Correlation femtoscopy R. Lednický, JINR Dubna & IP ASCR Prague

4-6.02.2006 R. Lednický dwstp'06 1

Correlation femtoscopy R. Lednický, JINR Dubna & IP ASCR Prague

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


Reviews, booksM.I. Podgoretsky, Sov. J. Part. Nucl. 20 (1989) 266; ЭЧАЯ 20 (1989) 628

D.H. Boal et al., Rev. Mod. Phys. 62 (1990) 553

U.A. Wiedemann, U. Heinz, Phys. Rep. 319 (1999) 145

T. Csorgo, Heavy Ion Phys. 15 (2002) 1

R. Lednicky, Phys. Atom. Nucl. 67 (2004) 72

M. Lisa et al., Ann. Rev. Nucl. Part. Sci. 55 (2005) 357

R.M. Weiner, B-E correlations and subatomic interference, John Wiley & sons, LTD

3

History

GGLP’60: observed enhanced ++ , vs +

measurement of space-time characteristics R, c ~ fm

KP’71-75: settled basics of correlation femtoscopy

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

• 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


QS symmetrization of production amplitude momentum correlations in particle physics

CF=1+(-1)Scos qx

p1

p2

x1

x2

q = p1- p2 , x = x1- x2nnt , t

, nns , s

2

1

0 |q|

1/R0

total pair spin

2R0

KP’75: different from Astronomy where the momentum correlations are absentdue to “infinite” star lifetimes

5

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

p1

p2

x1

x2

x3

x4

stardetectors-antennas tuned to mean frequency

Correlation ~ cos px34

|p|-1

|x34|

Space-time correlation measurement in Astronomy source momentum picture |p|=|| star angular radius ||

orthogonal tomomentum correlation measurement in particle physics source space-time picture |x|

KP’75 no info on star lifetimeSov.Phys. JETP 42 (75) 211 & longitudinal size

no explicit dependenceon star space-time size


momentum correlation (GGLP,KP) measurements are impossiblein 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’63-66Intensity-correlation spectroscopy Measuring phase of x-ray scattering amplitude

& spectral line shape and widthFetter’65

Glauber’65

Michelson cf HBT interferometers

IA ~ | iexp[i(i+kixA)] |2

~ N+ 2 i<j cos[(i- j)+(ki-kj)xA] Product of intensities averaged over ’s:IA IB =IAIB[1+(2/N2)i<jcos(kijxAB)]

=IAIB [1+|(xA-xB)|2]

Actually measured product of electric currents after filters (0<|i-j|<F) integrated in a time T

ST=∫dt JA JB ~ (Ne2/) T |(0,xA-xB)|2

normalized to r.m.s.(ST) ~ Ne (T/F)1/2

Field intensity in antenna A:

A

IA+B ~ |iexp[i(i+kixA)] + jexp[i(j+kjxB)]|2= 2N+ 2Reiexp[ki(xA-xB)]

IA+B = IA+IB[1+Re(xA-xB)] Fourier transform exp[ik(xA-xB)](k)d4k

B

filter

filter

Required ST /r.m.s.(ST) > 1 T > (2 /Ne)2/F


HBT paraboloid mirrors focusing the light from a star on photomultipliers


(1954) A new type of interferometer for use in radio astronomy

L. Mandel and E. Wolf (1995): Optical coherence and quantum optics

J. Perina (1984): Quantum statistics of linear and nonlinear phenomena

(1956) Correlation between photons in two coherent beams of light

(1956) A test of a new type of stellar interferometer on Sirius

(1956) The question of correlations between photons in coherent light rays

+ E.M. Purcell (1956)

R. Hanbury Brown and R.Q. Twiss:


ST / ST2- ST 2 ½

Normalized to 1 at d=0

Ne ~ 108 e/sec, f ~ 1013 Hz, fF ~ 5-45 MHz

Required T ~ (2 /Ne)2/F ~ hours

HBT measurement of the angular size of Sirius


Coincidence measurements

A. Adam, L. Janossy, P. Varga (1955) 1011 yearsE. Brannen, H.I.S. Ferguson (1956) 103 years

HBT (1956) minutes-hours

Required time

compare to HBT technique

E.M. Purcell: Brown and Twiss did not count individual photoelectrons and coincidences, and were able to work with a primary photoelectric current some 104 times greater than that of Brannen and Ferguson. … This onlyadds lustre to the achievement of Brown and Twiss.

F.T. Arechi, E. Gatti, A. Sona (1966) hours B.L. Morgan, L. Mandel (1966) hours

12

Formal analogy of photon correlationsin astronomy and particle physics

Grishin, Kopylov, Podgoretsky’71:for conceptual case of 2 monochromatic sources and 2 detectors

R and d are distance vectors between sources and detectorsprojected in the plane perpendicular to the emission direction

Correlation ~ cos(Rd/L)

“…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.”

correlation takes the same form both in astronomy and particle physics:

L >> R, d is distance between the emitters and detectors

13

The analogy triggered misunderstandings: Shuryak’73: “The interest to correlations of identical quanta is due

Cocconi’74: “The method proposed is equivalent to that used …

“For a stationary source

of the measurement of star radii.”

! Correlation(q) = cos(q d)

Grassberger’77 (ISMD):

case the opposite happens”“While .. interference builds up mostly .. near the detectors .. in our

! Same mistake: many others ..

astronomy and is the basis of Hanbury Brown and Twiss methodstructure of the source of quanta. This idea originates from radioto the fact that their magnitude is connected with the space and time

is the standard one |q d| 1”condition for interference(such as a star) the

… by radio astronomers to study angular dimensions of radio sources”


GGLP effect often called HBT, though:

• HBT did not count quanta – they measured the product of currents ( field intensities) from two antennas – intensity interferometry -

useless technique for correlation femtoscopy• Being of classical origin (Superposition Principle), HBT

effect would survive when h 0 and quantum interference vanished

• Even if quanta measurement were done in Astronomy, it would be orthogonal to that of GGLP


GGLP’60 data plotted as CF

GGLP data plotted as KP CF=N(++,--)/N(+-)

0 0.1 0.2Q2= -(p1-p2)

2 (GeV/c)2

0

1

3

2

Lorstad JMPA 4 (89) 286

R0~1 fm

p p 2+ 2 - n0


Examples of present data: NA49 & STAR

3-dim fit: CF=1+exp(-Rx2qx

2 –Ry2qy

2 -Rz

2qz2

-2Rxz2qx qz)

z x y

Correlation strength or chaoticity

NA49

Interferometry or correlation radii

KK STAR

Coulomb corrected

“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}

Rx2 =½ (x-vxt)2 , Ry

2 =½ (y)2 , Rz2 =½ (z-vzt)2

q0 = qp/p0 qv = qxvx+ qzvz

y side

x out transverse pair velocity vt

z long beam

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

Interferometry or correlation radii:

cos qx=1-½(qx)2+.. exp(-Rx2qx

2 -Ry2qy

2 -Rz

2qz2 -2Rxz

2qx qz)

Grassberger’77RL’78

Formalism of independent one-particle sourcesx|A = (2)-4 d4 uA() exp[-i (x-xA)]|x = exp(i x)|A = d4x |xx|A = uA() exp(i xA)

Momentum (femtoscopic) correlations:Ampl(p) = p|A = uA(p) exp(i pxA)Ampl(p1,p2) = 2-1/ 2 [uA(p1)uA(p2) exp(i p1xA+i p2xB) + 1 2]Corr(p1,p2) = 2Re{exp(i qx) uA(p1)uB(p2)uA

*(p2)uB*(p1) x

x [|uA(p1)uB(p2)| 2 +|uA(p2)uB(p1)|2]-1 } cos[(p1-p2)(xA-xB)]

Space-time (spectroscopic) correlations:Ampl(x) = x|A ~ exp[i pA(xA-x)] for ~ monochrom. sourceAmpl(x3,x4) ~ exp{i pA(xA-x3)+i pB (xB-x4)] + 3 4}

Corr(x3,x4) ~ cos[(pA-pB )(x3-x4)] ! No explicit dependence on xA, xB


Femtoscopy through Emission function G(p,x)

E d3N/d3p = |T(p)|2 = d4x d4x’ exp[-i p(x-x’)] (x)*(x’)One particle:

= d4x G(p,x) x,x’ x=½(x+x’), =x-x’ G(p,x) = partial Fourier transform of space-time

density matrix (x)*(x’)Two id. pions:

E1E2d6N/d3p1d3p2 = d4x1d4x2 [G(p1,x1;p2,x2)+ G(p,x1;p,x2)cos(qx)]p = ½(p1+p2) q = p1-p2 x = x1-x2

Corr(p1,p2) = d4x1d4x2G(p,x1;p,x2) cos(qx) / d4x1d4x2G(p1,x1;p2,x2) cos(qx) exp(- i Ri

2qi2 - 2q0

2) if G(p1,x1;p2,x2)= G(p1,x1)G(p2,x2) G(p,x) ~ exp(- i xi

2/2Ri2- x0

2/22)

20

Assumptions to derive KP formula

CF - 1 = cos qx

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

- smoothness approximation: Remitter Rsource |p| |q|peak

- incoherent or independent emission

~ OK, <f> 1 ? low pt fig.

~ OK in HIC, Rsource2 0.1 fm2 pt

2-slope of direct particles

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

- neglect of FSIOK for photons, ~ OK for pions up to Coulomb repulsion

21

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 CFsspectra & multiplicities

<f> rises up to SPSLisa ..’05

Multiboson effects Coherent emission: pion laser, DCC … Correlation strength < 1 due to coherence Fowler-Weiner’77

But: impurity, Long-Lived Sources (LLS), .. Deutschman’78

3 CF normalized to 2 CFs: get rid of LLS effect Heinz-Zhang’97 But: problem with 3 Coulomb & extrapolation to Q3=0

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

Widening of n distribution:

Increasing PSD:Poisson BE

Narrowing of spectrum:

/(2r0) < Widening of CFs:

width = 1/r0

= 1width

0 at fixed n

rare gas BE condensate

RL-Podgoretsky’79


3 data on chaotic fraction

Periph Mid-centr Centr

Within large (systematic) errors STAR data is consistent with full chaoticity

r3 =[C3(123) – C2(12) – C2(23) – C2(31) ]/[C2(12) C2(23) C2(31) ]½

C2 = CF2-1 cancel out Heinz-Zhang’97

Interpolate to r3(Q3=0), Q3 = (Q122+ Q23

2+ Q312)½

Construct ratio r3 in which LLS contributions to C3 = CF3-1 and

½r3(0) =½(3-2)/(2-)¾

½r3 STAR’03

2

Full chaoticity

Multiboson effects on n & spectra

Poisson ~ n/n!

BE ~ n

Rare gasWidth=Condensate

Measure of PSD: =/(r0+½)3 1

Width=/(2r0)½


Multiboson effects on CFsCFn(0) fixed n

n

CF(q) inclusive CF(q) semi-inclusive nnmax

nmax

2 120

undershoot

Intercept dropswith n faster

for softer pions

Width logarithmicallyincreases with PSD

Intercept stays at 2

60

n =33.5


Probing source shape and emission duration

Static Gaussian model with space and time dispersions

R2, R||2, 2

Rx2 = R2 +v22

Ry2 = R2

Rz2 = R||

2 +v||22

Emission duration2 = (Rx

2- Ry2)/v2

(degree)

Rsi

de2

fm2

If elliptic shape also in transverse plane RyRside oscillates with pair azimuth

Rside (=90°) small

Rside =0°) large

z

A

B

Out-of reaction plane

In reaction plane

In-planeCircular

Out

-of

plan

e

KP (71-75) …


Probing source dynamics - expansionDispersion of emitter velocities & limited emission momenta (T)

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

Interferometry radii decrease with pair velocity

Interference probes only a part of the sourceResonances GKP’71 ..Strings Bowler’85 ..Hydro

Pt=160 MeV/c Pt=380 MeV/c

Rout RsideRout Rside

Collective transverse flow F RsideR/(1+mt F2/T)½

Longitudinal boost invariant expansionduring proper freeze-out (evolution) time

Rlong (T/mt)½/coshy

Pratt, Csörgö, Zimanyi’90

Makhlin-Sinyukov’87

}1 in LCMS

…..

Bertch, Gong, Tohyama’88Hama, Padula’88

Mayer, Schnedermann, Heinz’92

Pratt’84,86Kolehmainen, Gyulassy’86

Longitudinal boost-invariant expansionel. sources of lifetime produced at t=z=0 uniformly distr. in

t= cosh() z= sinh()E= mt cosh(y) pz= mt sinh(y) E*= mt cosh(y- )

rapidity and decaying according to thermal law exp(-E*/T)

In LCMS: pair rapidity y=0 soG ~ exp(-E*/T)= exp(-mt cosh /T) exp(-mt/T) exp[-2 / 2(T/mt)]

2 (T/mt)

Rz2= (z-z)2 z’2 Ry

2= y’2 Rx2= (x’-vxt’)2

Rz2= ( sinh())2 = 2 (sinh())2 2 (T/mt)

Rx2= x’2-2vxx’t’+vx

2t’2 t’2 (-)2 ()2

Rz = evolution time Rx = emission durationif x’t’=0 & x’2= y’2


Transverse expansion

= exp[ - (0F2 r2/r0

2 + t2 - 2 0

Ft )x/r0) mt / 2T - r2/ 2r02]

Thermal law & gaussian tr. density profile exp(-r2/ 2r02)

& linear tr. flow velocity profile F(r) = 0Fr / r0

Nonrelativistic case: tT2 = F2 + t

2 - 2 Ft cos x = r cos (out) y = r sin (side) t

= tr. velocity tT = tr. thermal velocity

Note: for a box-like profile (r < R) x’2 < y’2

G ~ exp(-tT2 mt / 2T) exp(-r2/ 2r0

2)

y = 0 x = r0 t 0F / [0

F2+T/mt]

Ry2 = y’2 = x’2 = r0

2 / [1+ 0F2 mt /T]

30

AGSSPSRHIC: radii

STAR Au+Au at 200 AGeV 0-5% central Pb+Pb or Au+Au

Clear centrality dependence

Weak energy dependence

31

AGSSPSRHIC: radii vs pt

Rlong:increases smoothly & points to short evolution time ~ 8-10 fm/c

Rside , Rout :change little & point to strong transverse flow 0

F ~ 0.4-0.6 &short emission duration ~ 2 fm/c

Central Au+Au or Pb+Pb

32

Interferometry wrt reaction plane

STAR data: oscillations like for a

static out-of-plane sourcestronger then Hydro & RQMD

Short evolution time

Out-of-plane Circular In-planeTime

Typical hydro evolution STAR’04 Au+Au 200 GeV 20-30% &


hadronizationinitial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronic phaseand 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 outChemical freeze out

RHIC side & out radii: 2 fm/c

Rlong & radii vs reaction plane: 10 fm/c

Bass’02

34

Puzzle ?

3D Hydro

2+1D Hydro

1+1D Hydro+UrQMD

(resonances ?)

But comparing1+1D H+UrQMDwith 2+1D Hydro

kinetic evolution

at small pt

& increases Rside

~ conserves Rout,Rlong

Good prospect for 3D Hydro

Hydro assuming ideal fluid explains strong collective () flows at RHIC but not the interferometry results

+ hadron transport

Bass, Dumitru, ..

Huovinen, Kolb, ..

Hirano, Nara, ..

? not enough F

+ ? initial F

Why ~ conservation of spectra & radii?

qxi’ qxi +q(p1+p2)T/(E1+E2) = qxi

Sinyukov, Akkelin, Hama’02:

free streaming also in real conditions and thus

initial interferometry radii

ti’= ti +T, xi’ = xi + vi T , vi v =(p1+p2)/(E1+E2)

Based on the fact that the known analytical solutionof nonrelativistic BE with spherically symmetricinitial conditions coincides with free streaming

one may assume the kinetic evolution close to

~ conserving initial spectra and

~ justify hydro motivated freezeout parametrizations

Csizmadia, Csörgö, Lukács’98

36

Checks with kinetic modelAmelin, RL, Malinina, Pocheptsov, Sinyukov’05:

System cools

& expands

but initial

Boltzmann

momentum

distribution &

interferomety

radii are

conserved due

to developed

collective flow

~ ~ tens fm = = 0in static model

37

Hydro motivated parametrizations

Kniege’05

BlastWave: Schnedermann, Sollfrank, Heinz’93Retiere, Lisa’04

38

BW fit ofAu-Au 200 GeV

T=106 ± 1 MeV<InPlane> = 0.571 ± 0.004 c<OutOfPlane> = 0.540 ± 0.004 cRInPlane = 11.1 ± 0.2 fmROutOfPlane = 12.1 ± 0.2 fmLife time () = 8.4 ± 0.2 fm/cEmission duration = 1.9 ± 0.2 fm/c2/dof = 120 / 86

Retiere@LBL’05

39

Other parametrizationsBuda-Lund: Csanad, Csörgö, Lörstad’04 Similar to BW but T(x) & (x)hot core ~200 MeV surrounded by cool ~100 MeV shellDescribes all data: spectra, radii, v2()

Krakow: Broniowski, Florkowski’01

Describes spectra, radii but Rlong

Single freezeout model + Hubble-like flow + resonances

Kiev-Nantes: Borysova, Sinyukov, Erazmus, Karpenko’05

closed freezeout hypersurfaceGeneralizes BW using hydro motivated

Additional surface emission introducesx-t correlation helps to desribe Rout

at smaller flow velocity

volume emission

surface emission

? may account for initial F

Fit points to initial 0F of ~ 0.3


Final State InteractionSimilar to Coulomb distortion of -decay Fermi’34:

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

eicAcF=1+ _______ + …kr+kr

ka

Coulomb

s-wavestrong FSIFSI

fcAc(G0+iF0)}

}

Bohr radius}

Point-likeCoulomb factor k=|q|/2

CF nnpp

Coulomb only

|1+f/r|2

FSI is sensitive to source size r and scattering amplitude fIt 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)|2Migdal, Watson, Sakharov, … Koonin, GKW, ...

Assumptions to derive “Fermi” formula

CF = |-k(r)|2

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

- same as for KP formula in case of pure QS &

- equal time approximation in PRF

typical momentum transfer in production

RL, Lyuboshitz’82 eq. time condition |t*| r*2

OK fig.

RL, Lyuboshitz ..’98

same isomultiplet only: + 00, -p 0n, K+K K0K0, ...

& account for coupledchannels within the


Effect of nonequal times in pair cmsRL, Lyuboshitz SJNP 35 (82) 770; RL nucl-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

particles

OK within 5%even for pions if0 ~r0 or lower

Note: v ~ 0.8

CFFSI(00)


FSI effect on CF of neutral kaons

STAR data on CF(KsKs)

Goal: no Coulomb. But R may go up by ~1 fm if neglected FSI in

= 1.09 0.22R = 4.66 0.46 fm 5.86 0.67 fm

KK (~50% KsKs) f0(980) & a0(980)RL-Lyuboshitz’82 couplings from

t

Achasov’01,03 Martin’77

no FSI

Lyuboshitz-Podgoretsky’79: KsKs from KK also showBE enhancement


NA49 central Pb+Pb 158 AGeV vs RQMDLong tails in RQMD: r* = 21 fm for r* < 50 fm

29 fm for r* < 500 fm

Fit CF=Norm [Purity RQMD(r* Scaler*)+1-Purity]

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


p CFs at AGS & SPS & STAR

Fit using RL-Lyuboshitz’82 with consistent with estimated impurityR~ 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

=0.50.2R=4.50.7 fm

Scattering lengths, fm: 2.31 1.78Effective radii, fm: 3.04 3.22

singlet triplet

AGS SPS STAR

R=3.10.30.2 fm


Correlation study of particle interaction

-

+& & p scattering lengths f0 from NA49 and STAR

NA49 CF(+) vs RQMD with SI scale: f0 sisca f0 (=0.232fm)

sisca = 0.60.1 compare ~0.8 fromSPT & BNL data E765 K e

Fits using RL-Lyuboshitz’82

NA49 CF() data prefer |f0()| f0(NN) ~ 20 fm

STAR CF(p) data point to Ref0(p) < Ref0(pp) 0

Imf0(p) ~ Imf0(pp) ~ 1 fm

pp

47

Correlation study of particle interaction

-

+ scattering length f0 from NA49 CF

Fit CF(+) by RQMD with SI scale: f0 sisca f0

input f0

input = 0.232 fm

sisca = 0.60.1 Compare with

~0.8 from SPT & BNL E765

K e

+

CF=Norm [Purity RQMD(r* Scaler*)+1-Purity]


interaction potential from LEP CF = Norm (1 e-R2Q2)

=0.620.09R=0.110.02 fm

=0.540.10R=0.110.03 fm

=0.600.07R=0.100.02 fm

Pure QS: = ½(1+P2) < 0.3Feed-down & PID: ~ 0.5

Polarization < 0.3 }String picture: lstring~ 2mt/~2 fm ~1 fmRz (T/mt)½ ~ 0.3 fm R > Rz /3 ~ 0.17 fm

QS fit yields too low R & too big

FSI potential core RL (02)

=0.6 fixedR=0.290.03 fm

NSC97eneglected

Spin-orbit &Tensor parts

R OK but potential

tuningrequired

PLB 475 (00) 395

CF at LEP dominated by ! Direct core signal


Correlation asymmetries

CF of identical particles sensitive to terms even in 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 negative k*-projection

k*x on a given direction x and study CF-ratio CF+x/CFx


Simplified idea of CF asymmetry(valid for Coulomb FSI)

x

x

v

v

v1

v2

v1

v2

k*/= v1-v2

p

p

k*x > 0v > vp

k*x < 0v < vp

Assume emitted later than p or closer to the center

p

p

Longer tint

Stronger CF

Shorter tint Weaker CF

CF

CF


CF-asymmetry for charged particlesAsymmetry 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)r*|a|

k*1/r* Bohr radius

}

±226 fm for ±p±388 fm for +±

CF+x/CFx 1+2 x* /ak* 0

x* = x1*-x2* rx* Projection of the relative separation r* in pair cms on the direction x

In LCMS (vz=0) or x || v: x* = t(x - vtt)

CF asymmetry is determined by space and time asymmetries


Large lifetimes evaporation or phase transitionx || v |x| |t| CF-asymmetry yields time delay

Ghisalberti (95) GANILPb+Nb p+d+X

CF+(pd)

CF(pd)

CF+/CF< 1

Deuterons earlier than protonsin agreement with coalescence

e-tp/ e-tn/ e-td/(/2) since tp tn td

Two-phase thermodynamic

model

CF+/CF< 11 2 3

1

2

3

Strangeness distillation: K earlier than K in baryon rich QGP

Ardouin et al. (99)


ad hoc time shift t = –10 fm/c

CF+/CF

Sensitivity test for ALICEa, fm

84

226

249CF+/CF 1+2 x* /a

k* 0

Here x*= - vt

CF-asymmetry scales as - t/a

Erazmus et al. (95)

Delays of several fm/ccan be easily detected


Usually: x and t comparable RQMD Pb+Pb p +X central 158 AGeV : x = -5.2 fm

t = 2.9 fm/cx* = -8.5 fm+p-asymmetry effect 2x*/a -8%

Shift x in out direction is due to collective transverse flow

RL’99-01 xp > xK > x > 0& higher thermal velocity of lighter particles

rt

y

x

F

tT

t

F= flow velocity tT = transverse thermal velocity

t = F + tT = observed transverse velocity

x rx = rt cos = rt (t2+F2- t

T2)/(2tF) y ry = rt sin = 0 mass dependence

z rz sinh = 0 in LCMS & Bjorken long. exp.

out

side

measures edge effect at yCMS 0

pion

Kaon

Proton

BW Retiere@LBL’05

Distribution of emissionpoints at a given equal velocity: - Left, x = 0.73c, y = 0 - Right, x = 0.91c, y = 0

Dash lines: average emission Rx

Rx() < Rx(K) < Rx(p)

px = 0.15 GeV/c px = 0.3 GeV/c

px = 0.53 GeV/c px = 1.07 GeV/c

px = 1.01 GeV/c px = 2.02 GeV/c

For a Gaussian density profile with a radius RG and flow velocity profile F (r) = 0 r/ RG

RL’04, Akkelin-Sinyukov’96 :

x = RG x 0 /[02+T/mt]

NA49 & STAR out-asymmetriesPb+Pb central 158 AGeV not corrected for ~ 25% impurityr* RQMD scaled by 0.8

Au+Au central sNN=130 GeV corrected for impurity

Mirror symmetry (~ same mechanism for and mesons) RQMD, BW ~ OK points to strong transverse flow

pp K

(t yields ~ ¼ of CF asymmetry)


Spin correlations , tt, ..

p

p

n2

n1

Joint angular distribution of decay analyzers n1 and n2 is determined by:

16²W(n1,n2) = 1+ 1P1n1+ 2P2n2+ 12ikTik n1in2k

Decay asymmetry parameters:1 = 2 = (p) = 0.642

polarization vectors Pi= icorrelation tensor Tik = 1k2k

W(x) = ½[1+ ½ 12SpT x]

Distribution of correlation x = n1n2 = cos12 is determined by SpT = sSpTsinglet + tSpTtriplet = -3 s+ t

= 4 t-3

s and t are singlet and triplet fractions, s+ t

= 1:3Alexander-Lipkin (95), RL (99)

58

spin correlations at LEP ALEPH distributions of

correlation x=n1n2= cos12

of directions of decay protonsSlopes ~ SpT = 4 t-3

New femtoscopy tool: t =t/0 triplet state forbidden at Q=0

Noninteracting unpolarized s Check two-particle QM coherence:

violation of Bell-type inequalityRL-Lyuboshitz (01) SpT 1 t½

t = t/

Q 0

t=¾(1e-r02Q2)

s=¼(1e-r02Q2)

=st

r0=0.140.09 fm

Bell-type inequalityx = cos12

Summary• Assumptions behind femtoscopy theory in HIC seem OK• Wealth of data on correlations of various particle species

(,K0,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 ?+ F

initial & 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

• Promising results from Spin correlations


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

• ……

Kniege’05


Hydro wrt reaction planeHeinz, Kolb, hep-ph/0111075 Though Hydro

transforms out-of planesource into in-plane one,the expansion dynamics

leads to qualitativelysimilar dependence as

for the static out-of planesource

Quantitative differences:• Rs too small, Ro,l too big• oscill. amplit. too small

63

Finite-size effectsr* ~ 10 fm but ~30-40 fm and ’ ~900 fm

UrQMD: pNi 2 at 24 GeV ~1% ’, ~19%

ML

’

ML ~ r*2/[1+(r*/r0)2a]2b

short-distance parametrization

’ and

contributionswell fitted basedon exponential

decay law

64

DIRAC CF: CF=N{ |-k*(r*)|2SLS +(1- )}[1+s Q]

SLS determined by:

ML(r0,a,b), fML=1-f-f’

’, f’

, f

Nr0 fmabff’s

f = 17 6% ML

G2fm

G3fm

’


=0.89

r*=16 fm

=0.93

r*=24 fm

=0.81

r*=18.4 fm

=0.76

r*=18.1 fm

=0.94

r*=24.4 fm

=0.91

r*=22.9 fm

Tails in RQMD: r* = 21 fm for r* < 50 fm

29 fm for r* < 500 fm

Strong FSI on

>

++

+-

Strong FSI important for +-

1-G fit: (++) 0.8, r* 25% 2-G fit: ++ +-

r*QS < r*Coul

1-G fit

2-G fit


Femtoscopy with nonidentical particles

CF = |-k* (r*)|2Be careful when comparing

QS (++ ..) and FSI correlations (+..) different sensitivity to r*-distribution tails

QS & strong FSI: non-Gaussian r*-tail influences only first few bins in Q=2k* and its effect is mainly

absorbed in suppression parameter Coulomb FSI: sensitive to r*-tail up to r* ~ Bohr radius

|a|=|z1z2e2|-1

fm K p KK pp388 249 223 110 58

In Gaussian fits one may expect r0(++) < r0(+)

Use realistic models like transport codes


Coalescence: deuterons ..

Edd3N/d3pd = B2 Epd3N/d3pp End3N/d3pn pp pn ½pd

WF in continuous pn spectrum -k*(r*) WF in discrete pn spectrum b(r*)

Coalescence factor: B2 = (2)3(mpmn/md)-1t|b(r*)|2 ~ R-3

Triplet fraction = ¾ unpolarized Ns

Usually: n p

Much stronger energy dependenceof B2 ~ R-3 than expected from

pion and proton interferometry radii

B2

R(pp) ~ 4 fm from AGS to SPS

Lyuboshitz (88) ..


collective flow chaotic source motion

x-p correlation yes no

x2-p correlation yes yesTeff with m yes yesR with mt yes yes

x 0 yes noCF asymmetry yes yes if t 0

Documents

Correlation femtoscopy R. Lednický, JINR Dubna & IP ASCR Prague