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5.08.2005

R. Lednický qm'05

1

Correlation Femtoscopy

R. Lednický, JINR Dubna & IP ASCR Prague


History


QS correlations


FSI correlations


Correlation asymmetries


Summary

2

History

GGLP’60:

observed enhanced

+

+

,





vs

+




measurement of space
-
time characteristics
R, c


~ fm

KP’71
-
75:
settled basics of correlation femtoscopy



proposed
CF= N
corr
/N
uncorr

& mixing techniques to construct
N
uncorr



clarified role of space
-
time

characteristics in various production models



noted an analogy
Grishin,KP’71
& differences
KP’75
with

HBT
effect in Astronomy (see also
Shuryak’73
,
Cocconi’74
)

Correlation femtoscopy

:

in > 20 papers

at small opening angles



interpreted as BE enhancement

of particle production using particle correlations

3

QS

symmetrization of production amplitude


CF=1+(
-
1)
S

cos

q

x









p
1


p
2

x
1


x
2

q =

p
1
-

p
2
,

x = x
1
-

x
2

nn
t

,


t


,

nn
s

,


s

2

1

0


|q|

1/R
0

total pair spin

2R
0


4

Intensity interferometry of
classical

electromagnetic fields in
Astronomy

HBT‘56


product of single
-
detector currents

cf

conceptual
quanta

measurement


two
-
photon counts

p
1

p
2

x
1

x
2

x
3

x
4

star

detectors
-
antennas tuned
to mean frequency




Correlation ~


cos


p

x
34






p

-
1

|

x
34

|

Space
-
time correlation

measurement in
Astronomy



source
momentum picture


p

=




star angular radius


orthogonal

to

momentum correlation

measurement in
particle physics



source
space
-
time picture


x




KP’75



no info on star lifetime

5



momentum correlation

(
GGLP
,
KP
) measurements are
impossible

in
Astronomy

due to extremely large stellar space
-
time dimensions



space
-
time correlation

(
HBT
) measurements can be
realized



also in

Laboratory:

while

Phillips, Kleiman, Davis’67
:

linewidth measurement from

a mercurury discharge lamp

900 MHz


t nsec

Goldberger,Lewis,Watson’63
-
66

Intensity
-
correlation spectroscopy


Measuring phase of x
-
ray scattering amplitude

& spectral line shape and width

Fetter’65

Glauber’65

6

GGLP’60 data plotted as CF

GGLP
data plotted as
KP
CF=N(++,--
)/N(+-)
0
0.1
0.2
Q
2
= -(p
1
-p
2
)
2
(GeV/c)
2
0
1
3
2
Lorstad

JMPA 4

(89)

286
R
0
~1 fm

p p


2

+

2


-

n

0

7

Examples of present data: NA49 & STAR

3
-
dim fit:

CF
=1+

exp(
-
R
x
2
q
x
2

R
y
2
q
y
2

-
R
z
2
q
z
2

-
R
xz
q
x

q
z
)

z

x

y

Correlation strength or chaoticity

NA49

Interferometry or correlation radii

KK

STAR




Coulomb corrected

8

“General” parameterization at |q|


0

Particles on mass shell & azimuthal symmetry


5 variables:

q
=

{
q
x
,
q
y
,
q
z
}


{q
out
,
q
side
,
q
long
}
, pair velocity

v
= {v
x
,0,v
z
}


R
x
2

=
½


(

x
-
v
x

t)
2


,
R
y
2

=
½


(

y)
2


,
R
z
2

=
½


(

z
-
v
z

t)
2





q
0
=
qp
/p
0


qv
= q
x
v
x
+ q
z
v
z



y


side

x


out



transverse


pair velocity
v
t

z


long



beam

Podgoretsky’83
;

often called cartesian or
BP’95

parameterization

Interferometry radii
:


cos q

x

=1
-
½

(
q

x)
2




exp(
-
R
x
2
q
x
2

R
y
2
q
y
2

-
R
z
2
q
z
2

-
R
xz
2
q
x
q
z
)

Grassberger’77

RL’78

9

Probing source shape and emission duration


Static Gaussian model with
space and time dispersions
R

2
, R
||
2
,

2


R
x
2
= R

2
+v

2

2



R
y
2
= R

2




R
z
2
= R
||
2
+v
||
2

2

Emission duration


2
= (R
x
2
-

R
y
2
)/v

2


f
(degree)

R
side
2
fm
2

If elliptic shape also in transverse plane



R
y

R
side

oscillates with pair
azimuth
f

R
side

(
f
=90
°
)

small

R
side
(
f
=0
°
)

large

z

A

B

Out
-
of reaction plane

In reaction plane

In
-
plane

Circular

Out
-
of plane

KP (71
-
75) …

10

Probing source dynamics
-

expansion

Dispersion of emitter velocities & limited emission momenta (
T
)



x
-
p correlation
: interference dominated by pions from nearby emitters



Interferometry radii decrease with pair velocity



䥮瑥f晥f敮捥e灲潢敳潮汹⁡⁰慲琠潦⁴桥⁳潵捥

Resonances
GKP’71 ..

Strings
Bowler’85 ..

Hydro

P
t
=
160

MeV/c

P
t
=
380

MeV/c

R
out

R
side

R
out

R
side

Collective transverse flow

t




R
side

R/(1+m
t

t
2
/T)
½


Longitudinal boost invariant expansion

during proper freeze
-
out (evolution) time

††††



R
long


(T/m
t
)
½

/coshy

Pratt, Cs
ö
rg
ö
, Zimanyi’90

Makhlin
-
Sinyukov’87

}

1

in LCMS

…..

Bertch,Gong, Tohyama’88

Hama, Padula’88

Mayer, Schnedermann, Heinz’92

Pratt’84,86

Kolehmainen, Gyulassy’86

11

AGS

SPS

RHIC:



radii


STAR
Au+Au at 200 AGeV


0
-
5% central Pb+Pb or Au+Au


Clear centrality dependence


Weak energy dependence


12

AGS

SPS

RHIC:



radii vs
p
t


R
long
:

increases

smoothly &

points to short
evolution

time



~ 8
-
10 fm/c


R
side

,

R
out

:

change little &

point to strong
transverse flow


t

~ 0.4
-
0.6
&

short emission
duration



~ 2 fm/c

Central Au+Au or Pb+Pb

13

Interferometry wrt reaction plane

STAR

data:

f

潳捩汬慴楯湳汩k攠景f⁡

獴慴挠
潵
-

-
灬慮

獯畲捥

stronger

then Hydro & RQMD



Short evolution time

Out
-
of
-
plane

Circular

In
-
plane

Time

Typical hydro evolution


STAR’04

Au+Au 200 GeV 20
-
30%




+

+

&





14

hadronization

initial state

pre
-
equilibrium

QGP and

hydrodynamic expansion

hadronic phase

and freeze
-
out

PCM & clust. hadronization
NFD
NFD & hadronic TM
PCM & hadronic TM
CYM & LGT
string & hadronic TM
Expected evolution of HI collision vs RHIC data

dN/dt

1 fm/c

5 fm/c

10 fm/c

50 fm/c

time

Kinetic freeze out

Chemical freeze out

RHIC side & out radii:




㈠晭⽣

R
long

& radii
vs
reaction plane:




㄰1晭⽣

Bass’02

15

Puzzle ?

3D Hydro

2+1D Hydro

1+1D Hydro+UrQMD

(resonances ?)

But comparing

1+1D H+UrQMD

with 2+1D Hydro



kinetic evolution

at small p
t

& increases R
side

~
conserves

R
out
,R
long



Good prospect

for
Hirano ..

3DH

Hydro assuming ideal fluid explains strong collective

(

⤠晬fw猠慴⁒ 䥃f扵琠湯琠瑨攠楮瑥牦敲潭整特

敳畬es

+ hadron transport

Bass, Dumitru, ..

Huovinen, Kolb, ..

Hirano, Nara, ..

? not enough

t


+ ? initial

t


Why ~ conservation of spectra & radii?


qx
i




qx
i

+q(p
1
+p
2
)T/(E
1
+E
2
) =
qx
i

Sinyukov, Akkelin, Hama’02

close to
free streaming
also

in real

conditions

and

small ~ conserved interferometry radii

t
i
’= t
i
+T,

x
i


=

x
i

+

v
i
T

, v
i



v
=(
p
1
+
p
2
)/(E
1
+E
2
)



Based on the fact that the known analytical solution

of nonrelativistic BE with

spherically

symmetric

initial conditions
coincides with
free streaming

they proposed that the kinetic evolution can be

thus ~ conserve the spectra and lead to

~ justifies hydro motivated freezeout parametrizations

17

Checks with kinetic model

Amelin, RL, Malinina, Pocheptsov, Sinyukov’05:

System cools

& expands

but initial

Boltzmann

momentum

distribution &

interferomety

radii are

conserved due

to developed

collective flow

18

Hydro motivated parametrizations

Kniege’05

BlastWave:
Schnedermann, Sollfrank, Heinz’93

Retiere, Lisa’04

19

Au
-
Au 200 GeV

T=106
±

1 MeV

<

InPlane
> = 0.571
±

0.004 c

<

OutOfPlane
> = 0.540
±

0.004 c

R
InPlane

= 11.1
±

0.2 fm

R
OutOfPlane

= 12.1
±

0.2 fm

Life time (

) = 8.4
±

0.2 fm/c

Emission duration = 1.9
±

0.2 fm/c

c
2
/dof = 120 / 86

Retiere@LBL’05

20

Other parametrizations

Buda
-
Lund
:
Csanad, Cs
ö
rg
ö
, L
ö
rstad’04

Similar to BW but
T(x)

&

⡸(

桯琠捯h攠
縲〰⁍敖

獵牲潵湤敤⁢礠捯潬
縱〰⁍敖

獨敬

䑥獣物扥猠慬 摡瑡d⁳灥捴牡Ⱐ牡摩Ⱐv
2
(

)

䭲慫潷

Broniowski, Florkowski’01

Describes spectra, radii but
R
long

Single

freezeout model +
Hubble
-
like flow +
resonances


Kiev
-
Nantes
:
Borysova, Sinyukov,

Erazmus, Karpenko’05

closed

freezeout hypersurface

Generalizes BW using hydro motivated

Additional
surface emission

introduces

x
-
t

correlation


helps to desribe
R
out

at smaller flow velocity

volume emission

surface

emission

? may account for initial

t


Fit points to initial

t

of ~ 0.3

21

F
inal
S
tate
I
nteraction

Similar to Coulomb distortion of

-
摥捡礠
Fermi’34
:

RL, Lyuboshitz’82


eq. time condition
|t*|




r*
2


e
-
i
kr




-
k
(
r
)



[ e
-
i
kr
+f(
k
)e
ikr
/
r
]

e
i

c

A
c

F=1+
_______
+ …

kr
+kr

k
a

Coulomb

s
-
wave

strong FSI

FSI

f
c

A
c

(G
0
+iF
0
)

}

}

Bohr radius

}

Point
-
like

Coulomb factor


k=|
q
|/2

CF

nn

pp

Coulomb only



|
1+f/r|
2




FSI is sensitive to source size
r

and scattering amplitude
f

It
complicates CF analysis

but makes possible



Femtoscopy with nonidentical particles


K
,


p
,

..
&



Study relative space
-
time asymmetries

delays
,

flow



Study “exotic” scattering


,


K
,
KK
,


,

p

,


,

..

Coalescence
deuterons
,

..


|

-
k
(
r
)|
2


22

FSI effect on CF of neutral kaons

STAR

data on CF(K
s
K
s
)

Goal:

no Coulomb.
But

R

may

go up by
~1 fm

if neglected FSI in



= 1.09


〮㈲

删㴠R⸶㘠


0.46 fm


5.86


〮㘷⁦

KK

(~50%
K
s
K
s
)


f
0
(980)

&
a
0
(980)

RL
-
Lyuboshitz’82

couplings from

t



Achasov’01,03



Martin’77



湯 䙓c

Lyuboshitz
-
Podgoretsky’79:


K
s
K
s

from
KK

also show

BE enhancement

23

NA49
central Pb+Pb 158 AGeV
vs RQMD

Long

tails in RQMD:

r*



21

fm for
r*
<
50

fm

29

fm for
r*
<
500

fm

Fit
CF=
Norm

[
Purity

RQMD(
r*



卣慬e


⤫)
-
偵物瑹


Scale=0.76

Scale=0.92

Scale=0.83



RQMD overestimates

r*
by
10
-
20%

at
SPS

cf

~
OK

at
AGS


worse

at
RHIC



p



24

p


CFs at AGS & SPS & STAR

Fit using
RL
-
Lyuboshitz’82

with



捯湳c獴敮琠e楴栠敳e業慴搠業灵物瑹

R~ 3
-
4 fm

consistent with the radius from
pp

CF

Goal
: No Coulomb suppression as in
pp

CF &

Wang
-
Pratt’99

Stronger sensitivity to
R


㴰⸵

〮0

R=4.5

〮㜠晭

Scattering lengths
,

fm
:

2.31 1.78

Effective radii
,

fm
:

3.04 3.22

singlet triplet

AGS

SPS

STAR

R=3.1

〮0

〮㈠晭

25

Correlation study of particle interaction

-


+


&






獣慴s敲楮朠汥湧桳

f
0

from NA49 and STAR

NA49 CF(

+


) vs RQMD with

SI scale:

f
0



獩s捡

f
0

(=
0.232fm
)

sisca

=
0.6

〮ㄠ
捯c灡e

縰⸸~
晲潭


c
偔 ☠䉎& 摡瑡⁅㜶㔠
K


e



Fits using
RL
-
Lyuboshitz’82


NA49 CF(

⤠摡瑡d灲敦敲


|
f
0
(

⥼)


f
0
(
NN
) ~ 20 fm

STAR CF(
p

) data prefer


Re
f
0
(
p

)< Re
f
0
(
pp
)


〠0



pp

26

Correlation asymmetries

CF of
identical particles

sensitive to terms
even

in
k*r*

(e.g. through

cos

2
k*r*

)


measures only

dispersion

of the components of relative separation

r
*

= r
1
*
-

r
2
*

in pair cms

CF of
nonidentical particles

sensitive also to terms
odd

in
k*r*



measures also relative
space
-
time asymmetries

-

shifts

r
*


RL, Lyuboshitz, Erazmus, Nouais
PLB 373

(1996)
30



Construct
CF
+x

and
CF
-
x

with
positive

and
negative

k*
-
projection

k*
x

on a given
direction

x

and study CF
-
ratio
CF
+x
/CF

x


27

Simplified idea of CF asymmetry

(valid for Coulomb FSI)

x

x

v

v

v
1

v
2

v
1

v
2

k*
/


v
1
-
v
2









k*
x
> 0

v


>
v
p

k*
x
< 0

v


<
v
p

Assume


敭楴瑥搠
污瑥t

瑨慮


捬潳敲

瑯 瑨攠捥湴敲


p







䱯L来g
t
int

Stronger CF
+

Shorter
t
int


Weaker CF




CF
+

CF


28

CF
-
asymmetry for charged particles

Asymmetry arises mainly from Coulomb FSI

CF


A
c
(

)

|F(
-
i

,1,i

)|
2



=(k*a)
-
1
,

=
k
*
r
*
+k*r*

F


1+





= 1+r*/
a
+
k
*
r
*
/(k*
a
)

r*

|a|

k*

1/r*

Bohr radius

}

±
226 fm

for

±
p

±
388 fm

for

+

±



CF
+x
/CF

x


1+2

x*


/a

k*


0


x* = x
1
*
-
x
2
*


r
x
*



Projection of the relative separation

r
*

in pair cms on the direction
x


In LCMS (
v
z
=0
) or
x

||
v
:


x* =

t
(

x
-

v
t

t)



CF asymmetry is determined by
space

and
time

asymmetries

29

Usually:

x


and

t


comparable


RQMD
Pb+Pb



p

+X

central 158 AGeV :



x


=
-
5.2

fm


t


=
2.9

fm/c


x*


=
-
8.5

fm


+
p
-
asymmetry effect
2

x*

/a


-
8%



Shift

x


in
out
direction is due to collective transverse flow

RL’99
-
01


x
p


>

x
K


>

x



> 0

& higher thermal velocity of lighter particles

r
t

y

x


F


t
T



t

f


F

= flow velocity


t
T


= transverse thermal velocity


t

=

F

+


t
T

=
observed transverse velocity


x



r
x


=

r
t

cos
f



=


r
t

(

t
2
+

F
2
-


t
T
2
)/(2

t

F
)




y



r
y


=

r
t

sin
f



= 0

mass dependence


z



r
z






sin
h


= 0

in LCMS & Bjorken long. exp.

out

side

measures edge effect

at y
CMS



0

30

pion

Kaon

Proton

BW
Retiere@LBL’05

Distribution of emission

points at a given equal velocity:


-

Left,

x

= 0.73c,

y

= 0


-

Right,

x

= 0.91c,

y

= 0


Dash lines: average emission R
x




R
x
(

)


<


R
x
(
K
)


<


R
x
(
p
)




p
x

= 0.15 GeV/c

p
x

= 0.3 GeV/c

p
x

= 0.53 GeV/c

p
x

= 1.07 GeV/c

p
x

= 1.01 GeV/c

p
x

= 2.02 GeV/c

For a Gaussian density profile
with a radius
R
G
and flow
velocity profile

F

(r) =

0

r/
R
G

RL’04, Akkelin
-
Sinyukov’96

:



x


=
R
G




0

/[

0
2
+T/
m
t
]

NA49 & STAR out
-
asymmetries

Pb+Pb central 158 AGeV

not corrected for ~ 25% impurity

r* RQMD scaled by 0.8

Au+Au central

s
NN
=130
GeV

corrected for impurity



Mirror symmetry
(~ same mechanism for
+

and


mesons)



RQMD, BW ~ OK


灯楮i猠瑯⁳瑲潮朠瑲g湳癥牳攠晬fw


p


p




(

t


yields ~ ¼ of CF asymmetry)

32

Summary


Wealth of data on correlations of various particle species
(


,K

0
,p

,

,

) is available & gives unique
space
-
time

info
on production characteristics including
collective flows


Rather direct
evidence
for strong
transverse flow

in HIC at
SPS & RHIC comes from
nonidentical particle
correlations


Weak energy dependence of correlation radii contradicts to
2+1D hydro

& transport
calculations which strongly
overestimate out&long radii at RHIC
. However, a good
perspective seems to be for
3D hydro

& transport

?


A number of succesful hydro motivated parametrizations give
useful hints for the microscopic models


Info on two
-
particle strong interaction:


&


&
p


scattering lengths

from HIC at SPS and RHIC. Good
perspective at RHIC and LHC

33

Apologize for skipping


Coalescence data (new
d, d

from
NA49
)


Problem of non
-
Gaussian form
Cs
ö
rg
ö

..


Imaging technique
Brown, Danielewicz, ..


Correlations of penetrating probes


Comparison of different colliding systems


Multiple FSI effects
Wong, Zhang, ..; Kapusta, Li; Cramer, ..


Spin correlations
Alexander, Lipkin; RL, Lyuboshitz


……


34

Kniege’05

35

collective flow chaotic source motion

x
-
p correlation yes no

x
2
-
p correlation yes yes

T
eff


with m yes yes

R


w楴i 
t

yes yes


x




0
yes no

CF asymmetry yes yes if

t




0