May 18, 2006 Hot Quarks 2006 1

Unturned Stones for Electromagnetic Probes of Hot and Dense Matter

Kevin L. Haglin

St. Cloud State University, Minnesota, USA

Hot Quarks 2006, May 15-20, 2006, Villasimius, Sardinia, Italy

May 18, 2006 Hot Quarks 2006 2

What’s under those stones?

1) Photons

a) thermometry

b) flow

2) Dileptons

c) vector meson spectroscopy

d) collective many-body effects

3) Diphotons

e) thermal production - thermometry

f) scalar and tensor meson spectral functions

g) hadron spectroscopy

4) J/ & c

, * [e+e-, +-],

J/, c

May 18, 2006 Hot Quarks 2006 3

3) DiphotonsIt turns out that studies of photon pair production have a fairly long history….

• R. Yoshida, T. Miyazaki, M. Kadoya, PRD 35, 388 (1987).

• K. Redlich, PRD 36, 3378 (1987).

• J. Letessier and A. Tounsi, PRD 40, 2914 (1989).

• R. Baier, H. Nakkagawa, A. Niegawa, K. Redlich, PRD 45, 4323 (1992).

• M. Hentschel, B. Kampfer, O.P. Pavlenko, K. Redlich, G. Soff, Z. Fur

Phys. C, 333 (1997).

2qq 22 0 ,

+ crossed + contact+ crossed diagram

May 18, 2006 Hot Quarks 2006 4

Motivation: That is, suggestions at the time (1990) were….

1) at fixed temperature

2) ratio of dN / dydM to (dNch /dydM)2 should exhibit a more abrupt change in slope when the phase boundary is crossed as compared to ordinary hadronic matter

HGμμ

QGPμμ

HGγγ

QGPγγ

R

R

R

R

Difficulties:

a) Fold the rates to predict yields, and the “effect” diminishes owing to the long lifetime of the hadron phase

b) Drell-Yan “like” photon pairs dominates at some point

May 18, 2006 Hot Quarks 2006 5

New idea… let’s use the diphoton signal to do

1) Thermometry

rate is proportional to exp(- M / T) times a function of T

2) Spectroscopy

tensor mesons couple to 2[f2(1270), a2(1320), f2’(1525), …]

f1f1.3 MeV

scalar, pseudoscalar mesons couple to 2’f0, a0

3) Heavy quark physics

c2with rate 7.4 keV (full width is 17.3 MeV)

c02 with rate 2.6 keV (full width is 10.1 MeV)What are the major background contributions?

do spectroscopy!

May 18, 2006 Hot Quarks 2006 6

KK

** KK

Hadron processes QCD processes

qq

Meson spectral functions

)1285(1f

)1320(2a

Singles masquerading as doubles

qqg

gqq X

gg

charmonium

c

0c

Inventory

May 18, 2006 Hot Quarks 2006 7

)/(4

1)()2(2

112

23

42TMK

M

mTMM

dM

dRhad

2

2

2

2

2

2

22

4ln

41

4)(

m

M

M

m

MM

mM when

Hadron annihilation processes

M. Hentschel, B. Kampfer, O.P. Pavlenko, K. Redlich, G. Soff, Z. Fur Phys. C, 333 (1997).

May 18, 2006 Hot Quarks 2006 8

QCD annihilation processes [screened, net (resummed) rate]

2

21/23

3

24qq

2

QGPγγ

α)lnexp(

2

π

4π

αΣ

T

cMM/T

MTN

e

dM

dR

sc

where c is approximately 0.42. The range of validity is M > T.

q

q

R. Baier, H. Nakkagawa, A. Niegawa, K. Redlich, PRD 45, 4323 (1992).

May 18, 2006 Hot Quarks 2006 9

Hadron phenomenology

μμvppvpp V P P gL �

t

m tf p

2

22

Λ

Λ)(

,K

,K

,K

,K

,K

,K

Vertex form factors:

GeV 1.0 Λ

May 18, 2006 Hot Quarks 2006 10

More phenomenology…

Chiral Lagrangian from KH, C. Gale, PRC 63, 065201 (2001).

,K*

,K*

,K*

,K*

,K*

,K*

UD UDF

L μμTr

8

2π

chiral

πF

iU

2exp

Rμ

Lμμμ igUAUigAUUD

2μ2

μμint ρφ,Tr

2φφ,ρ Tr

gigL

2νμ2

νμνμ ρ,ρTr

4ρ,ρρTr

g ig

P V,VigL βανμμναβVVPVVP Tr

May 18, 2006 Hot Quarks 2006 11

Comments:

1) Quark rate comes from re-summed (HTL) thermal field theory

2) Pion and kaon results are diagrammatic calculations w/o form factors

3) V +V - use chiral Lagrangian to identify the interactions

use Wess-Zumino interaction

KLH, to be published.

The QCD rate seems to be quite similar to the HG rate!

May 18, 2006 Hot Quarks 2006 12

Hadron thermal decay into photon pairs

)()(

)(1

12 2 23

3

2 sM/T

sM/TK

MΓm M

MΓγγaΓ

2π

4Mg

dM

dRs

a2

aγγ Σ

=

+ others

a

May 18, 2006 Hot Quarks 2006 13KLH, to be published.

Results:

1) Diphoton rate from QGP vs. HG seems roughly the same at fixed temperature.

This is the same conclusion one had with single photons.

2) A temperature can be extracted – thermometry

3) Meson spectral properties at finite temperature can be probed – spectroscopy, in-medium physics

4) Chiral restoration f1 spectral function should approach equivalence with

May 18, 2006 Hot Quarks 2006 14

Singles “looking like doubles”

E

pd

pddR

E

dMMppE

pdpd

dRE

Epd

pddR

E

dR3

3

22221

2

23

232

1

13

131

TENepd

dRE /

3

243 GeV fm105 N

And we take

where

zz

T

M

edzMT

N

dM

dR 4

1

02

Parameterization from J. Kapusta, P. Lichard, D. Seibert, PRD 44, 2774 (1991).

May 18, 2006 Hot Quarks 2006 15

Two comments:

1) HG and QGP can now be compared directly on this figure---they are very similar.

2) The singles’ corruption of the double is negligible.

May 18, 2006 Hot Quarks 2006 16

Next, let’s establish the relative importance of form factors.

Of course, at high mass off-shell behavior will become more important.

Results of monopole form factors:

•Low mass pairs are reduced by a factor of 2

•High mass pairs suffer an order of magnitude suppression.

May 18, 2006 Hot Quarks 2006 17

4) Charmonium: “suppression of c as QGP indicator”!

The same idea for J/ suppression carries over to c.

Full width for c is 17.3 MeV. It should stand “tall and proud” unless it is disturbed by the QGP!!

The other charmonium states represent additional tools---it’s all good.

May 18, 2006 Hot Quarks 2006 18

Summary

1) Bursts of electromagnetic energy cleanly probe the full space-time extent of the strongly-interacting system.

Further studies underway…

a) More complete hadron description, i.e. form factors

b) space-time evolution for yields; add DY-like pairs

2) Photons allow thermometry

3) Dileptons provide spectroscopic information on vector mesons at finite energy density

4) Diphotons open the door for both thermometry and spectroscopy

5) Charmonium (eta-charm) suppression could be a very useful QGP diagnostic (if experimental resolution is sufficient).

May 18, 2006 Hot Quarks 2006 19

That’s all folks…

Research supported in part by the National Science Foundation under grant number PHY-0555521.