Femtoscopy in HIC' Theory R' Lednick, JINR Dubna

1
Femtoscopy in HIC. Theory R. Lednický, JINR
Dubna IP ASCR Prague

• History
• QS correlations
• FSI correlations
• Correlation asymmetries
• Summary

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History
Correlation femtoscopy
measurement of space-time characteristics R, c?
fm
of particle production using particle correlations

• GGLP60 observed enhanced ?? , ???? vs ???

at small opening angles
interpreted as BE enhancement
KP71-75 settled basics of correlation
femtoscopy
in gt 20 papers
proposed CF Ncorr /Nuncorr mixing techniques
to construct Nuncorr
clarified role of space-time characteristics in
various production models
noted an analogy Grishin,KP71 differences
KP75 with
HBT effect in Astronomy (see also Shuryak73,
Cocconi74)
3
Formal analogy of photon correlationsin
astronomy and particle physics
Grishin, Kopylov, Podgoretsky71
for conceptual case of 2 monochromatic sources
and 2 detectors
correlation takes the same form both in astronomy
and particle physics
Correlation cos(?R?d?/L)
R? and d? are distance vectors between sources
and detectors projected in the plane
perpendicular to the emission direction
L gtgt R?, d? is distance between the emitters and
detectors
study of energy correlation allows one to get
information about the source lifetime, and study
of angular correlations about its spatial
structure. The latter circumstance is used to
measure stellar sizes with the help of the
Hanbury Brown Twiss interferometer.
4
The analogy triggered misunderstandings


Shuryak73 The interest to correlations of
identical quanta is due
to the fact that their magnitude is connected
with the space and time
structure of the source of quanta. This idea
originates from radio
astronomy and is the basis of Hanbury Brown and
Twiss method
of the measurement of star radii.
Cocconi74 The method proposed is equivalent to
that used
by radio astronomers to study angular
dimensions of radio sources
While .. interference builds up mostly .. near
the detectors .. in our
case the opposite happens
Grassberger77 (ISMD)
For a stationary source
(such as a star) the
condition for interference
is the standard one q d ? ?1
! Correlation(q) cos(q d)
! Same mistake many others ..
5
QS symmetrization of production amplitude ?
momentum correlations in particle physics
KP75 different from Astronomy where
the momentum correlations are absent
total pair spin
due to infinite star lifetimes

• CF1(-1)S?cos q?x?

p1
2
x1
??, nns , ??s
x2
1/R0
1
p2
2R0
nnt , ??t
q p1- p2 , ?x x1- x2
q
0
6
Intensity interferometry of classical
electromagnetic fields in Astronomy HBT56 ?
product of single-detector currentscf
conceptual quanta measurement ? two-photon counts

p1
Correlation ? cos ?p?x34?
x1
x3
no explicit dependence
??p?-1
p2
x4
on star space-time size
x2
detectors-antennas tuned to mean frequency ???
star
?x34
Space-time correlation measurement in Astronomy
?

source momentum picture ??p?????? ? star
angular radius ????
? no info on star lifetime
KP75
orthogonal to
longitudinal size
Sov.Phys. JETP 42 (75) 211
momentum correlation measurement in particle
physics ?
source space-time picture ??x?
7

• momentum correlation (GGLP,KP) measurements are
  impossible

in Astronomy due to extremely large stellar
space-time dimensions
while

• space-time correlation (HBT) measurements can be
  realized

also in Laboratory
Goldberger,Lewis,Watson63-66
Intensity-correlation spectroscopy
Measuring phase of x-ray scattering amplitude
Fetter65
spectral line shape and width
Glauber65
Phillips, Kleiman, Davis67
linewidth measurement from
a mercurury discharge lamp
900 MHz
?t nsec
8
GGLP60 data plotted as CF
p p ? 2? 2? - n?0
R01 fm
9
Examples of present data NA49 STAR
3-dim fit CF1?exp(-Rx2qx2 Ry2qy2 -Rz2qz2
-2Rxz2qx qz)
Correlation strength or chaoticity
Interferometry or correlation radii
STAR ??
KK
NA49
Coulomb corrected
z
x
y
10
General parameterization at q ? 0
Particles on mass shell azimuthal symmetry ? 5
variables q qx , qy , qz ? qout , qside ,
qlong, pair velocity v vx,0,vz
q0 qp/p0 ? qv qxvx qzvz
y ? side
Grassberger77
RL78
x ? out ?? transverse pair
velocity vt
z ? long ?? beam
?cos q?x?1-½?(q?x)2?..? exp(-Rx2qx2 -Ry2qy2
-Rz2qz2 -2Rxz2qx qz)
Interferometry radii
Rx2 ½ ? (?x-vx?t)2 ?, Ry2 ½ ? (?y)2 ?, Rz2 ½ ?
(?z-vz?t)2 ?
Podgoretsky83 often called cartesian or BP95
parameterization
11
Assumptions to derive KP formula
CF - 1 ?cos q?x?
- two-particle approximation (small freeze-out PS
density f)
OK, ltfgt ?? 1 ? low pt fig.
- smoothness approximation Remitter ?? Rsource ?
??p? ?? ?q?peak
OK in HIC, Rsource2 ?? 0.1 fm2
? pt2-slope of direct particles
- neglect of FSI
OK for photons, OK for pions up to Coulomb
repulsion
- incoherent or independent emission
2? and 3? CF data consistent with KP formulae
CF3(123) 1F(12)2F(23)2F(31)22ReF(12)F
(23)F(31)
CF2(12) 1F(12)2 , F(q) ?eiqx?
12
Phase space density from CFs and spectra
Bertsch94
Lisa ..05
ltfgt rises up to SPS
May be high phase space density at low pt ? ? ?
Pion condensate or laser ? Multiboson effects on
CFs spectra multiplicities
13
Probing source shape and emission duration
KP (71-75)
Static Gaussian model with space and time
dispersions R?2, R2, ??2
Rx2 R?2 v?2??2 ? Ry2 R?2 ? Rz2
R2 v2??2
Emission duration ??2 (Rx2- Ry2)/v?2
If elliptic shape also in transverse plane ?
Ry?Rside oscillates with pair azimuth f
Rside2 fm2
Out-of plane
In-plane
Circular
Rside (f90) small
Out-of reaction plane
A
Rside (f0) large
In reaction plane
z
B
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Probing source dynamics - expansion
Dispersion of emitter velocities limited
emission momenta (T) ? x-p correlation
interference dominated by pions from nearby
emitters
Resonances GKP71 ..
? Interference probes only a part of the source
Strings Bowler85 ..
? Interferometry radii decrease with pair velocity
Hydro
Pratt84,86
Kolehmainen, Gyulassy86
Makhlin-Sinyukov87
Pt160 MeV/c
Pt380 MeV/c
Bertch, Gong, Tohyama88
Hama, Padula88
Pratt, Csörgö, Zimanyi90
Rout
Rside
Mayer, Schnedermann, Heinz92
Rout
Rside
..
Collective transverse flow ?t
? Rside?R/(1mt?t2/T)½
Longitudinal boost invariant expansion during
proper freeze-out (evolution) time ?
1 in LCMS

? Rlong? (T/mt)½?/coshy
15
AGS?SPS?RHIC ?? radii
Clear centrality dependence
Weak energy dependence
STAR AuAu at 200 AGeV
0-5 central PbPb or AuAu
16
AGS?SPS?RHIC ?? radii vs pt
Central AuAu or PbPb
Rlongincreases smoothly points to short
evolution time ? 8-10 fm/c Rside , Rout
change little point to strong transverse
flow ?t 0.4-0.6 short emission duration ??
2 fm/c
17
Interferometry wrt reaction plane
STAR04 AuAu 200 GeV 20-30
Typical hydro evolution
pp p-p-
Out-of-plane
Circular
In-plane
Time
STAR data ? oscillations like for a static
out-of-plane source stronger then Hydro
RQMD ? Short evolution time
18
Expected evolution of HI collision vs RHIC data
Bass02
QGP and hydrodynamic expansion
hadronic phase and freeze-out
initial state
hadronization
pre-equilibrium
Kinetic freeze out
dN/dt
Chemical freeze out
RHIC side out radii ?? ?2 fm/c
Rlong radii vs reaction plane ? ?10 fm/c
1 fm/c
5 fm/c
10 fm/c
50 fm/c
time
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Puzzle ?
Hydro assuming ideal fluid explains strong
collective (?) flows at RHIC but not the
interferometry results
But comparing
Bass, Dumitru, ..
11D HydroUrQMD
11D HUrQMD
Huovinen, Kolb, ..
21D Hydro
with 21D Hydro
Hirano, Nara, ..
3D Hydro
? kinetic evolution
? not enough ?t
conserves Rout,Rlong
increases Rside
at small pt
(resonances ?)
? Good prospect
for 3D Hydro
hadron transport
? initial ?t
20
Why conservation of spectra radii?
Sinyukov, Akkelin, Hama02
Based on the fact that the known analytical
solution
of nonrelativistic BE with spherically symmetric
initial conditions coincides with free streaming
ti ti T, xi xi vi T , vi ? v
(p1p2)/(E1E2)
one may assume the kinetic evolution close to
free streaming also in real conditions and thus

conserving initial spectra and
Csizmadia, Csörgö, Lukács98
initial interferometry radii
qxi ? qxi q(p1p2)T/(E1E2) qxi
justify hydro motivated freezeout
parametrizations
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Checks with kinetic model
Amelin, RL, Malinina, Pocheptsov, Sinyukov05
System cools expands but initial Boltzmann
momentum distribution interferomety radii
are conserved due to developed collective flow
? ?? ? tens fm
? ?? ? 0
in static model
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Hydro motivated parametrizations
BlastWave Schnedermann, Sollfrank, Heinz93
Retiere, Lisa04
Kniege05
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BW fit of Au-Au 200 GeV
Retiere_at_LBL05
T106 1 MeV ltbInPlanegt 0.571 0.004
c ltbOutOfPlanegt 0.540 0.004 c RInPlane 11.1
0.2 fm ROutOfPlane 12.1 0.2 fm Life time
(t) 8.4 0.2 fm/c Emission duration 1.9
0.2 fm/c c2/dof 120 / 86
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Other parametrizations
Buda-Lund Csanad, Csörgö, Lörstad04
Similar to BW but T(x) ?(x)
hot core 200 MeV surrounded by cool 100 MeV
shell
Describes all data spectra, radii, v2(?)
Krakow Broniowski, Florkowski01
Single freezeout model Hubble-like flow
resonances
Describes spectra, radii but Rlong
? may account for initial ?t
Kiev-Nantes Borysova, Sinyukov,
volume emission
Erazmus, Karpenko05
Generalizes BW using hydro motivated
closed freezeout hypersurface
Additional surface emission introduces
x-t correlation ? helps to desribe Rout
surface
emission
at smaller flow velocity
Fit points to initial ?t of 0.3
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Final State Interaction
??-k(r)2?
Similar to Coulomb distortion of ?-decay Fermi34
Migdal, Watson, Sakharov, Koonin, GKW, ...
fc?Ac?(G0iF0)
s-wave strong FSI
FSI

e-ikr ? ?-k(r) ? e-ikr f(k)eikr/r
nn
CF
Coulomb
pp
?1f/r2?
krkr
F1 _______
ei?c?Ac
ka


Bohr radius
Point-like Coulomb factor
Coulomb only
kq/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,
..
Coalescence deuterons, ..
? Study exotic scattering ??, ?K, KK, ??, p?,
??, ..
? Study relative space-time asymmetries delays,
flow
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Assumptions to derive Fermi formula
CF ? ?-k(r)2 ?
- same as for KP formula in case of pure QS
- equal time approximation in PRF
RL, Lyuboshitz82 ? eq. time condition t ??
?r2
OK fig.
- tFSI ?? tprod ? k ½q ??
hundreds MeV/c

• typical momentum

RL, Lyuboshitz ..98
transfer in production
account for coupled
channels within the
same isomultiplet only ???? ?0?0, ?-p ? ?0n,
KK?? K0K0, ...
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Effect of nonequal times in pair cms
RL, Lyuboshitz SJNP 35 (82) 770 RL
nucl-th/0501065
Applicability condition of equal-time
approximation t ?? ?r2
r02 fm ?02 fm/c
r02 fm v0.1
?CFFSI(?0?0)
? OK for heavy particles ? OK within 5 even
for pions if ????0 r0 or lower
Note ?v?? 0.8
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FSI effect on CF of neutral kaons
Lyuboshitz-Podgoretsky79 KsKs from KK also show
Goal no Coulomb. But R may go up by 1 fm
if neglected FSI in
BE enhancement
KK (50 KsKs)? f0(980) a0(980)
STAR data on CF(KsKs)
RL-Lyuboshitz82 couplings from
? Martin77
? Achasov01,03
? no FSI
l 1.09 ? 0.22 R 4.66 ? 0.46 fm 5.86 ?
0.67 fm
t
29
NA49 central PbPb 158 AGeV vs RQMD
Long tails in RQMD ?r? 21 fm for r lt 50
fm
29 fm for r lt 500 fm
Fit CFNorm Purity RQMD(r ?
Scale?r)1-Purity
? RQMD overestimates r by 10-20 at SPS cf
OK at AGS
worse at RHIC
Scale0.76
Scale0.92
Scale0.83
??p??
30
p? CFs at AGS SPS STAR
Goal No Coulomb suppression as in pp CF
Wang-Pratt99 Stronger sensitivity to R
singlet triplet
Scattering lengths, fm 2.31 1.78
Fit using RL-Lyuboshitz82 with
Effective radii, fm 3.04 3.22
? consistent with estimated impurity
R 3-4 fm consistent with the radius from pp CF
STAR
AGS
SPS
?0.5?0.2
R4.5?0.7 fm
R3.1?0.3?0.2 fm
31
Correlation study of particle interaction
??? ?? p? scattering lengths f0 from NA49 and
STAR
Fits using RL-Lyuboshitz82
pp
STAR CF(p?) data point to Ref0(p?) lt Ref0(pp) ?
0 Imf0(p?) Imf0(pp) 1 fm
?
NA49 CF(???) vs RQMD with SI scale f0 ? sisca
f0 (0.232fm)
-
sisca 0.6?0.1 compare 0.8 from
S?PT BNL data E765 K ? e???
NA49 CF(??) data prefer f0(??) ?? f0(NN) 20
fm
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Correlation asymmetries
CF of identical particles sensitive to terms even
in kr (e.g. through ?cos 2kr?) ? measures
only dispersion of the components of relative
separation r r1- r2 in pair cms

• CF of nonidentical particles sensitive also to
  terms odd in kr
• measures also relative space-time asymmetries -
  shifts ?r?

RL, Lyuboshitz, Erazmus, Nouais PLB 373 (1996) 30
? Construct CFx and CF-x with positive and
negative k-projection kx on a given direction x
and study CF-ratio CFx/CF?x
33
Simplified idea of CF asymmetry(valid for
Coulomb FSI)
Assume ? emitted later than p or closer to the
center
?
x
v
Longer tint Stronger CF?
v1
?
CF?
?
kx gt 0 v? gt vp
p
v2
p
k/? v1-v2
x
Shorter tint Weaker CF?
v
CF?
?
v1
kx lt 0 v? lt vp
p
?
v2
p
34
CF-asymmetry for charged particles
Asymmetry arises mainly from Coulomb FSI
CF ? Ac(?) ?F(-i?,1,i?)2?
?(ka)-1, ?krkr
r??a
F ? 1 ? ? 1r/akr/(ka)
k?1/r

226 fm for ?p 388 fm for ??
Bohr radius
k ? 0
? CFx/CF?x ? 12 ??x? /a
?x x1-x2? rx
? Projection of the relative separation r in
pair cms on the direction x
?x ?t(?x - vt?t)
In LCMS (vz0) or x v
? CF asymmetry is determined by space and time
asymmetries
35
Usually ??x? and ??t? comparable
RQMD PbPb ? ?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
higher thermal velocity of lighter particles
?xp? gt ?xK? gt ?x?? gt 0
RL99-01
x
out
?tT
?F
?tT
flow velocity
transverse thermal velocity
side
?t
?t
?F ?tT observed transverse velocity
y
?F
?
?x?? ?rx? ?rt cos? ? ?rt (?t2?F2-
?tT2)/(2?t?F) ?
mass dependence
?y?? ?ry? ?rt sin? ? 0
rt
?z?? ?rz? ? ?? sinh?? 0
in LCMS Bjorken long. exp.
measures edge effect at yCMS ? 0
36
BW Retiere_at_LBL05
pion
Distribution of emission points at a given equal
velocity - Left, bx 0.73c, by 0 - Right,
bx 0.91c, by 0 Dash lines average emission
Rx ? ?Rx(p)? lt ?Rx(K)? lt ?Rx(p)?
px 0.3 GeV/c
px 0.15 GeV/c
Kaon
px 0.53 GeV/c
px 1.07 GeV/c
For a Gaussian density profile with a radius RG
and flow velocity profile ?F (r) ?0 r/
RG RL04, Akkelin-Sinyukov96 ?x? RG bx ?0
/?02T/mt
Proton
px 1.01 GeV/c
px 2.02 GeV/c
37
NA49 STAR out-asymmetries
AuAu central ?sNN130 GeV
PbPb central 158 AGeV
not corrected for 25 impurity
corrected for impurity
r RQMD scaled by 0.8
?p
?K
?p
Mirror symmetry ( same mechanism for ? and ?
mesons)
?
?
RQMD, BW OK ? points to strong transverse flow
(??t? yields ¼ of CF asymmetry)
38
Summary

• Assumptions behind femtoscopy theory in HIC seem
  OK
• 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 21D hydro transport
  calculations which strongly overestimate outlong
  radii at RHIC. However, a good perspective seems
  to be for 3D hydro ? ?Finitial transport
• A number of succesful hydro motivated
  parametrizations give useful hints for
  microscopic models (but fit ? ? true ?)
• Info on two-particle strong interaction ?? ??
  p? scattering lengths from HIC at SPS and RHIC.
  Good perspective at RHIC and LHC

39
Apologize for skipping

• Coalescence (new d, d data from NA49)
• Beyond Gaussian form RL, Podgoretsky, ..Csörgö
  .. Chung ..
• Imaging technique Brown, Danielewicz, ..
• Multiple FSI effects Wong, Zhang, .. Kapusta,
  Li Cramer, ..
• Spin correlations Alexander, Lipkin RL,
  Lyuboshitz

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Kniege05
41
collective flow chaotic source motion
x2-p correlation yes
yes
Teff ? with m yes
yes
R ? with mt yes
yes
x-p correlation yes
no
??x? ? 0 yes
no
CF asymmetry yes
yes if ??t? ? 0