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

1. Femtoscopy in HIC. Theory R. Lednický, JINR Dubna & IP ASCR Prague • History • QS correlations • FSI correlations • Correlation asymmetries • Summary R. Lednický wpcf'05

2. History 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)

3. 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.”

4. 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 ..

5. 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 p1 2 x1 ,nns,s x2 1/R0 1 p2 2R0 nnt,t q =p1- p2 , x = x1- x2 |q| 0

6. 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 no explicit dependence |p|-1 p2 x4 on star space-time size 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 lifetime KP’75 orthogonalto & longitudinal size Sov.Phys. JETP 42 (75) 211 momentum correlation measurement in particle physics  source space-time picture |x|

7. 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

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

9. 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

10. “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-Rz2qz2-2Rxz2qx 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

11. 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

12. Phase space density from CFs and spectra 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

13. 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

14. 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 t RsideR/(1+mtt2/T)½ Longitudinal boost invariant expansion during proper freeze-out (evolution) time  1 in LCMS }  Rlong(T/mt)½/coshy

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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   ~  ~ tens fm   =  = 0 in static model

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

23. 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

24. 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 surface emission at smaller flow velocity Fit points to initial t of ~ 0.3

25. |-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

26. 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 OKfig. - 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, ...

27. 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 CFFSI(00)  OK for heavy particles OK within 5% even for pions if 0 ~r0 or lower Note: v ~ 0.8

28. Lyuboshitz-Podgoretsky’79: 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 t

29. 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

30. 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

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. 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)

38. Summary • 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

39. 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 • ……

40. Kniege’05

41. 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