6 June 2005 - KLH Electromagnetic Probes of Hot and Dense Matter1 The Puzzle EM Probes of Hot and Dense Matter ECT, Trento, Italy 3-10 June 2005 Kevin.

6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter

11

The The Puzzle Puzzle

EM Probes of Hot and Dense Matter

ECT, Trento, Italy

3-10 June 2005

Kevin Haglin

St. Cloud State University

Minnesota, USA


22

• Background – why is this a puzzle?

• Spectral properties for the atT > 0

• Decay rate at finite temperature

• decays allowed inside the fireball

• Yield estimates

• Progress assembling the puzzle pieces

J/

Learning outcomes, i.e. presentation outline


33

K

K

+

+

-

-

PLB 491, 59 (2000)

T = 305 ± 15 MeV

PLB 555, 147 (2003)

T = 228 ± 10 MeV

NA49: K K+ -

NA50: + -

45 fm/c

10 fm/c

fireball

?!?

Background:


44

Model the degrees of freedom and the interactions

with a three-flavor chiral Lagrangian

) U UTr(8

0

FL

F

i2exp U

MeV 135 F†

3

262

62

0

0

KK

K

Κ

Nonlinear Sigma Model

Where the pseudoscalar multiplet is


55

3

2

3

2662

662

*0

*0

KK

K

Κ

V

*

*

RL igUAUigA UUDU

The chiral covariant derivative

introduces nonet of vector mesons

i.e. vector mesons are dynamically generated.

AVA L 2

1

AVA R 2

1


66

meson self energy

The leading one-loop contributions

K

K

Two-loop contributions

K

K,

,

* + many others

PVVgVVP

L


77

propagation, decay, scattering

K

K

one loop: decays

two loop: scattering

K

K

KK

K*

plus many others


88

Four-point interactions are required to conserve the current [gauge invariance]

K

K

gg 22

e.g. + K + K M = M + M + M a b c

(a)(b) (c)


99

Self-energy calculation to one-loop order

)()(2g

] ))[((

)(2)(2

)(2g )( 224

42

22224

42

KKK mp

pd

mkpmp

kpkppdk

KKKK

] ))[(()(2g 22224

42

mkpmp

Ipd

where

pk kppkppk kkp kppkI 22222

References:

Gale & Kapusta, Nucl. Phys. B 357, 65 (1991)

Haglin & Gale, Nucl. Phys. B 421 (1994)


1010

From the self energy to the propagator

TL PkGPkF k )()()(

222222VV

T

V

L

mk

kk

G m k

P

F m k

P D

)( Im1

) ( 22vac

mkFm

then, finally, the propagator is

We make contact with observable decay rates

)( Im1

) ( 22vac

mkFm

KK KK


1111

One-loop thermal effects are quite small!


1212

0 )0( 022

0 T,k,kFmk

eff0 Mk

Effective mass extraction at finite temperature

(a pole in the propagator)

The effects are again quite small!


1313

Note: the real part of cannot simply be absorbed into the definition of mass.

Furthermore, the kaon and the channel have competing influences.


1414

Two loops contribute to collision broadening of the

424

13

3

coll )(2)(22

M

i iE

pd

n

g 432143214 11 ffffpppp

Particles contributing:

K

K*

b1

References:

K. Haglin, NPA 584, 719 (1995).

L. Alvarez-Ruso and V. Koch, PRC 65, 054901 (2002).

coll Im


1515

Finally, the spectral function

ImRe

Im122

02

mM

Reone loop

Retwo loop

Im

Im


1616

decay at T > 0A. Weldon, Ann. Phys.,

228, 43 (1993)

fpppR N 21

vac2

tot22

tot3344 2

)()( fRf m

mms

/m

qd xd

dN

qd xd

dN

feq

(2)3

1

1 )( 4 nxd

dNT


1717

decay at T > 0

(consistency check)

= 1.3 fm/c

vacuum


1818

higher order effects??

K

*

K

K

K

K*

kaon spectral function picks up a finite width

2222

22

)(Im)(

Im1 )(

mkmk


1919

spectral properties of and

(some of the) diagrams contributing to collision broadening

K K

K *a 1

pion rho


2020

(in medium) lifetime with in-medium daughters

fN

n

qd dRN f4

)( )( dRKKdR dR

vac12221133 2)()( )( 12)( sdssdsssρ

qdxd

dNdR

sqq 20

K

K

where


2121

(leading) branching ratio and enhancement factor

vacmed


2222

Symmetric Flow (Siemens-Rassmusen)

[but generalized to include Bose-Einstein effects]

Siemens and Rassmusen, PRL 42, 880 (1979).

s

sT

s

s

s

Tmes

dydmm

nd T/sms )cosh()sinh()(

)(2

1t

1

1s2

tt

2t

T

p where

pd

ndE

pd

ndE

3

3

3

3

)p(EE

)( Epp

p

p

)(eq Ef

KLH, nucl-th/0404069;Laura Holt and KLH,

J. Phys. G: Nucl. Part.

Phys., 31, S245 (2005).


2323

We propose a scenario in which

Observable occurs early (higher T, lower flow)

Observable K occurs late (lower T, higher flow)

+ -

+ -


2424

Follow the evolution to estimate yields as functions of mass

qd dq xd d qd xd

dNdN f

f3

03

44

vac

1

10 0

2

430

30

2 2

3 0

f.0.

fR

T

T

f MMUqf dzq

q dqV

T

dTT

dM

dN

2

FWHM 20 MeV!


2525

KK is a surface effect, with T = 135 MeV and v = 0.6

FWHM = 4.4 MeV

three-volume is a shell of thickness 1-2 fm

free-space behavior!


2626

Summary & Conclusions

self energy was calculated with 1, 2 and 3-loop effects included spectral function at finite temperature is modified significantly as

compared with the vacuum decay rate at finite temperature was estimated: with in-medium

daughters it increased dramatically

decay lifetime of the is shortened by the hadronic medium m distributions for K K and show different

temperatures and different flow values

mass distributions for K K and have different widths

in the model by a factor of 4-5

+

+

-

-

+

+ -

T

-


2727

THE ENDTHE END

This research has been supported in part by the National Science Foundation.

6 June 2005 - KLH Electromagnetic Probes of Hot and Dense Matter1 The Puzzle EM Probes of Hot and Dense Matter ECT, Trento, Italy 3-10 June 2005 Kevin.

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