Transcript Thermal Photons - Texas A&M University

Thermal Photons in Strong Interactions
Ralf Rapp
Cyclotron Inst. + Physics Dept.
Texas A&M University
College Station, USA
College Station, 24.09.04
Introduction I: E.M. Probes in Strong Interactions
• g-ray spectroscopy of atomic nuclei: collective phenomena
• DIS off the nucleon: - parton model, PDF’s (high Q2)
- nonpert. structure of nucleon [JLAB]
• thermal emission: - compact stars (?!)
- heavy-ion collisions
What is the electromagnetic spectrum of matter?
cPT many-body
(2 ↔ 2)
consistent
0
0.05
120
½r0
degrees of freedom? QGP
(3-body,...)
extrapolate
0.3
150-160
2r0
(resonances?)
pQCD
0.75
175
5r0
e[GeVfm-3]
T [MeV]
rhadron
Outline
1. Introduction
2. Thermal Photon Emission Rates
2.1 Generalities
2.2 Quark-Gluon Plasma: Complete LO
2.3 Hadronic Matter: - Meson Gas
- Baryonic Contributions
- Medium Effects
3. Relativistic Heavy-Ion Collisions
3.1 Nonthermal Sources
3.2 Thermal Evolution
3.3 Comparison to SPS and RHIC Data
4. High-Density QCD: Colorsuperconductor
5. Conclusions
Introduction II: Electromagnetic Emission Rates

E.M. Correlation Function: Π em (q)  i d x e
e+
e-
γ
dN ee
d 4qd 4 x
q0
4
iqx
  2 f B Im Πem(M,q)
dN g
3
4
d qd x
  f B Im Πem(q0=q)
jem ( x) jem (0) T
= O(1)
= O(αs )
also: e.m susceptibility (charge fluct): χ = Πem(q0=0,q→0)
In URHICs:
• source strength: depend. on T, mB, mp ; medium effects, …
• system evolution: V(t), T(t), mB(t) ; transverse expansion, …
• nonthermal sources: e+e-: Drell-Yan, open-charm; g: initial/
• consistency!
pre-equil.
2. Thermal Photon Radiation
2.1 Generalities
Emission Rate per 4-volume and 3-momentum

T
q0 3   2 f B (q0 , T ) Im Πem
(q0=q)
d q
p
transverse photon selfenergy
many-body γ
in-medium effects,
language:
resummations, …
cut
3
2
d
p1,2,3
dR
( 4)
p
γ
q0 3  N 

(...)
kinetic
9
d q
8 E1,2,3 (2p )
theory:
dRg
p
r
r
p
 f ( E1 ) f ( E 2 ) [1  f ( E3 )] |M|2
2.2 Quark-Gluon Plasma
“Naïve” Leading Order Processes: q + q (g) → g (q) + γ
q
dRg s 2 -q / T  2.912 q0 

q0 3  2 T e
ln 
d q 3p
 4p s T 
[Kapusta etal ’91, Baier etal ’92]
q g
0
But: other contributions to O(αs)
collinear enhanced Dg=(t-mD2)-1 ~ 1/αs
Bremsstrahlung
Pair-ann.+scatt.
+ ladder resummation (LPM)
[Aurenche etal ’00, Arnold,Moore+Yaffe ’01]
2.3.1 Hot Hadronic Matter: p-r-a1 Gas
Chiral Lagrangian + Axial/Vector-mesons, e.g. HLS or MYM:
fp2
1
2

2
L
Tr[( Dm U )  M (U  U  2)]  Tr[ Fm
]  m02Tr[ Am2 ]  L' ( ,  )
4
2
• (g0,m0,,) fit to mr,a1 , Gr,a1
[Song ’93, Halasz etal ’98,…]
D/S and G(a1→pγ) not optimal
HLS
MYM
Kap.’91 (no a1)
• Photon-producing reactions:
p
γ
p
p
r
r
γ
p,a1
p
mostly at
dominant (q0>0.5GeV)
q0<0.5GeV a1-strength problematic
p,a1
gauge invariance!
2.3.1.b Hadronic Formfactors
• quantitative analysis: account for finite hadron size
• improves a1 phenomenology
• t-channel exchange: gauge invariance nontrivial [Kapusta etal ’91]
simplified approach:
[Turbide,Gale+RR ’04]
 2Λ 
F(t)   2 
 2Λ  t 


2
2
with
t  2q0 m x x  p , a1 ,...
Factor 3-4 suppression
at intermediate and
high photon energies
2.3.2 Further Meson Gas Sources
(i) Strangeness Contributions: SU(3)F MYM
p
γ
K
K*
~25% of
pp 
(ii) w t-Channel
[Turbide,Gale
+RR ’04]
p
K*
p
w
r
γ
p
p
γ
K
~40% of
prp !
Gwrp large!
potentially important …
(iii) Higher Resonances
Ax-Vec: a1,h1→pg, Vec:
f1→rg , K1→Kg
w,w’,w’’→pg other: p(1300)→pg
K*→Kg
a2(1320)→pg
2.3.3 Baryonic Contributions
• use in-medium r –spectral funct:
Im  em 
m r4
Im Drmed ( q0  q )
g r2
abs

4p 
gA ( q0 )
• constrained by nucl. g-absorption:

Im  em ( q0  q )
A
q0 r N
r
Sp
Sp
B*,a1,K1...
>
N,p,K…
g N → p N,D
g N → B*
>
[Urban,Buballa,RR+Wambach ’98]
gN
gA
p-ex
2.3.3(b) Photon Rates from r Spectral Function:
Baryons + Meson-Resonances
• baryonic contributions
dominant for q0<1GeV
(CERES enhancement!)
mB=220MeV
• also true at RHIC+LHC:
r B  r B  1.3r0
at T=180MeV, mB=0
2.3.4 HG Emission Rates: Summary
• w t-channel (very) important
at high energy
• formfactor suppression (2-4)
• strangeness significant
• baryons at low energy
mB=220MeV
[Turbide,RR+Gale ’04]
2.3.5 In-Medium Effects
• many-body approach: encoded in vector-spectral function,
relevant below M , q0 ~ 1-1.5 GeV
• “dropping masses”:
large enhancement due
to increased phase space
[Song+Fai ’98, Alam etal ’03]
unless:
vector coupling decreases
towards Tc (HLS, a→1)
[Harada+Yamawaki ’01,
Halasz etal ’98]
2.3.6 Hadron Gas vs. QGP Emission
• complete LO QGP rate
~2-3 above tree-level rate
• in-med HG + Meson-Ex
(bottom-up)
≈
complete LO QGP
(top-down)
“quark-hadron duality” ?!
• Similar findings for
thermal dilepton rates
not yet understood …
3. Relativistic Heavy-Ion Collisions
e+
e-
J/y
Au + Au
r
QGP ?!
Hadron Gas
“Freeze-Out”
Signatures of the QGP?
• Suppression of J/y Mesons
• Decays of r-Mesons
• Photons
…
Au + Au → X
3.1 Nonthermal Sources
Initial hard production: pp → γX
Nuclear Effects: pA → gX
scaling with xT=2pT /√s ,
+ power-law fit [Srivastava ’01]
•“Cronin”: gaussian kt-smear.
• cf. pA → πX
• AA: <Dkt2>AA≈ 2<Dkt2>pA
3.2 Thermal Evolution: QGP→ Mix→ HG
HG:HG:
chemistry
and trans.
chemistry
[LHC]flow
T [GeV]
QGP: initial conditions [SPS]
• t0=1fm/c → t0=0.5fm/c: ~2-3
• s=CdQGT3; dQG=40 → 32: ~2
• pre-equilibrium?!
• R~exp(3
mp) for
pg , …
• conserved
BB pr
use→entropy
• yield
up at of
lowmqpt>0
, down
above
• build-up
(Np=const)
• large
blue shiftcooling
from coll. flow
• accelerated
3.3 Comparison to Data I: WA98 at SPS
Hydrodynamics: QGP + HG
[Huovinen,Ruuskanen+Räsänen ’02]
• T0≈260MeV, QGP-dominated
• still true if pp→gX included
Expanding Fireball + Initial
[Turbide,RR+Gale’04]
• initial+Cronin at qt >1.5GeV
 T0=205MeV suff., HG dom.
3.3 Comp. to Data II: WA98 “Low-qt Anomaly”
Expanding Fireball Model
[Turbide,RR+Gale’04]
• current HG rate much below
• 30% longer tFB  30% increase
Include pp→ppg S-wave
• slight improvement
• in-medium “” or D ?!
3.3 Perspectives on Data III: RHIC
Predictions for Central Au-Au
• large “pre-equilibrium” yield
from parton cascade (no LPM)
• thermal yields ~ consistent
• QGP undersat. small effect
PHENIX Data
• consistent with initial only
• disfavors parton cascade
• not sensitive to thermal yet
4. Photon Emission from Colorsuperconductor
Cold Quark Matter → (qq) Cooper pairs, Dqq≈100MeV
mq » ms2 : u-d-s symmetrically paired (Color-Flavor-Locking)
 ciral symmetry broken, Goldstone bosons,
mp2 ~ mq2 ≈ (10MeV)2
Photon Emissivities
Effective theory description
of “hadronic” processes:
p̂
p̂
p̂
γ
p̂
γ
r̂
r̂
p̂
 exceeds e+e-→γγ for T≥5MeV
[Vogt,Ouyed+RR]
5. Conclusions
• significant progress in E.-M. radiation from QCD matter:
- QGP: soft collinear enhancement → complete leading order
- HG: more complete (strangeness, baryons, w t-chan, FF’s)
• extrapolations into phase transition region
 HG and QGP shine equally bright
deeper reason? lattice calculations?
• phenomenology for URHIC’s compares favorably
with existing data
• consistency with dileptons
• much excitement ahead: PHENIX, NA60, HADES, ALICE,…
and theory!
Additional Slides
Photon Properties in Colorsuperconductors
r
Sp
Sp
B*,a1,K1...
+
N,p,K…
(i) r(770)
>
>
2.2.2 1± Mesons:
Significance of high rB at low M
Constraints:
- branching ratios B,M→rN,rp
- gN, gA absorpt., pN→rN
- QCD sum rules
Elab=20-40AGeV optimal?!
2.2.4 In-Medium Baryons: D(1232)
 long history in nuclear physics ! ( pA , gA )
e.g. nuclear photoabsorption: MD, GD up by 20MeV
 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
(i) Check: D in Vacuum and in Nuclei
3
 
4
d
p N
Im
G
(
M
)
1
D
GD (q0 ) 
f ( E p , m N ) GD ( E N  q0 , p  q )
 33 ( M )  tan

3
r N (2p )
Re GD ( M )
2 fp2N M N 3
2
GD ( M ) 
k
F
(

,
k
)
→ ok !
p cm
2 M cm
3mp
(ii) D(1232) in URHICs
 broadening: Bose factor, pD→B
 repulsion: pDN-1, pNN-1
not yet included: GNmed ( E , p) (pN→D)
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)
2.2.6 Observables in URHICs
(i) Lepton Pairs
2 1 B
  3 2 f (q0 , T ) Im
4
d q
p M
dRee
e+
eΠem(M,q)
γ
q0
dR g
3
dq
(ii) Photons

 B
f (q0 , T )
2
p
Im Πem(q0=q)
[Turbide,Gale+RR ’03]
baryon density effects!
• consistent with dileptons
• pp Brems with soft  at low q?