A Hidden Local Symmetry Theory of Dileptons in Relativistic Heavy

Ion Collisions

Gerry Brown*

4/25/08

State University of New York

*G. E. Brown, M. Harada, J. W. Holt, M. Rho, C. Sasaki http://www.arXiv.org/abs/0804.3196

Brown-Rho scaling in normal nucleiJ. W. Holt et al., PRL 100 (2008) 062501

D. Miller, Phys. Rept. 443 (2007) 55

Melting of Soft Glue and the Flash Temperature

aa GG

g

gTG

2

)()(2

Mesons at and above Tc

• Degenerate SU(4) above Tc

• Massless at Tc H.-J. Park et al., NPA 774 (2006) 889

M. Asakawa et al., NPA 715 (2003) 863c

STAR 2004 Experiment

.)(syst037.0(stat)003.0169.00

Assuming equilibrium at freezeout:

40

104

P. Braun-Munzinger et al., nucl-th/0304013

.)(syst027.0(stat)001.0183.00

AuAu peripheral at

GeV200NNs

pp

AuAu

• Standard scenario: many generations• HLS prediction: one generation

J. Adams et al, PRL 92 (2004) 092301

HBT

3

42

)(1514

)(

c

T

V

TE c

• Stefan-Boltzmann law of radiation for massless bosons at Tc

equalT

1.3)(

)(3

flash

c

c

flash

T

T

TV

TV

• Between Tc and Tflash hadrons propagate relatively freely

3

42

)(152

1657)(

c

T

V

TE equalequal

• Energy density at Tequal

defined as temperature at which mesons go back on-shell

’s ’s

MeV13879.073

28)()(

4/1

equal

equal

ccequal T

T

TTETE

• 1 fm to equilibrate

2*3*

5**

g

g

m

m

qq

qq

66 pions result at flash point

32 SU(4) Multiplet (massless at Tc)

(18),a0(4),a1(27),(3),(2),

=f1285(12)

16.0)322(

30

Hadronic Freedom

freezeoutflash TT

(between Tc and Tflash)G. Brown et al, PRC 74 (2006) 024906

S. Damjanovic, NA60

Claim:

Brown-Rho scaling ruled out

NA60 Dileptons

Dileptons as a probe for Brown-Rho scaling

Not a good probe:

(1) Hadronic freedom: mass-shifted mesons don’t decay until after Tflash, where most mass regained(2) Violation of vector dominance: near Tc dileptons produced independent of

ea

g

21

1a

(3) Wave function suppression

(4) Phase space suppression

2)0(

S. Damjanovic, NA60

• mass shifted most

Blue shifted hadrons

• Teff() 300 MeV

TTT

Teff

1

1

NA60 reconstruction of on-shell

S. Damjanovic, NA60

Tfreezeout = 110 MeV

• Most ’s seen are just the on-shell vacuum ones

Role of the a1

• Number of on-shell ’s doubled at flash point

• a1 goes on-shell at Tflash

• Off-shell: cut down by factor ~ ¼

Low mass pion pairs

Summary:

(1) Violation of vector dominance ~ ¼ suppression(2) Kinematical factor ~ ½ that for off-shell ’s compared to on-shell ones

2)0(

(3) Number of on-shell ’s doubled at flash point from decay of a1

• Mass shifted off-shell ’s suppressed by a factor of ~ 1/10 compared to on-shell ’s