1. 11.07.2006R. Lednický Subatech Nantes1 Correlation Femtoscopy R. Lednický, JINR Dubna & IP ASCR Prague History QS correlations FSI correlations Correlation asymmetries Summary

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

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

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

5. 5 Kopylov & Podgoretsky KP’71-75: settled basics of correlation femtoscopy in > 20 papers proposed CF= N corr /N uncorr & mixing techniques to construct N uncorr 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. 6 QS symmetrization of production amplitude  particle momentum correlations are sensitive to space-time structure of the source CF=1+(-1) S  cos q  x  p 1 p 2 x1x1 x 2 q = p 1 - p 2,  x = x 1 - x 2 nn t,  t , nn s,  s 2 1 0 |q| 1/R 0 total pair spin 2R 0 KP’71-75 exp(-ip 1 x 1 )

7. 7 Intensity interferometry of classical electromagnetic fields in Astronomy HBT‘56  product of single-detector currents cf conceptual quanta measurement  two-photon counts p1p1 p2p2 x1x1 x2x2 x3x3 x4x4 star detectors-antennas tuned to mean frequency    Correlation ~  cos  p  x 34    p  -1 |  x 34 | Space-time correlation measurement in Astronomy  source momentum picture  p  =   star angular radius  orthogonal to momentum correlation measurement in particle physics  source space-time picture  x  KP’75  no info on star R,τ

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

9. 9  S T  /  S T 2 -  S T  2  ½ Normalized to 1 at d=0 N e ~ 10 8 e/sec,  f ~ 10 13 Hz,  f F ~ 5-45 MHz Required T ~ (2  /N e ) 2 /  F ~ hours HBT measurement of the angular size of Sirius

10. 10  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: while Phillips, Kleiman, Davis’67: linewidth measurement froma 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 width Fetter’65 Glauber’65

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

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

13. 13 “General” parameterization at |q|  0 Particles on mass shell & azimuthal symmetry  5 variables: q = {q x, q y, q z }  {q out, q side, q long }, pair velocity v = {v x,0,v z } R x 2 =½  (  x-v x  t) 2 , R y 2 =½  (  y) 2 , R z 2 =½  (  z-v z  t) 2  q 0 = qp/p 0  qv = q x v x + q z v z y  side x  out  transverse pair velocity v t z  long  beam Podgoretsky’83 ; often called cartesian or BP’95 parameterization Interferometry or correlation radii:  cos q  x  =1-½  (q  x) 2  …  exp(-R x 2 q x 2 –R y 2 q y 2 -R z 2 q z 2 -R xz 2 q x q z ) Grassberger’77 RL’78

14. 14 Probing source shape and emission duration Static Gaussian model with space and time dispersions R  2, R || 2,  2 R x 2 = R  2 +v  2  2  R y 2 = R  2  R z 2 = R || 2 +v || 2  2 Emission duration  2 = (R x 2 - R y 2 )/v  2  (degree) R side 2 fm 2 If elliptic shape also in transverse plane  R y  R side oscillates with pair azimuth  R side (  =90°) small R side  =0°) large z A B Out-of reaction plane In reaction plane In-planeCircular Out-of plane KP (71-75) …

15. 15 Probing source dynamics - expansion Dispersion 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 source Resonances GKP’71.. Strings Bowler’85.. Hydro P t =160 MeV/cP t =380 MeV/c R out R side R out R side Collective transverse flow  F  R side  R/(1+m t  F2 /T) ½ Longitudinal boost invariant expansion during proper freeze-out (evolution) time   R long  (T/m t ) ½  /coshy Pratt, Csörgö, Zimanyi’90 Makhlin-Sinyukov’87 } 1 in LCMS ….. Bertch, Gong, Tohyama’88 Hama, Padula’88 Mayer, Schnedermann, Heinz’92 Pratt’84,86 Kolehmainen, Gyulassy’86

16. 16 AGS  SPS  RHIC:  radii STAR Au+Au at 200 AGeV0-5% central Pb+Pb or Au+Au Clear centrality dependenceWeak energy dependence

17. 17 AGS  SPS  RHIC:  radii vs p t R long : increases smoothly & points to short evolution time  ~ 8-10 fm/c R side, R out : change little & point to strong transverse flow  t ~ 0.4-0.6 & short emission duration  ~ 2 fm/c Central Au+Au or Pb+Pb

18. 18 Interferometry wrt reaction plane STAR data:  oscillations like for a static out-of-plane source stronger then Hydro & RQMD  Short evolution time Out-of-planeCircularIn-plane Time Typical hydro evolution STAR’04 Au+Au 200 GeV 20-30%     &    

19. 19 hadronization initial state pre-equilibrium QGP and hydrodynamic expansion hadronic phase and freeze-out Expected evolution of HI collision vs RHIC data dN/dt 1 fm/c5 fm/c10 fm/c50 fm/c time Kinetic freeze out Chemical freeze out RHIC side & out radii:   2 fm/c R long & radii vs reaction plane:   10 fm/c Bass’02

20. 20 Puzzle ? 3D Hydro 2+1D Hydro 1+1D Hydro+UrQMD (resonances ?) But comparing 1+1D H+UrQMD with 2+1D Hydro  kinetic evolution at small p t & increases R side ~ conserves R out,R long  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

21. Why ~ conservation of spectra & radii? qx i ’  qx i +q(p 1 +p 2 )T/(E 1 +E 2 ) = qx i Sinyukov, Akkelin, Hama’02 : free streaming also in real conditions and thus initial interferometry radii t i ’= t i +T, x i ’ = x i + v i T, v i  v =(p 1 +p 2 )/(E 1 +E 2 ) Based on the fact that the known analytical solution of nonrelativistic BE with spherically symmetric initial 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

22. 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   ~  ~ tens fm   =  = 0 in static model in kinetic model 1 2 3

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

24. BW fit of Au-Au 200 GeV T=106 ± 1 MeV = 0.571 ± 0.004 c = 0.540 ± 0.004 c R InPlane = 11.1 ± 0.2 fm R OutOfPlane = 12.1 ± 0.2 fm Life time (  ) = 8.4 ± 0.2 fm/c Emission duration = 1.9 ± 0.2 fm/c  2 /dof = 120 / 86 Retiere@LBL’05 R β z =z/  β x = β 0 (r/R)

25. 25 Other parametrizations Buda-Lund: Csanad, Csörgö, Lörstad’04 Similar to BW but T(x) &  (x) hot core ~200 MeV surrounded by cool ~100 MeV shell Describes spectra, radii, v 2 (  ) Krakow: Broniowski, Florkowski’01 Describes spectra, radii but R long Single freezeout model + Hubble-like flow + resonances Kiev-Nantes: Borysova, Sinyukov, Erazmus, Karpenko’05 closed freezeout hypersurface Generalizes BW using hydro motivated Additional surface emission introduces x-t correlation  helps to desribe R out at smaller flow velocity volume emission surface emission ? may account for initial  F Fit points to initial  0 F of ~ 0.3

26. 26 Final State Interaction Similar to Coulomb distortion of  -decay Fermi’34: e -ikr   -k ( r )  [ e -ikr +f( k )e ikr / r ] eicAceicAc F=1+ _______ + … kr+kr kaka Coulomb s-wave strong FSI FSI f c  A c  (G 0 +iF 0 ) } } Bohr radius } Point-like Coulomb factor k=|q|/2 CF nn pp Coulomb only  | 1+f/r| 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,.. &  Study relative space-time asymmetries delays, flow  Study “exotic” scattering ,  K, KK, , p , ,.. Coalescence deuterons,..  |  -k (r)| 2  Migdal, Watson, Sakharov, … Koonin, GKW,...

27. 27 FSI effect on CF of neutral kaons STAR data on CF(K s K s ) Goal: no Coulomb. But R may go up by ~1 fm if neglected FSI in = 0.9  0.2 R = 4.1  0.5 fm 5.3  0.6 fm KK (~50% K s K s )  f 0 (980) & a 0 (980) RL-Lyuboshitz’82 t Lyuboshitz-Podgoretsky’79: KsKs from KK also show BE enhancement

28. 28 NA49 central Pb+Pb 158 AGeV vs RQMD Long tails in RQMD:  r*  = 21 fm for r* < 50 fm 29 fm for r* < 500 fm Fit CF=Norm [ Purity RQMD(r*  Scale  r*)+1-Purity] Scale=0.76Scale=0.92 Scale=0.83  RQMD overestimates r* by 10-20% at SPS cf ~ OK at AGS worse at RHIC  p  

29. 29 p  CFs at AGS & SPS & STAR Fit using RL-Lyuboshitz’82 with consistent with estimated impurity R~ 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 =0.5  0.2 R=4.5  0.7 fm Scattering lengths, fm: 2.31 1.78 Effective radii, fm: 3.04 3.22 singlet triplet AGSSPS STAR R=3.1  0.3  0.2 fm

30. 30 m t scaling – transverse flow π, K, p, Λ radii show m t scaling expected in hydrodynamics ππ pΛpΛ pΛpΛ K s K s

31. Correlation study of particle interaction -  +   &  & p  scattering lengths f 0 from NA49 and STAR NA49 CF(  +   ) vs RQMD with SI scale: f 0  sisca f 0 (= 0.232fm ) sisca = 0.6  0.1 compare ~0.8 from S  PT & BNL data E765 K  e  Fits using RL-Lyuboshitz’82 NA49 CF(  ) data prefer | f 0 (  )|  f 0 (NN) ~ 20 fm STAR CF( p  ) data point to Re f 0 ( p  ) < Re f 0 ( pp )  0 Im f 0 ( p  ) ~ Im f 0 ( pp ) ~ 1 fm  pp

32. 32 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 * = r 1 * - r 2 * 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 /CF  x

33. 33 Simplified idea of CF asymmetry (valid for Coulomb FSI) x x v v v1v1 v2v2 v1v1 v2v2 k*/  = v 1 -v 2   p p k* x > 0 v  > v p k* x < 0 v  < v p Assume  emitted later than p or closer to the center p   p Longer t int Stronger CF  Shorter t int Weaker CF   CF  CF 

34. 34 CF-asymmetry for charged particles Asymmetry arises mainly from Coulomb FSI CF  A c (  )  |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 /CF  x  1+2  x*  /a k*  0  x* = x 1 *-x 2 *  r x *  Projection of the relative separation r* in pair cms on the direction x In LCMS ( v z =0) or x || v :  x* =  t (  x - v t  t)  CF asymmetry is determined by space and time asymmetries

35. 35 Usually:  x  and  t  comparable RQMD Pb+Pb   p +X central 158 AGeV :  x  = -5.2 fm  t  = 2.9 fm/c  x*  = -8.5 fm  + p-asymmetry effect 2  x*  /a  -8%  Shift  x  in out direction is due to collective transverse flow RL’99-01  x p  >  x K  >  x   > 0 & higher thermal velocity of lighter particles rtrt y x FF tTtT tt  FF = flow velocity tTtT = transverse thermal velocity tt =  F +  t T = observed transverse velocity  x   r x  =  r t cos   =  r t (  t 2 +  F2 -  t T2 )/(2  t  F )   y   r y  =  r t sin   = 0 mass dependence  z   r z    sinh  = 0 in LCMS & Bjorken long. exp. out side measures edge effect at y CMS  0

36. pion Kaon Proton BW Retiere@LBL’05 Distribution of emission points at a given equal velocity: - Left,  x = 0.73c,  y = 0 - Right,  x = 0.91c,  y = 0 Dash lines: average emission R x   R x (  )  <  R x (K)  <  R x (p)  p x = 0.15 GeV/c p x = 0.3 GeV/c p x = 0.53 GeV/cp x = 1.07 GeV/c p x = 1.01 GeV/cp x = 2.02 GeV/c For a Gaussian density profile with a radius R G and flow velocity profile  F (r) =  0 r/ R G RL’04, Akkelin-Sinyukov’96 :  x  = R G  x  0 /[  0 2 +T/m t ]

37. 37 Decreasing R(p t ): x-p correlation usually attributed to collective flow taken for granted femtoscopy the only way to confirm x-p correlations  x 2  -p correlation:yes  x  -p correlation:yes Non-flow possibility hot core surrounded by cool shell important ingredient of Buda-Lund hydro picture Csörgő & Lörstad’96  x 2  -p correlation:yes  x  -p correlation:no  x  = R G  x  0 /[  0 2 +T/m t +  T/T  r ] radial gradient of T  decreasing asymmetry ~1

38. NA49 & STAR out-asymmetries Pb+Pb central 158 AGeV not corrected for ~ 25% impurity r* RQMD scaled by 0.8 Au+Au central  s NN =130 GeV corrected for impurity  Mirror symmetry (~ same mechanism for  and  mesons)  RQMD, BW ~ OK  points to strong transverse flow pp pp KK (  t  yields ~ ¼ of CF asymmetry)

39. 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 ?+  F initial & 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. 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. 41 Kniege’05

42. 42 Coalescence: deuterons.. E d d 3 N/d 3 p d = B 2 E p d 3 N/d 3 p p E n d 3 N/d 3 p n p p  p n  ½p d WF in continuous pn spectrum  -k* (r*)  WF in discrete pn spectrum  b (r*) Coalescence factor: B 2 = (2  ) 3 (m p m n /m d ) -1  t  |  b (r*)| 2  ~ R -3 Triplet fraction = ¾  unpolarized Ns Usually: n  p Much stronger energy dependence of B 2 ~ R -3 than expected from pion and proton interferometry radii B2B2 R(pp) ~ 4 fm from AGS to SPS Lyuboshitz (88)..