, -a1, … medium effects → precursor!)
0 0.05 0.3 0.75 [GeVfm-3] 120, 0.50 150-160, 20 175, 50 T[MeV], had
PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD
-
1.0 T/Tc
m‹qq›-lattice QCD
3. Hadrons in Medium: Light Sector (u,d)
3.1.1 0± Mesons: and “”
3.1.2 1± : (770) and a1(1260)
3.2 Chiral + Resonance Scheme3.3 Baryons: (1232), N3.4 Comparison to Lattice3.5 URHICs: E.M. Probes (and Resonances)
3.1.1 Pion and Sigma in Medium
D=[k02-k
2-(k0,k)]-1
>
>= +N,
N-1,-1
• N prevalent, smeared at T>0
D → D at Tc Precursor in nuclei ?!A→()S-WaveA
URHICs: - fluct. (0,q→0) - M-spectra - (very) soft photons
>
>
B*,a1,K1...
N,,K…
Constraints:- B,M→N, - N,A,N→N- QCDSRs, lattice
3.1.2 (Axial-) Vector Mesons in Medium
D(M,q:B,T)=[M2-m2--B-M ]-1
(a) Hadronic Many-Body Theory
medmed DvD 2
]ff[vD MMMM,B
2
Propagator:
[Chanfray etal, Herrmann etal, RR etal, Koch etal, Weise etal, Post etal, Eletsky etal, Oset etal, …]
(b) Effective Field TheoryHLS with L≡(“VM”); vacuum: loop exp. OO(p/, m/, g)
In-Med.: T-dep. of bare m(0), g via matching to OPE, match<
+ RG-running to on-shell dropping -mass
[Harada, Yamawaki, Sasaki etal]
[RR+Gale ’99]
(i) -Mesons at SPS
• -meson “melts” in hot and dense matter
• baryon densityB more important than temperature
B/0 0 0.1 0.7 2.6
Hot+Dense Matter Hot Meson Gas
[RR+Wambach ’99]
[Eletsky etal ’01]
Model Comparison
[RR+Wambach ’99]
(ii) Vector Mesons at RHIC
baryon effects important even at B,net=0 :sensitive to B,tot=+B , more robust ↔ OZI -
e+e- Emission Rates: dRee/dM ~ f B Imem
Quark-Hadron Duality ?!
in-med HG ≈ in-med QGP !
[qq→ee][qq+O(s)]
--
(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 =
3.2 Towards a Chiral + Resonance SchemeOptions 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.
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
3.3 In-Medium Baryons: (1232) and N(939)
long history in nuclear physics ! ( A , A )
e.g. nuclear photoabsorption: M, up by 20-40MeV
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
in Nuclear Absorption
in Nuclei and Heavy-Ion Collisions
broadening: Bose factor, →B repulsion: N-1, NN-1
(1232) Spectral Fct. at RHIC Nucleon Spectral Fct. at RHIC
substantial broadening due to resonant N → B scattering
3.4 Lattice Studies of Medium Effects
)2/sinh(
))2/1(cosh(),(Im),(
0
00
00 Tq
TqTqdqT
calculatedon lattice
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)
3.5 Observables in URHICs
(i) Dileptons (ii) Photons
)T,q(fMqd
dR Bee023
2
4
1
Im Πem(M,q) ),( 0230 Tqfqd
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?
4. Heavy-Quark Modes
4.1 Charmed Mesons below Tc
4.2 Heavy-Quark Equilibration4.3 Charmonium in QGP4.4 URHICs: Suppression vs. Regeneration
4.1 Charmed Mesons in Hadronic Matter
reduced threshold for → DD J/ robust
’ fragile: ’→ DD decays
reldiss vf
kd
,
,3
31
)2(
[Grandchamp+RR ’03]
mD(T,B) expected to decrease
(Chiral Symmetry Restoration)
[Weise etal ’01]
2
2)(
p
fD
p
pf
t
f
1-D Fokker Planck Eq.
kpkwkdp ),(323 ),(
2
1 kpkwkdD
scatt. rate
diff. const.
TEtpp peetpf /2/)]([ 220
2
1),(
)1()( 22 teD
t
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]
)](),()()([),( 3 pfkpwkpfkpwkdt
ftpf
t coll
e.g.: pQCD Xsections, T=500MeV, s=0.6(0.3)
=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
h.c. c)v(
qG DDDcq 2
1L
• effective model with pseudo/scalar + axial/vector “D-mesons”
c + q → “D” → c + q
551 ,,,
“Light”-Quark Resonances
1.4Tc
[Asakawa+ Hatsuda ’03]
_ _
• chirally symmetric for light quarks
• heavy-quark symmetry j conserved to LO(1/mc)
• parameters: mD(0), GD
[van Hees+RR ’04]
4.2.2 Heavy-Quark Thermalization Times in QGP
• resonance scatt. isotropic• secondary open-charm ?! [50% for ])ccgg( 3
[van Hees+RR ’04]
pQCD
“D”
Charm Quarks Bottom vs. Charm
• bottom quarks “barely” thermalize at RHIC
4.2.3 Single-e± Spectra at RHIC: D → e+X
• dynamical origin of resonances? cc production? • onset of pQCD regime: pt>5-6GeV ? open bottom?
_ [Müller etal ’95, Molnar’04]
practically indistinguishable
PHENIX130AGeV e±
B
D
[Batsouli etal. ’02]
pt-Spectra: p-p vs Hydro Ellitpic Flow + Coalescence
jet- quench[Djordjevic etal ’04]
does charm equilibrate?
4.2 Charmonium in QGP• Lattice: c, J/ survive up to ~2Tc
• mass m≈ const ~ 2mc*
• width: reldiss
gqgq vTf
kd
,
,3
31 )(
)2(
[Datta etal ’03]
gluo-dissociation
“quasifree” diss.
[Bhanot+Peskin ‘84]
[Grandchamp+RR ‘01]
Cross Sections Dissociation Times
“jumps” at Tc sensitive to
rather direct link to lattice QCD!
*, ccc mN
4.3.1 Charmonium Regeneration vs. Suppression
• statistical coalescence at Tc: chem.+therm. equil.
• charmonia above Tc
formation in QGP: detailed balance!
)NN(d
dN eq
for thermalized c-quarks:
Equilibration close to Tc ?!
[PBM etal ’01, Gorenstein etal ’02, …]
[Thews etal ’01, Ko etal ’02 … Grandchamp+RR ’02]
J/ + g c + c + X←→ -
• QGP regeneration dominant• sensitive to: mc* , open-charm degeneracy, (Ncc)2 ↔ rapidity, √s, A
[Grandchamp +RR ’03]
4.3.2 Charmonium in A-A SPS RHIC
J/ Excitation Function
[Lumpkins, Grandchamp, van Hees, Sun +RR ’05]
4.3.3 Upsilon in A-A
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. “”)
• 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
(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±15)MeV mean-field: MeVGmM VBB 55)(
2
3
2
3 )()(
(1232) Spectral Fct. at RHIC
(ii) (1232) in URHICs
broadening: Bose factor, →B repulsion: N-1, NN-1
not yet included: (N↔ ),( pEGmedN
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]
J/Width from Lattice QCD
E.M. Emission Rates
[RR+Wambach ’99]
3.1 Continuity?!
Light Hadron “Masses”
However: peak in susceptibilities at Tc
↔ m→ 0
Observables ? e+e-+, fluct, , J/
qqchiral m
m
2
2
TrFyxdeconf
QQeTrLTrLLL/)(22 ,
[Shuryak, Zahed, Brown ’04]
[Turbide,Gale+RR ’03]
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
• 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
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]