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

1. Correlation Femtoscopy R. Lednický, JINR Dubna & IP ASCR Prague • History • QS correlations • FSI correlations • Correlation asymmetries • Summary R. Lednický Subatech Nantes

2. History Correlation femtoscopy : measurement of space-time characteristics R, c ~ fm Fermi’34:e± NucleusCoulomb FSI in β-decay modifies the relative momentum (k) distribution → Fermi (correlation) factor F(k,Z,R) is sensitive to Nucleusradius R if charge Z » 1 of particle production using particle correlations

3. Fermi factor in β-decay = |-k(r)|2 ~ (kR)-(Z/137)2 Z=83 (Bi) β- 2 fm 4 R=8 β+

4. 2xGoldhaber, Lee & Pais GGLP’60: enhanced ++, --vs +- at small opening angles – interpreted as BE enhancement depending on fireball radius R0 p p  2+ 2 - n0 R0 = 0.75 fm

5. Kopylov & Podgoretsky 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 models • noted an analogy Grishin,KP’71 & differences KP’75 with HBT effect in Astronomy (see also Shuryak’73, Cocconi’74)

6. QS symmetrization of production amplitude particle momentum correlations are sensitive to space-time structure of the source KP’71-75 total pair spin CF=1+(-1)Scos qx exp(-ip1x1) p1 2 x1 ,nns,s x2 1/R0 1 p2 2R0 nnt,t q =p1- p2 , x = x1- x2 |q| 0

7. Intensity interferometry of classical electromagnetic fields in AstronomyHBT‘56  product of single-detector currentscf conceptual quanta measurement  two-photon counts p1 Correlation ~  cos px34 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   no info on star R,τ orthogonalto KP’75 momentum correlation measurement in particle physics  source space-time picture x

8. HBT paraboloid mirrors focusing the light from a star on photomultipliers Measured product ST of electric currents from the two photomultipliers integrated during time T ~ hours and studied  ST / ST2- ST 2 ½ vs mirror distance d

9. HBT measurement of the angular size of Sirius Ne ~ 108e/sec, f ~ 1013 Hz, fF ~ 5-45MHz Required T ~ (2 /Ne)2/F ~ hours  ST / ST2- ST 2 ½ Normalized to 1 at d=0

10. 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: Intensity-correlation spectroscopy Goldberger,Lewis,Watson’63-66 Measuring phase of x-ray 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

11. GGLP’60 data plotted as CF p p  2+ 2 - n0 R0~1 fm

12. 3-dim fit: CF=1+exp(-Rx2qx2 –Ry2qy2-Rz2qz2-2Rxz2qxqz) Examples of present data: NA49 & STAR Correlation strength or chaoticity Interferometry or correlation radii STAR  KK NA49 Coulomb corrected z x y

13. “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 Grassberger’77 RL’78 x  out transverse pair velocity vt z  long beam cos qx=1-½ (qx)2…exp(-Rx2qx2 –Ry2qy2-Rz2qz2-Rxz2qx qz) Interferometry or correlation 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

14. 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 Circular In-plane Rside(f=90°) small Out-of reaction plane A Rside (f=0°) large In reaction plane z B

15. 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’84,86 Kolehmainen, Gyulassy’86 Makhlin-Sinyukov’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 F RsideR/(1+mt F2/T)½ Longitudinal boost invariant expansion during proper freeze-out (evolution) time  1 in LCMS }  Rlong(T/mt)½/coshy

16. AGSSPSRHIC: radii Clear centrality dependence Weak energy dependence STAR Au+Au at 200 AGeV 0-5% central Pb+Pb or Au+Au

17. AGSSPSRHIC: radii vs pt Central Au+Au or Pb+Pb Rlong:increases 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

18. Interferometry wrt reaction plane STAR’04 Au+Au 200 GeV 20-30% Typical hydro evolution p+p+ & 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

19. Expected evolution of HI collision vs RHIC data Bass’02 QGP and hydrodynamic expansion hadronic phase and freeze-out initial state pre-equilibrium 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

20. 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 F ~ conserves Rout,Rlong & increases Rside at small pt (resonances ?)  Good prospect for 3D Hydro + hadron transport + ? initial F

21. 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

22. Checks with kinetic model Amelin, RL, Malinina, Pocheptsov, Sinyukov’05: System cools & expands but initial Boltzmann momentum distribution & interferomety radii are conserved due to developed collective flow 1 2 3   ~  ~ tens fm   =  = 0 in static model in kinetic model

23. Hydro motivated parametrizations BlastWave: Schnedermann, Sollfrank, Heinz’93 Retiere, Lisa’04 Kniege’05

24. BW fit of Au-Au 200 GeV Retiere@LBL’05 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 R βz=z/ βx=β0(r/R)

25. 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 spectra, radii, v2() Krakow: Broniowski, Florkowski’01 Single freezeout model + Hubble-like flow + resonances Describes spectra, radii but Rlong ? may account for initial F 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 surface emission at smaller flow velocity Fit points to initial 0F of ~ 0.3

26. |-k(r)|2 Similar to Coulomb distortion of -decay Fermi’34: Final State Interaction Migdal, Watson, Sakharov, … Koonin, GKW, ... fcAc(G0+iF0) s-wave strong FSI FSI } nn e-ikr  -k(r)  [ e-ikr +f(k)eikr/r ] CF pp Coulomb |1+f/r|2 kr+kr F=1+ _______ + … eicAc ka } } Bohr radius Coulomb only Point-like 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 particlesK,p, .. & Coalescence deuterons, .. Study “exotic” scattering,K, KK,, p,, .. Study relative space-time asymmetriesdelays, flow

27. Lyuboshitz-Podgoretsky’79: FSI effect on CF of neutral kaons KsKs from KK also show BE enhancement STAR data on CF(KsKs) Goal: no Coulomb. But R may go up by ~1 fm if neglected FSI in KK (~50% KsKs) f0(980) & a0(980) l = 0.9  0.2 R = 4.1 0.5 fm 5.3  0.6 fm RL-Lyuboshitz’82 t

28. 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 Scale=0.76 Scale=0.92 Scale=0.83 p

29. 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 STAR AGS SPS =0.50.2 R=4.50.7 fm R=3.10.30.2 fm

30. mt scaling – transverse flow π, K, p, Λ radii show mt scaling expected in hydrodynamics ππ KsKs pΛ pΛ

31. Correlation study of particle interaction +&  & pscattering lengthsf0 from NA49 and STAR Fits using RL-Lyuboshitz’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: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

32. 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

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  k*x > 0 v > vp p p v2 k*/= v1-v2 x Shorter tint Weaker CF v CF  v1 k*x < 0 v < vp p  v2 p

34. 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* 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/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

35. 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 x RL’99-01 out tT F tT = flow velocity = transverse thermal velocity side t t = F+tT = observed transverse velocity y F  xrx= rtcos =rt (t2+F2-tT2)/(2tF)  mass dependence yry= rtsin = 0 rt zrz sinh = 0 in LCMS & Bjorken long. exp. measures edge effectat yCMS 0

36. pion 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 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, Akkelin-Sinyukov’96: x = RG bx0/[02+T/mt] Proton px = 1.01 GeV/c px = 2.02 GeV/c

37. Decreasing R(pt): x-p correlation • usually attributed to collective flow • taken for granted • femtoscopy the only way to confirm x-p correlations x2-p correlation: yes x-p correlation: yes • Non-flow possibility • hot core surrounded by cool shell • important ingredient of Buda-Lund hydro pictureCsörgő & Lörstad’96 x2-p correlation: yes x-p correlation: no radial gradient of T x = RG bx0/[02+T/mt+T/Tr] decreasing asymmetry ~1

38. 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 p K p Mirror symmetry (~ same mechanism for  and  mesons)   RQMD, BW ~ OK  points to strong transverse flow (t yields ~ ¼ of CF asymmetry)

39. Summary • 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 the microscopic models (but fit  may true ) • Info on two-particle strong interaction:  &  & pscattering lengths from HIC at SPS and RHIC. Good perspective at RHIC and LHC

40. Apologize for skipping • Coalescence data (new d, d from NA49) • Problem of non-Gaussian form Csörgö .. • Imaging technique Brown, Danielewicz, .. • Correlations of penetrating probes • Comparison of different colliding systems • Multiple FSI effects Wong, Zhang, ..; Kapusta, Li; Cramer, .. • Spin correlations Alexander, Lipkin; RL, Lyuboshitz • ……

41. Kniege’05

42. WF in continuouspnspectrum -k*(r*) WF in discrete pn spectrum b(r*) Coalescence: deuterons .. Edd3N/d3pd= B2 Epd3N/d3ppEnd3N/d3pnpppn½pd Coalescencefactor: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