In collaboration with Rupa Chatterjee

hardtofindcurtainUrban and Civil

Nov 16, 2013 (3 years and 9 months ago)

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In collaboration with
Rupa

Chatterjee

Direct photons are penetrating probes
for the bulk matter produced in
nuclear collisions, as they do not
interact strongly. They have a large
mean free path.

hadronic phase

qgp

phase

mixed phase

pre
-
equilibrium


phase

z

t

Penetrating probes:
emitted at all stages

then
survive

unscathed (
α
e
<<
α
s
).


“Historians” of the heavy ion collision:

encode all sub
-
processes at all times

Rate

Fries, Mueller,
& DKS,
PRL 90 (2003) 132301.

FMS Results: Comparison to Data

r
1
r
2
k
d
dN
3
E
2
3
1
3
2
1
k
d

k
d
dN
E
E
2
3
2
1
3
1
2
3
1
3
2
1
2
1
k
d
dN
E

k
d
dN
E
k
d

k
d
dN

E

E
)
k
,
C(k

r
1

r
2

x
1

k
1

k
2

Δ
R

x
2

Quantum statistical
correlation

)/2
k
k
(
K


,
k
k
q
2T
1T
T
2T
1T
T











sinh
sinh
k
k
q
2
2
1
1
2z
1z
long
y
k
y
k
T
T







K
K
q
q
)
-
(
cos

k
2k
k
k
k
-
k
T
T
T
out
2
1
2T
1T
2T
2
1T
2
2T
2
1T
2









)
ψ
-
cos(
ψ

k
2k
k
k
)
ψ
-
(
ψ
cos
1
k
2k
T
T
out
T
side
2
1
2T
1T
2T
2
1T
2
2
1
2
2T
T
1
K
K
q
q
q








q
out

q
side

q
long

k
1

k
2

q

q
out

q
side

q
long

R
side

R
out

k
1

k
2

q


One can show that R
out



R
side

is a measure of the duration of the emission.

1950

1960

1980

1994

2004

gg

gg

gg

pp

pp

astronomy

intermediate
energies

relativistic
energies

relativistic
energies

intermediate
energies

Chronology of intensity correlation experiments

C(
q
out,
q
side
=
q
long
=0)

C(
q
long,
q
out
=
q
side
=0)

C(
q
side,
q
out
=
q
long
=0)

R
side

(K
1T
)

q
out
=
q
long
=0

R
long

(K
1T
)

q
out
=
q
side
=0

R
out
(K
1T
)

q
side
=
q
long
=0

C(
q
out,
q
side
=
q
long
=0)

C(
q
long,
q
out
=
q
side
=0)

C(
q
side,
q
out
=
q
long
=0)

R
side

(K
1T
)

q
out
=
q
long
=0

R
long

(K
1T
)

q
out
=
q
side
=0

R
out
(K
1T
)

q
side
=
q
long
=0

The

two
-
photon

correlation

function

for

average

photon

momenta

100

<

K
T

<

200

MeV
/c

(top)

and

200

<

K
T

<

300

MeV
/c

(bottom)
.

The

solid

line

shows

the

fit

result

in

the

fit

region

used

(excluding

the

p
0

peak

at

Q
inv



m
p
0

)

and

the

dotted

line

shows

the

extrapolation

into

the

low

Q
inv

region

where

backgrounds

are

large
.

M. M.
Aggarwal

et al
., [WA98 collaboration] PRL 93, 022301 (2004)

WA98 measures
R
inv

as 8.34
±

1.7 fm and
8.63
±

2.0 fm, respectively

For y
1
=y
2
=0 and

1
=

2
=0,
q
side
=q
long
=q
inv
=0,

but q
out
=k
1T
-
k
2T

.ne.0



2
long
2
side
2
out
2
2
1
2
1
2T
1T
2
2
0
2
2
1
inv
2
inv
2
inv
inv
q
q
q


q

where,

)]
-
cos(
-
)
y
-
[cosh(y

k
2k

q

q
-


)
k

-
(k
-


q
/2
R
q

-

exp


2
1


1


)
C(q














The

outward,

sideward,

and

longitudinal

correlation

functions

for

thermal

photons

produced

in

central

collision

of

gold

nuclei

at

RHIC

taking

t
0

=

0
.
2

fm/c
.

Symbols

denote

the

results

of

the

calculation,

while

the

curves

denote

the

fits
.

Correlation function in the two

phases can be approximated as

2
α
i,
α
i,
|
ρ
|
0.5
1
)
C(q


]
R
q

0.5


[

exp

I
2
i,
2
i
i
i,





where,

i
=out, side, and long


㴠qu慲欠浡tte爠⡑⤠潲
h慤a潮ic

浡tte爠⡈

i
=out, side, and long


㴠qu慲欠浡tt敲e(Q爠
h慤an楣

浡tt敲e(䠩


)
dN
dN

/(
dN
I

)
dN
dN

/(
dN
I
H
Q
H
H
H
Q
Q
Q




The final correlation function

can be approximated as:

)]
R

(q

cos

|
ρ
|

|
ρ
|

2



|
ρ
|


|
ρ
|

0.5[
1
)
C(q
i
H
i,
Q
i,
2
H

i,
2
Q
i,
i






R
i

stands for the space
-
time

separation of the two sources.

R
o,Q

= 2.8, R
o,H

= 7.0,

R
o

=12.3,

R
s,Q

≈ R
s,H

= 2.8,

R
s

≈ 0.,

R
ℓ,Q

= 0.3, R
ℓ,H

= 1.8,

R


≈ 0.

(all values are in fm.)

DKS and R.
Chatterjee

arXiv
: 0907.1360

The

outward,

sideward,

and

longitudinal

correlation

functions

for

thermal

photons

produced

in

central

collision

of

lead

nuclei

at

LHC

taking

t
0

=

0
.
2

fm/c
.

Symbols

denote

the

results

of

the

calculation,

while

the

curves

denote

the

fits
.

RHIC

RHIC

RHIC

LHC

LHC

LHC

T
C

dependence of the outward correlation function @RHIC

The side
-
ward

correlation is

only marginally

affected and is

not shown.

DKS and R.
Chatterjee
,

Phys. Rev. C 80, 054914
(2009)

Transverse momentum dependence of
fraction of thermal photons from quark
matter (I
Q
) and
hadronic

matter (I
H
)
at RHIC and LHC energy.

reaction

plane

q
out

q
side

q
long





= 0
°



= 90
°

R
side

(large)


R
side

(small)


Elliptic Flow of Thermal Photons:

Measure Evolution of Flow !

Chatterjee
,
Frodermann
, Heinz, and

DKS,

PRL
96
(
2006
)
202302
.

Quark Matter 2005
-

Zbigniew
Chajęcki for the STAR
Collaboration

37

Typical results for
pion

intensity
interferometry

Pion HBT radii from different
systems and at different energies
scale with

(dN
ch
/d
η
)
1/3


RHIC/AGS/SPS Systematics

<k
T
>≈
400
MeV (RHIC)

<k
T
>≈
390

MeV (SPS)

Lisa, Pratt, Soltz, Wiedemann, nucl
-
ex/
0505014

STAR DATA


(pp,dAu,CuCu,AuAu@62GeV
-

prelim.)



2
2
1
1
ikx
i
φ
ikx
i
φ
e
e
e
e

ρ(k)

2
1
A(k)


p
hase of source

r
eal function, characterizes the source strength

bosons / fermions





2
1
2
3
φ
φ
Δx

k

cos

1

ρ(k)
k
d
dN




x
1
-
x
2


0
e
2
1


i
φ
i
φ
Incoherent emission

2
3
(k)
k
d
dN








2
1
2
1
1
2
2
1
2
2
1
1
i
φ
i
φ
x
ik
x
ik
i
φ
i
φ
x
ik
x
ik
2
1
2
1
e
e
)
ρ(k

)
ρ(k

2
1
)
k

,
A(k












Δx

k

cos

1

)
ρ(k
)
ρ(k
k
d

k
d
dN
2
2
2
1
2
3
1
3




k
1
-
k
2



Δx

k
cos

1
)
,
(
2
1




k
k
C


Correlation function

r
1

r
2

x
1

k
1

k
2

Δ
R

x
2



2
.
3


)
(




1

~

)
(




x
k
i
e
x
x
d
k
C

Spatial evolution of a central collision in the nucleus
-
nucleus
centre of mass frame obtained with BUU calculation for the
system
181
Ta+
197
Au at 40A
MeV
.

x (fm)


z (fm)


g

production rate (
a.u
.)



Production rate of photons with an energy of
30
MeV

as a function
of the incompressibility K


of nuclear matter obtained with BUU
calculations for the system
181
Ta+
197
Au at
40
A
MeV

and b=
5
fm.

Time (fm/c)


Inclusive hard
photons at
q
lab
=90
0
.
Thermal (solid
squares) and
direct (sold
circles).

E
g

(
䵥M



⡣潵瑳t
䵥M



䜮⁍慲瑩e稠整⁡氮⁐hy獩捳⁌整t敲猠䈠㌴㤬′㌠⠱㤹㔩.

I
d

I
t


r

Initial

compression

2
nd

compression

r

Intensity


(r)



⡱(





-

爩



⡱⤠
X

e
iq



I
d


(r) +
I
t


(r
-

爩



⡱⤠
X (
I
d
+
I
t

e
iq

r
)

C
12
(q) =
1
+


數瀨
-

q
2
R
2
-

q
0
2
t
2
)
I
gg
⡱(

I
gg
(q) =
I
d
2
+
I
t
2
+
2
I
d
I
t

cos
(
q




The correlation function

F. M. Marques
et al
., Phys. Rept. 284, 91 (1997)

Fits to the
interferometry

data; showing interference

between two sources.

Q (
MeV
)

C
12