Photons and Dileptons

K. Dusling (NC) and I. Zahed

BNL 11

Outline

• Set up• Rates• Evolution• Experiments

AA Cartoon

time

Formally

rateevolution

acceptance

Acceptance: NA60 vs PHENIX

Hadronic Rates

Rate

)0(),()()(

41

21

604

2

2

2

2

23

2

4

JxJxexdqWqm

qm

qqddR xiqll

)0()()( with )(Im1

2),( *4

/

00

JxJTexdiqWqW

eqqW xiqFF

Tq

l+

l-

l+

l-π

π

N

π

π

N

Hadronic Expansion

i d4 x e iqx 0T*J (x)J(0)0 i

a d d4 x e iqx in

a (k)T*J (x)J(0) ina (k)

is,I dN d 4 x e iqx N in

s,I (k)T*J (x)J(0) N ins,I (k)

+2+3, …-Pi, +2+3, …-K

Resonance Gas: 0 ie J=ρ,ρ’,ρ’’,..

+2+3, …-N

Many Feyman Graphs:

l l

l l

,,

i d4 x e iqx 0T*J (x)J(0)0 + + …

l

l

,,,, 11 Ka

ia d d4 x e iqx in

a (k)T*J (x)J(0) ina (k) + …

ll

NN

,

,N ,N

is,I dN d4 x e iqx N in

s,I (k)T*J (x)J(0) N ins,I (k) + …

Chiral Ward Identities: κ

d3k n(k0)(2 3)2k0 f

2 W1F (q,k)

W1F 12q2 ImV (q2)

6(k q)2 ImA[(k q)2]

8((k q)2 m2q2)ImV (q2) Re[R (k q)]

(q q)

ia d d4 x e iqx in

a (k)T*J (x)J (0) ina (k)

Chiral Limit and zero-mtm pion:

)()(Im12)0,( 2221 qqqqW AV

F

κ

VA Mixing=LxR Restoration?

Dey, Eletsky, Ioffe 96

~κ

Expansion Parameter:

n

2m f2

n 3 d3k(2 )3 n(k )

= 0

0

“Dilute”

LXR

Chiral Ward Identities: κ^2

Input:

V (q2) 0 TVV 0

A (q2) 0 T jAjA 0

e+e- Decay

.

VA Mixing in

T=180 MeV

Typical Mixing in

a1a1

T=150 MeV μb=225 MeV

VA Mixing + Bremsstralung

QGP Rates

wQGP:

ImW11R

14

NC eq2

q

q

2 12Tq

ln n

n

l+

l-

l+

l-

wQGP: γ

Collinear Enhancement+ LPM Effect : Arnold, Moore, Yaffe 01

Hydro Evolution

Fireball: NA60

TC 160 MeVs /nB 42Tf ,o. 120 MeV

LH = 6 GeV/fm-3

Thermal Freeze-out

Cooper-Frye

Chemical Freezeout:

Fireball cools faster x Rates higher = w/μπ !

Experiments

NA60:

PHENIX:

Dusling+Z 07 Dusling+Z 09

28

STAR: 11’

PHENIX PRC 81 (2010) 034911

Minbias (value ± stat ± sys) Central (value ± stat ± sys)

STAR 1.53 ± 0.07 ± 0.41 (w/o ρ) 1.40 ± 0.06 ± 0.38 (w/ ρ)

1.72 ± 0.10 ± 0.50 (w/o ρ) 1.54 ± 0.09 ± 0.45 (w/ ρ)

PHENIX 4.7 ± 0.4 ± 1.5 7.6 ± 0.5 ± 1.3Difference 2.0 σ 4.2 σ

Enhancement factor in 0.15<Mee<0.75 Gev/c2

Note: Acceptance difference etc.

WA98: γ

0<qT (GeV) <4 0<qT (GeV)<0.8

N:x2

Rates at RHIC: γ

RHIC1 RHIC2

PHENIX: γ

RHIC1 RHIC2

PHENIX extrapolation: γ

PHENIX: M<<qv

1

Systematics of the Extrapolation

15% Systematics!

LHC: γ

0<qT(GeV)<2 1<qT (GeV)<5

Achievements

1. EM “OK”*2. LxR “restored”3. QGP “visible”

(* PHENIX)