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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 space-time characteristics R, c ~ fm. of particle production using particle correlations.

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

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Femtoscopy in hic theory r lednick jinr dubna ip ascr prague

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

  • History

  • QS correlations

  • FSI correlations

  • Correlation asymmetries

  • Summary

R. Lednický wpcf'05



Correlation femtoscopy :

measurement of space-time characteristics R, c ~ fm

of particle production using particle correlations

GGLP’60: observed enhanced ++, vs +

at small opening angles –

interpreted as BE enhancement

KP’71-75: settled basics of correlation femtoscopy

in > 20 papers

• proposed CF= Ncorr /Nuncorr& mixing techniques to construct Nuncorr

• clarified role of space-time characteristics in various production models

• noted an analogyGrishin,KP’71 & differencesKP’75 with

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

Formal analogy of photon correlations in astronomy and particle physics

Formal analogy of photon correlationsin astronomy and particle physics

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(Rd/L)

Randdare distance vectors between sources and detectors

projected in the plane perpendicular to the emission direction

L >> 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.”

Femtoscopy in hic theory r lednick jinr dubna ip ascr prague

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 ..

Qs symmetrization of production amplitude momentum correlations in particle physics

QS symmetrization of production amplitudemomentum correlations in particle physics

KP’75: different from Astronomy where

the momentum correlations are absent

total pair spin

due to “infinite”star lifetimes

CF=1+(-1)Scos qx











q =p1- p2 , x = x1- x2



Femtoscopy in hic theory r lednick jinr dubna ip ascr prague

Intensity interferometry of classical electromagnetic fields in AstronomyHBT‘56  product of single-detector currentscf conceptual quanta measurement  two-photon counts


Correlation ~  cos px34



no explicit dependence




on star space-time size


detectors-antennas tuned to mean frequency 



Space-time correlation measurement in Astronomy 

source momentum picture |p|=||  star angular radius ||

 no info on star lifetime



& longitudinal size

Sov.Phys. JETP 42 (75) 211

momentum correlation measurement in particle physics 

source space-time picture |x|

Femtoscopy in hic theory r lednick jinr dubna ip ascr prague

  • 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:

Intensity-correlation spectroscopy


Measuring phase of x-ray scattering amplitude


& spectral line shape and width


Phillips, Kleiman, Davis’67:

linewidth measurement from

a mercurury discharge lamp

900 MHz

t nsec

Gglp 60 data plotted as cf

GGLP’60 data plotted as CF

p p  2+ 2 - n0

R0~1 fm

Examples of present data na49 star

3-dim fit: CF=1+exp(-Rx2qx2 –Ry2qy2-Rz2qz2-2Rxz2qxqz)

Examples of present data: NA49 & STAR

Correlation strength or chaoticity

Interferometry or correlation radii




Coulomb corrected




General parameterization at q 0

“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



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 

Podgoretsky’83;often called cartesian or BP’95 parameterization

Assumptions to derive kp formula

Assumptions to derive KP formula

CF - 1 = cos qx

- two-particle approximation (small freeze-out PS density f)

~ OK, <f>  1 ? lowptfig.

- 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) = 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

Phase space density from cfs and spectra

Phase space density from CFs and spectra


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

Probing source shape and emission duration

f (degree)

KP (71-75) …

Probing source shape and emission duration

Static Gaussian model with space and time dispersions R2, R||2, 2

Rx2 = R2 +v22

 Ry2 = R2

Rz2 = R||2 +v||22

Emission duration

2 = (Rx2- Ry2)/v2

If elliptic shape also in transverse plane

 RyRsideoscillates with pair azimuth f

Rside2 fm2

Out-of plane



Rside(f=90°) small

Out-of reaction plane


Rside (f=0°) large

In reaction plane



Probing source dynamics expansion

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



Kolehmainen, Gyulassy’86



Pt=380 MeV/c

Bertch, Gong, Tohyama’88

Hama, Padula’88

Pratt, Csörgö, Zimanyi’90



Mayer, Schnedermann, Heinz’92




Collective transverse flow t


Longitudinal boost invariant expansion

during proper freeze-out (evolution) time 

1 in LCMS


 Rlong(T/mt)½/coshy

Ags sps rhic radii

AGSSPSRHIC: radii

Clear centrality dependence

Weak energy dependence

STAR Au+Au at 200 AGeV

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

Ags sps rhic radii vs p t

AGSSPSRHIC: radii vs pt

Central Au+Au or Pb+Pb


smoothly &

points to short evolution


 ~ 8-10 fm/c


change little &

point to strong transverse flow

t~ 0.4-0.6 &

short emission duration

 ~ 2 fm/c

Interferometry wrt reaction plane

Interferometry wrt reaction plane

STAR’04 Au+Au 200 GeV 20-30%

Typical hydro evolution

p+p+ & p-p-





STAR data:

 oscillations like for a

static out-of-plane source

stronger then Hydro & RQMD

Short evolution time

Expected evolution of hi collision vs rhic data

Expected evolution of HI collision vs RHIC data


QGP and

hydrodynamic expansion

hadronic phase

and freeze-out

initial state



Kinetic freeze out


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



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

Why conservation of spectra radii

Why ~ conservation of spectra & radii?

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

Checks with kinetic model

Checks with kinetic model

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

System cools

& expands

but initial



distribution &


radii are

conserved due

to developed

collective flow

  ~  ~ tens fm

  =  = 0

in static model

Hydro motivated parametrizations

Hydro motivated parametrizations

BlastWave: Schnedermann, Sollfrank, Heinz’93

Retiere, Lisa’04


Femtoscopy in hic theory r lednick jinr dubna ip ascr prague

BW fit of

Au-Au 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

Other parametrizations

Buda-Lund: Csanad, Csörgö, Lörstad’04

Other parametrizations

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, Florkowski’01

Single freezeout model + Hubble-like flow + resonances

Describes spectra, radii but Rlong

? may account for initial t

Kiev-Nantes: Borysova, Sinyukov,

volume emission

Erazmus, Karpenko’05

Generalizes BW using hydro motivated

closed freezeout hypersurface

Additional surface emission introduces

x-t correlation  helps to desribe Rout



at smaller flow velocity

Fit points to initial t of ~ 0.3

F inal s tate i nteraction


Similar to Coulomb distortion of -decay Fermi’34:

Final State Interaction

Migdal, Watson, Sakharov, … Koonin, GKW, ...



strong FSI




e-ikr  -k(r)  [ e-ikr +f(k)eikr/r ]






F=1+ _______ + …





Bohr radius

Coulomb only


Coulomb factor


 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 asymmetriesdelays, flow

Assumptions to derive fermi formula

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, Lyuboshitz’82  eq. time condition |t*| r*2


- tFSI tprod  |k*|= ½|q*| hundreds MeV/c

  • typical momentum

RL, Lyuboshitz ..’98

transfer in production

& account for coupled

channels within the

same isomultiplet only: + 00, -p  0n, K+K K0K0, ...

Effect of nonequal times in pair cms

Effect of nonequal times in pair cms

RL, Lyuboshitz SJNP 35 (82) 770; RLnucl-th/0501065

Applicability condition of equal-time approximation: |t*| r*2

r0=2 fm 0=2 fm/c

r0=2 fm v=0.1


OK for heavy


OK within 5%

even for pions if

0 ~r0 or lower

Note: v ~ 0.8

Fsi effect on cf of neutral kaons


KsKs from KK also show

FSI effect on CF of neutral kaons

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-Lyuboshitz’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


Na49 central pb pb 158 agev vs rqmd

Long tails in RQMD: r* = 21 fm for r* < 50 fm

NA49 central Pb+Pb 158 AGeV vs RQMD

29 fm for r* < 500 fm

Fit CF=Norm[Purity RQMD(r* Scaler*)+1-Purity]

RQMD overestimatesr* by 10-20% at SPS cf ~ OK at AGS

worse at RHIC





P cfs at ags sps star

Goal: No Coulomb suppression as in pp CF &

p CFs at AGS & SPS & STAR

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~ 3-4 fm consistent with the radius from pp CF





R=4.50.7 fm

R=3.10.30.2 fm

Correlation study of particle interaction

Correlation study of particle interaction

+&  & pscattering lengthsf0 from NA49 and STAR

Fits using RL-Lyuboshitz’82


STAR CF(p) data point to

Ref0(p) < Ref0(pp)  0

Imf0(p) ~ Imf0(pp) ~ 1 fm

NA49 CF(+) vs RQMD with

SI scale:f0siscaf0 (=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

Correlation asymmetries

Correlation asymmetries

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

  • 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 negativek*-projectionk*x on a given directionx and study CF-ratio CF+x/CFx

Simplified idea of cf asymmetry valid for coulomb fsi

Simplified idea of CF asymmetry(valid for Coulomb FSI)

Assume emitted later than p or closer to the center



Longer tint

Stronger CF



k*x > 0

v > vp




k*/= v1-v2


Shorter tint

Weaker CF




k*x < 0

v < vp




Cf asymmetry for charged particles

CF-asymmetry for charged particles

Asymmetry arises mainly from Coulomb FSI

CF  Ac() |F(-i,1,i)|2

=(k*a)-1, =k*r*+k*r*


F  1+  = 1+r*/a+k*r*/(k*a)



±226 fm for ±p

±388 fm for +±

Bohr radius

k*  0

 CF+x/CFx  1+2 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 (vz=0) or x || v:

CF asymmetry is determined by space and time asymmetries

Usually x and t comparable

Usually: x and t comparable

RQMD Pb+Pb p +X central 158 AGeV :

x = -5.2 fm

t = 2.9 fm/c

+p-asymmetry effect 2x*/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







= flow velocity

= transverse thermal velocity




= F+tT = observed transverse velocity



xrx= rtcos =rt (t2+F2-tT2)/(2tF) 

mass dependence

yry= rtsin = 0


zrz sinh = 0

in LCMS & Bjorken long. exp.

measures edge effectat yCMS 0

Bw retiere@lbl 05


BW Retiere@LBL’05

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


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, Akkelin-Sinyukov’96:

x = RG bx0/[02+T/mt]


px = 1.01 GeV/c

px = 2.02 GeV/c

Na49 star out asymmetries

NA49 & STAR out-asymmetries

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




Mirror symmetry (~ same mechanism for  and  mesons)

RQMD, BW ~ OK  points to strong transverse flow

(t yields ~ ¼ of CF asymmetry)



  • 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 2+1D hydro& transport calculations which strongly overestimate out&long 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

Apologize for skipping

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

  • ……

Femtoscopy in hic theory r lednick jinr dubna ip ascr prague


Femtoscopy in hic theory r lednick jinr dubna ip ascr prague

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

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