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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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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:
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
66
meson self energy
The leading one-loop contributions
K
K
Two-loop contributions
K
K,
,
* + many others
PVVgVVP
L
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
77
propagation, decay, scattering
K
K
one loop: decays
two loop: scattering
K
K
KK
K*
plus many others
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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)
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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)
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
1111
One-loop thermal effects are quite small!
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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!
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
1313
Note: the real part of cannot simply be absorbed into the definition of mass.
Furthermore, the kaon and the channel have competing influences.
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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Finally, the spectral function
ImRe
Im122
02
mM
Reone loop
Retwo loop
Im
Im
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
1717
decay at T > 0
(consistency check)
= 1.3 fm/c
vacuum
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
1818
higher order effects??
K
*
K
K
K
K*
kaon spectral function picks up a finite width
2222
22
)(Im)(
Im1 )(
mkmk
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
1919
spectral properties of and
(some of the) diagrams contributing to collision broadening
K K
K *a 1
pion rho
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
2121
(leading) branching ratio and enhancement factor
vacmed
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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).
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
2323
We propose a scenario in which
Observable occurs early (higher T, lower flow)
Observable K occurs late (lower T, higher flow)
+ -
+ -
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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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!
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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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!
6 June 2005 - KLH6 June 2005 - KLH Electromagnetic Probes of Hot anElectromagnetic Probes of Hot and Dense Matterd Dense Matter
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
-