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Femtoscopy in HIC. Theory R. Lednický, JINR Dubna & IP ASCR Prague. History QS correlations FSI correlations Correlation asymmetries Summary. History. Correlation femtoscopy :. measurement of spacetime characteristics R, c ~ fm. of particle production using particle correlations.
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R. Lednický wpcf\'05
Correlation femtoscopy :
measurement of spacetime characteristics R, c ~ fm
of particle production using particle correlations
GGLP’60: observed enhanced ++, vs +
at small opening angles –
interpreted as BE enhancement
KP’7175: settled basics of correlation femtoscopy
in > 20 papers
• proposed CF= Ncorr /Nuncorr& mixing techniques to construct Nuncorr
• clarified role of spacetime characteristics in various production models
• noted an analogyGrishin,KP’71 & differencesKP’75 with
HBT effect in Astronomy (see also Shuryak’73, Cocconi’74)
Grishin, Kopylov, Podgoretsky’71:
for conceptual case of 2 monochromatic sources and 2 detectors
correlation takes the same form both in astronomy and particle physics:
Correlation ~ cos(Rd/L)
Randdare distance vectors between sources and detectors
projected in the plane perpendicular to the emission direction
L >> R, dis 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.”
The analogy triggered misunderstandings:
Shuryak’73: “The interest to correlations of identical quanta is due
to the fact that their magnitude is connected with the space andtime
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.”
Cocconi’74: “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”
Grassberger’77 (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 ..
KP’75: different from Astronomy where
the momentum correlations are absent
total pair spin
due to “infinite”star lifetimes
CF=1+(1)Scos qx
p1
2
x1
,nns,s
x2
1/R0
1
p2
2R0
nnt,t
q =p1 p2 , x = x1 x2
q
0
Intensity interferometry of classical electromagnetic fields in AstronomyHBT‘56 product of singledetector currentscf conceptual quanta measurement twophoton counts
p1
Correlation ~ cos px34
x1
x3
no explicit dependence
p1
p2
x4
on star spacetime size
x2
detectorsantennas tuned to mean frequency
star
x34
Spacetime correlation measurement in Astronomy
source momentum picture p= star angular radius 
no info on star lifetime
KP’75
orthogonalto
& longitudinal size
Sov.Phys. JETP 42 (75) 211
momentum correlation measurement in particle physics
source spacetime picture x
momentum correlation (GGLP,KP) measurements are impossible
in Astronomy due to extremely large stellar spacetime dimensions
while
also in Laboratory:
Intensitycorrelation spectroscopy
Goldberger,Lewis,Watson’6366
Measuring phase of xray scattering amplitude
Fetter’65
& spectral line shape and width
Glauber’65
Phillips, Kleiman, Davis’67:
linewidth measurement from
a mercurury discharge lamp
900 MHz
t nsec
3dim fit: CF=1+exp(Rx2qx2 –Ry2qy2Rz2qz22Rxz2qxqz)
Examples of present data: NA49 & STARCorrelation strength or chaoticity
Interferometry or correlation radii
STAR
KK
NA49
Coulomb corrected
z
x
y
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
Grassberger’77
RL’78
x out transverse
pair velocity vt
z long beam
cos qx=1½(qx)2+..exp(Rx2qx2 Ry2qy2Rz2qz22Rxz2qx qz)
Interferometry radii:
Rx2 =½ (xvxt)2 , Ry2 =½ (y)2 , Rz2 =½ (zvzt)2
Podgoretsky’83;often called cartesian or BP’95 parameterization
CF  1 = cos qx
 twoparticle approximation (small freezeout PS density f)
~ OK, <f> 1 ? lowptfig.
 smoothness approximation: Remitter Rsource p qpeak
~ OK in HIC, Rsource20.1 fm2
pt2slope 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) = 1+F(12)2+F(23)2+F(31)2+2Re[F(12)F(23)F(31)]
CF2(12) = 1+F(12)2 , F(q) = eiqx
Bertsch’94
Lisa ..’05
<f> rises up to SPS
May be high phase space
density at low pt ?
? Pion condensate or laser
? Multiboson effects on CFs
spectra & multiplicities
KP (7175) …
Probing source shape and emission durationStatic Gaussian model with space and time dispersions R2, R2, 2
Rx2 = R2 +v22
Ry2 = R2
Rz2 = R2 +v22
Emission duration
2 = (Rx2 Ry2)/v2
If elliptic shape also in transverse plane
RyRsideoscillates with pair azimuth f
Rside2 fm2
Outof plane
Circular
Inplane
Rside(f=90°) small
Outof reaction plane
A
Rside (f=0°) large
In reaction plane
z
B
Dispersion of emitter velocities & limited emission momenta (T)
xp 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’84,86
Kolehmainen, Gyulassy’86
MakhlinSinyukov’87
Pt=160MeV/c
Pt=380 MeV/c
Bertch, Gong, Tohyama’88
Hama, Padula’88
Pratt, Csörgö, Zimanyi’90
Rout
Rside
Mayer, Schnedermann, Heinz’92
Rout
Rside
…..
Collective transverse flow t
RsideR/(1+mtt2/T)½
Longitudinal boost invariant expansion
during proper freezeout (evolution) time
1 in LCMS
}
Rlong(T/mt)½/coshy
Clear centrality dependence
Weak energy dependence
STAR Au+Au at 200 AGeV
05% central Pb+Pb or Au+Au
Central Au+Au or Pb+Pb
Rlong:increases
smoothly &
points to short evolution
time
~ 810 fm/c
Rside,Rout:
change little &
point to strong transverse flow
t~ 0.40.6 &
short emission duration
~ 2 fm/c
STAR’04 Au+Au 200 GeV 2030%
Typical hydro evolution
p+p+ & pp
Outofplane
Circular
Inplane
Time
STAR data:
oscillations like for a
static outofplane source
stronger then Hydro & RQMD
Short evolution time
Bass’02
QGP and
hydrodynamic expansion
hadronic phase
and freezeout
initial state
preequilibrium
hadronization
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
Hydro assuming ideal fluid explains strong collective
() flows at RHIC but not the interferometryresults
Puzzle ?But comparing
Bass, Dumitru, ..
1+1D Hydro+UrQMD
1+1D H+UrQMD
Huovinen, Kolb, ..
2+1D Hydro
with 2+1D 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
Sinyukov, Akkelin, Hama’02:
Based on the fact that the known analytical solution
of nonrelativistic BE with sphericallysymmetric
initial conditions coincides with free streaming
ti’= ti +T, xi’= xi+ vi T , vi v =(p1+p2)/(E1+E2)
one may assume the kinetic evolution close to
free streaming alsoin realconditionsand thus
~ conserving initial spectra and
Csizmadia, Csörgö, Lukács’98
initial interferometry radii
qxi’ qxi +q(p1+p2)T/(E1+E2) = qxi
~ justify hydro motivated freezeout parametrizations
Amelin, RL, Malinina, Pocheptsov, Sinyukov’05:
System cools
& expands
but initial
Boltzmann
momentum
distribution &
interferomety
radii are
conserved due
to developed
collective flow
~ ~ tens fm
= = 0
in static model
BlastWave: Schnedermann, Sollfrank, Heinz’93
Retiere, Lisa’04
Kniege’05
AuAu 200 GeV
T=106 ± 1 MeV
<bInPlane> = 0.571 ± 0.004 c
<bOutOfPlane> = 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
BudaLund: Csanad, Csörgö, Lörstad’04
Other parametrizationsSimilar to BW but T(x) & (x)
hot core ~200 MeV surrounded by cool ~100 MeV shell
Describes all data: spectra, radii, v2()
Krakow: Broniowski, Florkowski’01
Single freezeout model + Hubblelike flow + resonances
Describes spectra, radii but Rlong
? may account for initial t
KievNantes: Borysova, Sinyukov,
volume emission
Erazmus, Karpenko’05
Generalizes BW using hydro motivated
closed freezeout hypersurface
Additional surface emission introduces
xt correlation helps to desribe Rout
surface
emission
at smaller flow velocity
Fit points to initial t of ~ 0.3
Similar to Coulomb distortion of decay Fermi’34:
Final State InteractionMigdal, Watson, Sakharov, … Koonin, GKW, ...
fcAc(G0+iF0)
swave
strong FSI
FSI
}
nn
eikr k(r) [ eikr +f(k)eikr/r ]
CF
pp
Coulomb
1+f/r2
kr+kr
F=1+ _______ + …
eicAc
ka
}
}
Bohr radius
Coulomb only
Pointlike
Coulomb factor
k=q/2
FSI is sensitive to source size r and scattering amplitude f
It complicates CF analysis but makes possible
Femtoscopy with nonidentical particlesK,p, .. &
Coalescence deuterons, ..
Study “exotic” scattering,K, KK,, p,, ..
Study relative spacetime asymmetriesdelays, flow
CF = k(r)2
 same as for KP formula in case of pure QS &
 equal time approximation in PRF
RL, Lyuboshitz’82 eq. time condition t* r*2
OKfig.
 tFSI tprod k*= ½q* hundreds MeV/c
RL, Lyuboshitz ..’98
transfer in production
& account for coupled
channels within the
same isomultiplet only: + 00, p 0n, K+K K0K0, ...
RL, Lyuboshitz SJNP 35 (82) 770; RLnuclth/0501065
Applicability condition of equaltime approximation: t* r*2
r0=2 fm 0=2 fm/c
r0=2 fm v=0.1
CFFSI(00)
OK for heavy
particles
OK within 5%
even for pions if
0 ~r0 or lower
Note: v ~ 0.8
KsKs from KK also show
FSI effect on CF of neutral kaonsGoal: 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)
RLLyuboshitz’82 couplings from
Martin’77
Achasov’01,03
no FSI
l = 1.09 0.22
R = 4.66 0.46 fm
5.86 0.67 fm
t
Long tails in RQMD: r* = 21 fm for r* < 50 fm
NA49 central Pb+Pb 158 AGeV vs RQMD29 fm for r* < 500 fm
Fit CF=Norm[Purity RQMD(r* Scaler*)+1Purity]
RQMD overestimatesr* by 1020% at SPS cf ~ OK at AGS
worse at RHIC
Scale=0.76
Scale=0.92
Scale=0.83
p
Goal: No Coulomb suppression as in pp CF &
p CFs at AGS & SPS & STARWangPratt’99 Stronger sensitivity to R
singlet triplet
Scattering lengths, fm: 2.31 1.78
Fit using RLLyuboshitz’82 with
Effective radii, fm: 3.04 3.22
consistent with estimated impurity
R~ 34 fm consistent with the radius from pp CF
STAR
AGS
SPS
=0.50.2
R=4.50.7 fm
R=3.10.30.2 fm
+& & pscattering lengthsf0 from NA49 and STAR
Fits using RLLyuboshitz’82
pp
STAR CF(p) data point to
Ref0(p) < Ref0(pp) 0
Imf0(p) ~ Imf0(pp) ~ 1 fm
NA49 CF(+) vs RQMD with
SI scale:f0siscaf0 (=0.232fm)

sisca = 0.60.1 compare ~0.8 from
SPT & BNL data E765 K e
NA49 CF() data prefer
f0() f0(NN) ~ 20 fm
CF of identical particles sensitive to terms evenin k*r*
(e.g. through cos 2k*r*) measures only
dispersion of the components of relative separation
r* = r1* r2*in pair cms
RL, Lyuboshitz, Erazmus, Nouais PLB 373 (1996) 30
Construct CF+x and CFx with positive and negativek*projectionk*x on a given directionx and study CFratio CF+x/CFx
Assume emitted later than p or closer to the center
x
v
Longer tint
Stronger CF
v1
CF
k*x > 0
v > vp
p
p
v2
k*/= v1v2
x
Shorter tint
Weaker CF
v
CF
v1
k*x < 0
v < vp
p
v2
p
Asymmetry arises mainly from Coulomb FSI
CF Ac() F(i,1,i)2
=(k*a)1, =k*r*+k*r*
r*a
F 1+ = 1+r*/a+k*r*/(k*a)
k*1/r*
}
±226 fm for ±p
±388 fm for +±
Bohr radius
k* 0
CF+x/CFx 1+2 x* /a
x* = x1*x2* rx*
Projection of the relative separation
r* in pair cms on the direction x
x* = t(x  vtt)
In LCMS (vz=0) or x  v:
CF asymmetry is determined by space and time asymmetries
RQMD Pb+Pb p +X central 158 AGeV :
x = 5.2 fm
t = 2.9 fm/c
+pasymmetry effect 2x*/a 8%
x* = 8.5 fm
Shift x in out direction is due to collective transverse flow
& higher thermal velocity of lighter particles
xp > xK > x > 0
x
RL’9901
out
tT
F
tT
= flow velocity
= transverse thermal velocity
side
t
t
= F+tT = observed transverse velocity
y
F
xrx= rtcos =rt (t2+F2tT2)/(2tF)
mass dependence
yry= rtsin = 0
rt
zrz sinh = 0
in LCMS & Bjorken long. exp.
measures edge effectat yCMS 0
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) < Rx(K) < 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) = 0r/ RG
RL’04, AkkelinSinyukov’96:
x = RG bx0/[02+T/mt]
Proton
px = 1.01 GeV/c
px = 2.02 GeV/c
Au+Au central sNN=130 GeV
Pb+Pb 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)
collective flow chaotic source motion
x2p correlation yes yes
Teff with m yes yes
R with mt yes yes
xp correlation yes no
x 0 yes no
CF asymmetry yes yes if t 0