Correlation femtoscopy R' Lednicky, JINR Dubna

1
Correlation femtoscopy R. Lednicky, JINR Dubna
IP ASCR Prague

• History
• QS correlations Multiboson effects
• FSI correlations
• Correlation asymmetries
• Spin correlations
• Summary

2
History
Correlation femtoscopy measurement of
space-time characteristics of particle
production using particle correlations

• GGLP(60) observed enhanced ?? , ???? vs ???
  at small opening angles interpreted as BE
  enhancement

KP(71-75) found deep analogy with HBT effect in
Astronomy, introduced CF Ncorr /Nuncorr ,
settled basics of correlation femtoscopy
3
QS symmetrization of production amplitude
total pair spin

• 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
4
Intensity interferometry of classical
electromagnetic fields in Astronomy HBT (56) ?
product of single-detector currentscf
conceptual quanta measurement ? two-photon counts

Correlation ? ?p?x34?
p1
x1
x3
??p?-1
p2
x4
x2
detectors-antennas tuned to mean frequency ?
star
?x34
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?
5
Michelson cf HBT interferometers
?IAB? ? ?iexpi(?ikixA)
?jexpi(?jkjxB)2? 2N 2Re?iexpki(xA-xB)

filter
?IAB? ?IAIB?1Re?(xA-xB)
Fourier transform of ?(k)
Field intensity in antenna A
IA ?iexpi(?ikixA) 2 N 2 ?iltj cos(?i-
?j)(ki-kj)xA
filter
Product of intensities averaged over ?s

• ?IA IB? ?IA??IB?1(2/N2)?iltjcos(?kij?xAB)
• ?IA??IB? 1?(xA-xB)2
  
• Actually measured product of electric currents
  after filters (0lt?i-?jlt??F????) integrated in
  a time T
• ST?dt ?JA JB? (Ne2/??) T ?(0,xA-xB)2
• normalized to ST r.m.s. Ne (T/??F)1/2

A
B
Required T (2?? /Ne)2/??F hours
Ne 108 e/sec, ?f 1013 Hz, ?fF 40 MHz
6
GGLP(60) data plotted as CF
R01 fm
7
Examples of present data NA49 STAR
3-dim fit CF1?exp(-Rx2qx2 Ry2qy2 -Rz2qz2
-Rxzqx qz)
Correlation strength or chaoticity
Interferometry or correlation radii
STAR ??
KK
NA49
Coulomb corrected
z
x
y
8
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
RL (78)
x ? out ?? transverse pair
velocity vt
z ? long ?? beam
?cos q?x?1-½ ?(q?x)2?? exp(-Rx2qx2 Ry2qy2
-Rz2qz2 -Rxzqx qz)
Interferometry radii
Rx2 ½ ? (?x-vx?t)2 ?, Ry2 ½ ? (?y)2 ?, Rz2 ½ ?
(?z-vz?t)2 ?
Podgoretsky SJNP (83) 37 often called BP
parameterization (95)
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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 GKP (71) ..
? Interference probes only a part of the source
Strings Bowler (85) ..
? Interferometry radii decrease with pair velocity
Hydro
Pratt (84)
Pt160 MeV/c
Pt380 MeV/c
Makhlin-Sinyukov (87) ..
Rout
Rside
Rout
Rside
Collective transverse flow ?t
? Rside?R/(1mt?t2/T)½
1 in LCMS
Longitudinal boost invariant expansion during
proper freeze-out (evolution) time ?

? Rlong? (T/mt)½?/coshy
11
AGS?SPS?RHIC ?? radii vs pt
Pratt QM02
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
12
Interferometry wrt reaction plane
Typical hydro evolution
STAR minbias AuAu 130 GeV p p- Ray, Nantes
(02)
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
13
Hydro and RQMD overestimate evolution time
emission duration
Pure hydro Heinz, Kolb, NPA 702 (02) 269
HydrouRQMD Soff, Bass, .. NPA 715 (03) 801
14
Expected evolution of HI collision vs RHIC data
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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Phase space density from CFs and spectra
Bertsch (94)
May be high phase space density at low pt ? ?
Pion condensate or laser ? Multiboson effects on
CFs spectra multiplicities
NA49 PbPb central
STAR AuAu central
STAR AuAu peripheral
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Multiboson effects
? Coherent emission pion laser, DCC
?Correlation strength ? lt 1 due to coherence
Fowler-Weiner (77) But impurity, Long-Lived
Sources (LLS), .. RL-Podgoretsky (79)
?3? CF normalized to 2? CFs get rid of LLS
effect Heinz-Zhang (97) But problem with 3?
Coulomb extrapolation to Q30
? Coherence modification of FSI effect on 2? CFs
Akkelin .. (00) But requires precise
measurement at low Q
? Chaotic emission Podgoretsky (85), Zajc (87),
Pratt (93) ..
See RL et al. PRC 61 (00) 034901 refs therein
Heinz .. AP 288 (01) 325
rare gas ? BE condensate
Increasing PSD
Widening of n? distribution
Poisson
BE
?
?/(2r0?) lt ?
Narrowing of spectrum
width ? ? ? ? ? 0 at fixed n
Widening of CFs
width 1/r0 ? 1
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3? data on chaotic fraction ?
Construct ratio r3 in which LLS contributions to
C3 CF3-1 and
C2 CF2-1 cancel out Heinz-Zhang (97)
r3 C3(123) C2(12) C2(23) C2(31) /C2(12)
C2(23) C2(31) ½
Interpolate to r3(Q30), Q3 (Q122 Q232
Q312)½
Periph Mid-centr Centr
½r3
½r3
Full chaoticity
L3
p p-
STAR
?
½r3(0) ?½(3-2?)/(2-?)¾
2
Within large (systematic) errors STAR L3 data
consistent with full chaoticity
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Multiboson effects on n? spectra
Measure of PSD ??/(r0?½)3 ? 1
Rare gas Width?
Condensate
Width?/(2r0?)½ ? ?
BE ?n
Poisson ?n/n!
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Multiboson effects on CFs
CFn(0) fixed n
CF(q) semi-inclusive n?nmax
CF(q) inclusive
Intercept stays at 2
Width logarithmically increases with PSD
n
Intercept drops with n faster for softer pions
?n? 33.5
120
60
2
nmax
undershoot
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Final State Interaction
Similar to Coulomb distortion of ?-decay RL,
Lyuboshitz (82) ? condition t ?? ?r2
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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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 ? Too much
rescatterings
already at SPS
Scale0.76
Scale0.92
Scale0.83
??p??
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p? CFs at AGS SPS
Goal No Coulomb suppression as in pp CF
Wang-Pratt (99) Stronger sensitivity to R
singlet triplet
Scattering lengths, fm 2.31 1.78
Fit using RL-Lyuboshitz (82) with
Effective radii, fm 3.04 3.22
? consistent with estimated impurity
R 4 fm consistent with the radius from pp CF
AGS
SPS
?0.5?0.2
R4.5?0.7 fm
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Correlation study of particle interaction
??? ?? scattering lengths f0 from NA49
correlation data
Fit CF(???) vs RQMD with SI scale f0 ? sisca
f0 0.232 fm
Fit using RL-Lyuboshitz (82) with
fixed ?0.16 from feed-down and PID
sisca 0.6?0.1 compare 0.8 from
Data prefer f0 ?? f0(NN) 20 fm
S?PT BNL data E765 K ? e???
-
-
-
???
-
??
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?? interaction potential from LEP
CF Norm (1? ?e-R2Q2)
Pure QS
PLB 475 (00) 395
Feed-down PID ? 0.5

?? ½?(1P2) lt 0.3
Polarization lt 0.3
?0.62?0.09 R0.11?0.02 fm
String picture lstring 2m?t/?2 fm ? ? 1 fm
Rz? ?(T/m?t)½ 0.3 fm ? R gt Rz /?3 0.17 fm
?0.54?0.10 R0.11?0.03 fm
? QS fit yields too low R too big ?
? ?? CF at LEP dominated by
! Direct core signal
?0.60?0.07 R0.10?0.02 fm
FSI potential core RL (02)

NSC97e neglected Spin-orbit Tensor parts ?
R OK but potential tuning required
?0.6 fixed R0.29?0.03 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
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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
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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
28
Large lifetimes evaporation or phase transition
x v ?x ?? ?t ? CF-asymmetry yields time
delay
Ghisalberti (95) GANIL PbNb ? pdX
Strangeness distillation K? earlier than K? in
baryon rich QGP
Two-phase thermodynamic model
CF(pd)
1
Ardouin et al. (99)
CF?(pd)
CF/CF?lt 1
1
2
3
2
CF/CF?lt 1
Deuterons earlier than protons in agreement with
coalescence e-tp/? e-tn/? ? e-td/(?/2) since tp?
tn ? td
3
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ad hoc time shift ?t 10 fm/c
Sensitivity test for ALICE
Erazmus et al. (95)
CF/CF?
a, fm ?
k ? 0
CF/CF? ? 12 ??x? /a
?249
Here ??x? - ??v?t?
?
CF-asymmetry scales as - ??t?/a
?226
Delays of several fm/c can be easily detected
?84
30
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
RL (99-01)
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
31
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, BWP OK ? points to strong transv. flow
32
Spin correlations ??, tt, ..
?
p
n1
Decay asymmetry parameters ?1 ?2 ? (??p??)
0.642
?
??
Joint angular distribution of ? decay analyzers
n1 and n2 is determined by
?
p
n2
?
polarization vectors Pi ? ?i?
??
correlation tensor Tik ? ?1k??2k?
16?²W(n1,n2) 1 ?1P1n1 ?2P2n2 ?1?2?ikTik
n1in2k
Distribution of correlation x n1?n2 cos?12 is
determined by SpT ?sSpTsinglet
?tSpTtriplet -3 ?s ?t 4 ?t-3 ?s and ?t
are singlet and triplet fractions, ?s ?t 1
W(x) ½1 ½ ?1?2SpT x
Alexander-Lipkin (95), RL (99)
3
33
?? spin correlations at LEP
? ALEPH distributions of correlation xn1?n2
cos?12 of directions of decay protons Slopes
SpT 4 ?t-3 ?
?t ?t/?
Bell-type inequality
x cos?12
Q ?0
??s??t
? New femtometry tool ?t ?t/??0 triplet state
forbidden at Q0 Noninteracting unpolarized ?s
?t¾(1?e-r02Q2)
?s¼(1?e-r02Q2)
? Check two-particle QM coherence violation of
Bell-type inequality RL-Lyuboshitz (01) SpT? 1?
?t?½
r00.14?0.09 fm
34
Summary

• Particle correlations give unique information on
  space-time production characteristics including
  collective flows
• Strong transverse flow established in HIC at SPS
  RHIC. Rather direct evidence from nonidentical
  particle correlations
• Weak energy dependence of correlation radii
  contradicts to transport hydro calculations
  which strongly overestimate outlong radii at
  RHIC. The RHIC data thus points to a new physics
  Explosive fireball decay ?
• Phase space density likely increased at RHIC ?
• BE condensate effects may show up at small pt
  ?
• Promising results from Spin correlations
• Info on two-particle strong interaction ?? ??
  scattering lengths from HIC at SPS and evidence
  on ?? potential core from LEP

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Tails in RQMD ?r? 21 fm for r lt 50 fm
?0.94 ?r?24.4 fm
?0.91 ?r?22.9 fm
29 fm for r lt 500 fm
gt
?0.89 ?r?16 fm
?0.93 ?r?24 fm
??
Strong FSI on
??-
?0.81 ?r?18.4 fm
?0.76 ?r?18.1 fm
? Strong FSI important for ??-
? 1-G fit ?(??) ? 0.8, ?r? 25 ?
? 2-G fit ?? ? ??-
?r?QS lt ?r?Coul
36
Femtoscopy with nonidentical particles
Be careful when comparing QS (?? ..) and FSI
correlations (???..) ? different sensitivity to
r-distribution tails
CF ??-k (r)2?
? QS strong FSI non-Gaussian r-tail
influences only first few bins in Q2k and its
effect is mainly absorbed in suppression
parameter ?
? Coulomb FSI sensitive to r-tail up to r
Bohr radius

• az1z2e2?-1
• fm

?? ?K ?p KK pp 388 249
223 110 58
? In Gaussian fits one may expect r0(??) lt
r0(???)
? Use realistic models like transport codes
37
two-photon counts cfclassical intensity
interference

two-photon counts (completely polarized photons),
kp/h
NAB ?½expik1xAik2xB expik1xBik2xA2
1 cos(?k?xAB)
field intensity in detector A (wave 4-vectors k)
IA expi(?1k1xA) expi(?2k2xA)2 2
2cos(?1- ?2)(k1-k2)xA

Product of intensities averaged over ?s
?IA IB? 42 cos(?k?xAB)
38
Deep analogy ? deep misunderstanding
Unfortunately GGLP effect often called HBT,
though

• QS symmetrization ? Superposition principle
• HBT measurement is classical (not counting
  quanta) measure the product of currents (field
  intensities) from two antennas intensity
  interferometry
• Being of classical origin, HBT effect would
  survive when h ? 0 and quantum interference
  vanished
• Even if quanta measurement were done in
  Astronomy, it would represent orthogonal
  measurement to GGLP effect

39
Hydro wrt reaction plane
?
Though Hydro transforms out-of plane source into
in-plane one, the expansion dynamics leads to
qualitatively similar ? dependence as for the
static out-of plane source Quantitative
differences Rs too small, Ro,l too big
oscill. amplit. too small
Heinz, Kolb, hep-ph/0111075
40
Effect of nonequal times in pair cms
RL, Lyuboshitz SJNP 35 (82) 770
Applicability condition of equal-time
approximation t ?? ?r2
r02 fm ?02 fm/c
r02 fm v0.1
? OK for heavy particles ? OK within 5 even
for pions if ????0 r0 or lower
41
FSI effect on CF of neutral kaons
Goal no Coulomb. But R may go up by 0.5 fm due
to neglected FSI in KK (50 KsKs)? f0(980)
a0(980) RL-Lyuboshitz (82) couplings from
Preliminary STAR data points to larger R
than from charge kaon CFs
l 0.76 ? 0.29 R 5.75 ? 1.00
Morgan (93)
Martin (77)
R3.1 fm
KK
long
3.6
4.2
CF(KsKs)
3.3
4.3
side
3.6
4.0
4.5
4.9
out
42
Coalescence deuterons ..
WF in continuous pn spectrum ?-k(r) ? WF in
discrete pn spectrum ?b(r)
Edd3N/d3pd B2 Epd3N/d3pp End3N/d3pn pp?
pn? ½pd
Coalescence factor B2 (2?)3(mpmn/md)-1?t??b(r
)2? R-3
Triplet fraction ¾ ? unpolarized Ns
Lyuboshitz (88) ..
B2
Usually n ? p
Much stronger energy dependence of B2 R-3
than expected from pion and proton
interferometry radii
R(pp) 4 fm from AGS to SPS
43
Simulation data on CF-asymmetries
Simulation studies of method sensitivity
Erazmus et al. ALICE Note 95-43
Soff et al. JPG 23 (97) 2095
Voloshin et al. PRL 79 (97) 4766
Ardouin et al. PLB 446 (99) 191
Data on CF-asymmetries
pd GANIL PbPb, XeSn, XeTi 45-50 AMeV
Theses Ghisalberti (95), Nouais (96), Gourio (96)
?p AGS AuAu 11 AGeV Miskowiec, Catania (98)
?p, ??? NA49 PbPb central 158 AGeV
RL NA49 Note 210 (99) Palaiseau (01)
Ganz, Torino (99) Seyboth, Torino (00) Blume,
Nantes (02)
?K STAR AuAu ?sNN130 GeV Retiere, Palaiseau
(01), Nantes (02)
44
Balance function

• Motivated by the idea that hadrons
• are locally produced in (),(-) pairs.
• Early pairs separate due to Long. Exp.
• Later pairs correlated at small Dy

Bass, Danielewicz, Pratt, PRL 85 (2000) 2689

• BF width
• narrows with centrality
• late hadronization
• short ?? ?