1. 5.11.2013WPCF Catania, November 5-8, 20131 Femtoscopic aspects of FSI, resonances and bound states In memory of V.L.Lyuboshitz (19.3.1937-4.5.2013) R. Lednický @ JINR Dubna & IP ASCR Prague History QS correlations FSI correlations Coalescence Femtoscopy Correlation study of strong interaction Correlation asymmetries Summary Femtoscopy on marsh in Nantes’94 RL VLL MIP

2. 2 History Fermi’34: e ± Nucleus Coulomb FSI in β-decay modifies the relative momentum (k) distribution → Fermi (correlation) function 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 function(k,Z,R) in β-decay =  |  -k (r)| 2  ~ (kR) -(Z/137) 2 Z=83 (Bi) β-β- β+β+ R=8 4 2 fm k MeV/c

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 Modern correlation femtoscopy formulated by Kopylov & Podgoretsky KP’71-75: settled basics of correlation femtoscopy in > 20 papers proposed CF= N corr /N uncorr & showed that sufficiently smooth momentum spectrum allows one to neglect space-time coherence at small q* (for non-interacting identical particles)‏ mixing techniques to construct N uncorr clarified role of space-time characteristics in various models |∫ d 4 x 1 d 4 x 2  p 1 p 2 ( x 1,x 2 )... | 2 → ∫ d 4 x 1 d 4 x 2  p 1 p 2 ( x 1,x 2 )| 2...

6. 6 QS symmetrization of production amplitude  momentum correlations of identical particles 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 → {0,2k*}  x = x 1 - x 2 → {t*,r*} 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 ) CF →  |  S -k* ( r* )| 2  =  | [ e -ik*r* +(-1) S e ik*r* ]/√2 | 2  PRF

7. 7 Assumptions to derive KP formula CF - 1   cos q  x  - two-particle approximation (small freeze-out PS density f ) - smoothness approximation: R emitter  R source   |  p|    |q|  peak - incoherent or independent emission ~ OK,  1 ? low p t ~ OK in HIC, R source 2  0.1 fm 2  p t 2 -slope of direct particles 2  and 3  CF data approx. consistent with KP formulae: CF 3 (123) = 1+|F(12)| 2 +|F(23)| 2 +|F(31)| 2 +2Re[F(12)F(23)F(31)] CF 2 (12) = 1+|F(12)| 2, F(q)| =  e iqx  - neglect of FSI OK for photons, ~ OK for pions up to Coulomb repulsion

8. Resonances as emitters most of the produced pions come from resonance decays  symmetrization accounting for resonance propagator (M 2 -k r 2 -iM  ) -1 yields (in the limit  << M ) CF - 1 = Re  exp(-iq  x)/(1+iy)   1-½  [q(  x+l)] 2 +(q l) 2 ] , y=(k r q)/M  (q l) i.e. the width of BE enhancement is determined by the source size enhanced by the resonance decay length l = k r /M   -meson as a typical resonance  decay length in PRF l*~3.3 fm in contrast with correlation radii ~1 fm measured from q inv CFs in  p, pp or e + e - collisions explained by a rapid decrease of the slope of the resonance factor 1/(1+y 2 ) with increasing q 8 Grishin, Kopylov, Podgoretsky’71, Grassberger’77, RL’78, RL,Progulova’92

9. Resonances as emitters Note: the narrow resonance limit  resonance as a classical emitter with exponential decay law ~ exp(-  t) (used in transport codes) However, at q inv > 0.1 GeV it may lead to a substantial overestimation of the resonance correlation factor (by ~ 15% for  ) 9 It may be important for the interpretation of CF data from elementary particle collisions, though much less important for HIC (due to substantial fireball size) classical approx. M eff (  -  0 p)  -  0 +X  -  0 +X

10. “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, Bertsch, Pratt’95; so called out-side-long 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 -2R xz 2 q x q z ) Grassberger’77 RL’78 Csorgo, Pratt’91: LCMS v z = 0

11. 11 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) …

12. 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 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 Longitudinal boost invariant expansion

13. pion Kaon Proton , , Flow & Radii in Blast Wave model ← Emission points at a given tr. velocity p x = 0.15 GeV/c0.3 GeV/c p x = 0.53 GeV/c1.07 GeV/c p x = 1.01 GeV/c2.02 GeV/c For a Gaussian density profile with a radius R G and linear flow velocity profile  F (r) =  0 r/ R G : 0.73c0.91c R z 2   2  (T/m t ) R x 2 =  x’ 2  -2v x  x’t’  +v x 2  t’ 2  R z   = evolution time R x   = emission duration R y 2 =  y’ 2  R y 2 = R G 2 / [1+  0 2 m t /T] R x, R y   0 = tr. flow velocity p t –spectra  T = temperature  t’ 2    (  -  ) 2   (  ) 2 BW: Retiere@LBL’05  x  = R G  x  0 /[  0 2 +T/m t ]  hierarchy  x(  )  <  x(K)  <  x(p) 

14. 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/τ β x ≈ β 0 (r/R)

15. 15 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, LL,...

16. Assumptions to derive “Fermi-like” formula CF =  |  -k* (r*)| 2  t FSI (s-wave) = µf 0 /k*  |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 (usually, to several % even for pions) fig. RL, Lyuboshitz..’98 same isomultiplet only:  +     0  0,  - p   0 n, K + K   K 0 K 0,... & account for coupled channels within the - t FSI  d  dE >  t prod

17.  ∫d 3 r {W P (r,k) + W P (r,-kn) |  -k (r)| 2 + 2[W P (r,k)W P (r,-kn)] 1/2 Re[exp(ikr)  -k (r)]} where  -k (r) = exp(-ikr)+  -k (r) and n = r/r The usual moothness approximation: W P (r,-kn)  W P (r,k) is valid if one can neglect the k-dependence of W P (r,k), e.g. for k << 1/r 0 Caution: Smoothness approximation is justified for small k << 1/r 0 It should be generalized in the region k > ~100 MeV/c CF(p 1,p 2 )  ∫d 3 r W P (r,k) |  -k (r)| 2

18. 18 Effect of nonequal times in pair cms RL, Lyuboshitz SJNP 35 (82) 770; RL nucl-th/0501065 Applicability condition of equal-time approximation: |t * |  m 1,2 r *2 r 0 =2 fm  0 =2 fm/c r 0 =2 fm v=0.1  OK for heavy particles & small k*  OK within 5% even for pions if  0 ~r 0 or lower → |k * t * |  m 1,2 r *

19. Using spherical wave in the outer region (r>  ) & inner region (r<  ) correction  analytical dependence on scatt. amplitudes f L and source radius r 0 LL’81 19 Inner region: W(r)  W(0) & integral relation (single channel and no Coulomb) with the phase shifts  L and momentum derivative  L : ∫d 3 r[|  -k (r)| 2 -1]= (2  /k 3 )  L (2L+1){k  L -½[sin2(k  +  L )-sin2(k  )]+..}  FSI contribution to the CF of nonidentical particles, assuming Gaussian source function W(r)=exp(-r 2 /4r 0 2 )/(2  r 0 ) : for kr 0 << 1:  CF FSI = ½|f 0 /r 0 | 2 [1-d 0 /(2r 0  )]+2f 0 /(r 0  ) ~ r 0 -1 or r 0 -2 f 0 and d 0 are the s-wave scatt. length and eff. radius entering in the (L=0) amplitude f L (k) = sin  L exp(i  L )/k  (1/f L +½d L k 2 - ik) -1 for kr 0 >> 1:  CF FSI = (2  /k 2 )W(0)  L (2L+1)  L ~ r 0 -3  L =[(2L+1)/2k]sin(2  L ) - (d L /k 2L )sin 2  L

20. L-wave saturated by a resonance:  L =  /2, d L = 2k 2L+1 (  ) -1   L (k=k 0 ) = 2k 0 (  ) -1 20  for kr 0 >> 1:  CF r,L (k=k 0 )= 4  W(0)(2L+1) (  k 0 ) -1 & resonance yield in the narrow width limit  L (k) =   (k-k 0 )  r d 3 N r,L /d 3 p r = (2  ) 3 W(0)(2L+1)(  1  2 /  1 *  2 * )d 6 N 0 /(d 3 p 1 d 3 p 2 )  a problem with π +  -   * no room for direct production ! See also the talk by Petr Chaloupka on Wednesday Likely due to violation of eq. time approx. for a part of the coalescence contribution (|k * t * |  m 1,2 r * is valid for m 2 =m  only)

21. Resonance contribution to CF vs r-k correl. b  R peak (STAR) -----------  0.025  R peak (NA49) ----------  0.10  0.14  Smoothness assumption: W P (r,-kn)  W P (r,k) Exact W P (r,k) ~ exp[-r 2 /4r 0 2 + bkrcos  ];  = angle between r and k CF suppressed by a factor W P (0,k) ~ exp[-b 2 r 0 2 k 2 ] To leave a room for a direct production  b > 0.3 is required for π +  - system; however, BW  b ~ 0.2;  likely eq.-time approx. not valid for π +  - at k*~ 150 MeV/c  * (k=146 MeV/c), r 0 =5 fm  (k=126 MeV/c), r 0 =5 fm -----------

22. r-k correl. b  0.2 for K + K - CF indicates ~ ½ direct  -meson yield – in qualitative agreement with the difference between the measured rapidity width in central Pb+Pb collisions at SPS and expected from coalescence:   -2 =  K + -2 +  K - -2  -- K+K+ anti-    p+p K-K-  K + K - coalescence

23. 23 Bound state production Migdal, Watson, Sakharov,.. hadronic processes  Dominated by FSI provided a small binding energy  b  Closely related to production of free particles at k *  0 FSI theory: Fermi  -decay  Continuum : d 6 N/(d 3 p 1 d 3 p 2 )= d 6 N 0 /(d 3 p 1 d3p2)  |  -k* (r * )| 2  d 3 N/d 3 p b = (2  ) 3  b d 6 N 0 /(d 3 p 1 d 3 p 2 )  |  b (r * )| 2   Discrete spectrum: + x1x1 x2x2 x2x2 x1x1 p1p1 p2p2 p1p1 p2p2 pbpb r * = x 1 * - x 2 * = distance between particle emitters in pair cms p 1 /m 1 ≈ p 2 /m 2  p b /m b Basis of bound state coalescence femtoscopy

24. Universal relation between production of free and bound  ’s is used to determine pionium lifetime in DIRAC exp. at CERN : Assume only two types of pion sources Nemenov ‘85 Short-Lived Emitters SLE ( , ,..) r *  |a| = 387 fm both  ’s from SLE Long-Lived Emitters LLE ( , K s, ,..) r *  |a| one or both  ’s from LLE  Then, neglecting strong FSI  |  -k* (r * )| 2  = |  c -k* (0)| 2 + (1- ) |  c -k* (  )| 2  |  A (r * )| 2  = |  c A (0)| 2 + (1- ) |  c A (  )| 2 1A c (Q) 0 1/(  |na| 3 ) A={n,L=0}  d 6 N/(d 3 p 1 d 3 p 2 )= d 6 N 0 /(d 3 p 1 d 3 p 2 ) [ A c (Q) + (1- )]  d 3 N/d 3 p A = d 6 N 0 /(d 3 p 1 d 3 p 2 ) (2  ) 3  A /(  |na| 3 ), p 1 ≈ p 2 ≈ ½p A = SLE pair fraction

25. 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 Here is realized the opposite limit compared with r * <<|a| for  +  - atom: r * > deuteron radius =  -1 = (2  b ) -1/2   |  b (r * )| 2   W(0) ~ r 0 -3 Coalescence factor: B 2 = (2  ) 3 (m p m n /m d ) -1  t  |  b (r * )| 2  ~ r 0 -3 Triplet fraction = ¾  unpolarized Ns Assuming Gaussian r* distribution and accounting for a boost from LCMS to PRF: B 2  3  3/2 /(2m pt r 0 3 ) r 0 (pp) ~ 4 fm from AGS to RHIC Lyuboshitz’88.. B 2 d,d-bar at pt=1.3 GeV/c in central HICs d d-bar PHENIX B 2 at RHIC energies  with  p t and  centrality in agreement with B 2 ~ R -3 +fragmentation ? coalescence

26. Is there double counting in thermal model with FSI ? Global thermal equilibrium in nonrelativistic limit; T,  i > 1 and simultaneous emission: Jennings, Boal, Shillcock’86 the L-wave resonance contribution due to FSI of spin-0 particles d 3 N r,L /(d 3 p r ) = (2  ) 3 V -1 (2L+1)d 3 N 1 /d 3 p 1 d 3 N 2 d 3 p 2 = Vg r,L (2  ) -3 exp[-(E r -  r )/T] g r.L =2L+1,  r =  1 +  2, E r =E 1 +E 2  resonances due to FSI are also in thermal equilibrium in this limit Similarly, in the limit  V 1/3 >> 1 and simultaneous emission: d 3 N b /d 3 p b = (2  ) 3 V -1 d 3 N 1 /d 3 p 1 d 3 N 2 d 3 p 2 = V(2  ) -3 exp[-(E b -  b )/T] i.e., the (s-wave) coalescence bound state is also in thermal equilibrium

27. Is there double counting in thermal model with FSI ? No double counting with respect to direct thermal production since the latter is characterized by local thermal equilibrium (not reproduced by the coalescence states – as revealed e.g. by  -meson rapidity width)  besides the coalescence FSI contribution, one may expect essential direct contribution of resonances (with sufficiently long lifetime) and bound states (with sufficiently large binding energy)

28. 28 Correlation femtoscopy with nonid. particles p  CFs at AGS & SPS & STAR Fit using RL-Lyuboshitz’82 with consistent with estimated impurity r 0 ~ 3-4 fm consistent with the radius from pp CF & m t scaling Goal: No Coulomb suppression as in pp CF & Wang-Pratt’99 Stronger sensitivity to r 0 =0.5  0.2 r 0 =4.5  0.7 fm Scattering lengths, fm: 2.31 1.78 Effective radii, fm: 3.04 3.22 singlet triplet AGSSPS STAR r 0 =3.1  0.3  0.2 fm

29. Pair purity problem for p  CF @ STAR  PairPurity ~ 15% Assuming no correlation for misidentified particles and particles from weak decays   Fit using RL-Lyuboshitz’82 (for np)  but, there can be residual correlations for particles from weak decays requiring knowledge of , p , , , p , ,  correlations

30. 30 Correlation study of strong 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 But r 0 ( p  ) < r 0 ( p  ) ? Residual correlations  pp

31. Correlation study of strong interaction - -  scattering lengths f 0 from NA49 correlation data Fit using RL-Lyuboshitz (82) with fixed Pair Purity =0.16 from feed-down and PID Data prefer |f 0 | « f 0 (NN) ~ 20 fm  -  CF=1+ [  CF FSI +  S  S (-1) S exp(-r 0 2 Q 2 )]  0 = ¼(1-P 2 )  1 = ¼(3+P 2 ) P=Polar.=0  CF FSI = 2  0 [½|f 0 (k)/r 0 | 2 (1-d 0 0 /(2r 0  )) +2Re(f 0 (k)/(r 0  ))F 1 (r 0 Q) - 2Im(f 0 (k)/r 0 )F 2 (r 0 Q)] f S (k)=(1/f 0 S +½d 0 S k 2 - ik) -1 k=Q/2 F 1 (z)=  0 z dx exp(x 2 -z 2 )/z F 2 (z)=[1-exp(-z 2 )]/z

32. CF=N{1+ [  CF FSI -½exp(-r 0 2 Q 2 )]} N r0r0 f00f00 d00d00 fm B

33. 33 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

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. 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)

37. 37 Summary Assumptions behind femtoscopy theory in HIC seem OK at k  0. At k > ~ 100 MeV/c, the usual smoothness and equal-time approximations may not be valid. Wealth of data on correlations of various particles (  ,K  0,p , ,  ), yields of resonances and bound states 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 Info on two-particle strong interaction:  &  & p  scattering lengths from HIC at SPS and RHIC. Good perspective at RHIC & LHC (a problem of residual correlations is to be solved).

38. 38 Phase space density from CFs and spectra Bertsch’94 May be high phase space density at low p t ?  ? Pion condensate or laser ? Multiboson effects on CFs spectra & multiplicities rises up to SPS Lisa..’05

39. 39 Examples of NA49 & STAR data 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 ) zxy Correlation strength (purity, chaoticity,..) NA49 Interferometry or correlation radii KK STAR  Coulomb corrected

40. AGS  SPS  RHIC:  radii STAR Au+Au at 200 AGeV0-5% central Pb+Pb or Au+Au Clear centrality & m t dependence Weak energy dependence R ↑ with centrality &  with m t only R long slightly ↑ with energy  R side  R/(1+m t  F2 /T) ½ R long   (T/m t ) ½  tr. collective flow velocity  F  Evolution (freeze-out) time 

41. 41 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

42. Femto-puzzle I Contradiction with transport and simple hydro calcul. - small space-time scales - their weak energy dep. - R out /R side ~ 1 Basically solved due to the initial flow increasing with energy (likely related to the increase of the initial energy density and partonic energy fraction)

43. 43 Femtoscopy Puzzle I basically solved due to initial flow appearing in realistic IC

44. Femtoscopic signature of QGP onset 3D 1-fluid Hydrodynamics Rischke & Gyulassy, NPA 608, 479 (1996) With 1 st order Phase transition Initial energy density  0 Long-standing signature of QGP onset: increase in , R OUT /R SIDE due to the Phase transition hoped-for “turn on” as QGP threshold in  0 is reached  decreases with decreasing Latent heat & increasing tr. Flow (high  0 or initial tr. Flow)

45. Femto-puzzle II No signal of a bump in R out near the QGP threshold (expected at AGS- SPS energies) !? likely solved due to a dramatic decrease of partonic phase with decreasing energy e.g. in PHSD, Cassing, Bratkovkaya

46. 46 Cassing – Bratkovskaya: Parton-Hadron-String-Dynamics Perspectives at FAIR/NICA energies

47. Femtoscopy of Pb+Pb at LHC ALICE arXiv:1012.4035 All radii increase with N ch from RHIC to LHC (not from SPS to RHIC)! Multiplicity scaling of the correlation volume  universal freeze-out density Freezeout time  f from R long =  f (T/m t ) 1/2 The LHC fireball: - hotter - lives longer & - expands to a larger size

48. Ridge effect Dense matter (collective flows) also in pp collisions at LHC (for high N ch ) ? -  p t  increases with n ch and particle mass - BE CF vs n ch and p t points to expansion at high n ch - Ridge effect observed in angular correlations at high n ch R(k t )  at large N ch  expansion CMS

49. Caution: the strong FSI is enhanced by a logarithmic singularity for particles from resonance decays & a small source size LL’96 e.g. noticeable strong FSI effect even on CF of identical charged pions:  CF FSI ~ 2f 0 /l r *  2ln|B| f 0 /l r * For example, if res =  -meson:      0  0  +  -  CF FSI (k=0) -0.10 0.25 0.30

50. 50 Even stronger effect of KK-bar FSI on K s K s correlations in pp-collisions at LHC ALICE: PLB 717 (2012) 151 e.g. for k t < 0.85 GeV/c, N ch =1-11 the neglect of FSI increases by ~100% and R inv by ~40% = 0.64  0.07  1.36  0.15 > 1 ! R inv = 0.96  0.04  1.35  0.07 fm

51. Resonance FSI contributions to π +  -  K + K - CF’s Complete, inner and outer contributions of p-wave resonance (  *) FSI to π +  - CF for two cut parameters 0.4 and 0.8 fm and Gaussian radius of 5 fm  FSI contribution overestimates measured  * by a factor 4 (3) for r 0 = 5 (5.5) fm  factor 3 (2) if accounting for  out  -6 fm The same for p-wave resonance (  ) FSI contributions to K + K - CF  FSI contribution overestimates measured  by 20% for r 0 = 4.5 fm Little or no room for direct production when neglecting r-k correlation!  R peak (NA49)  0.10  0.14 after purity correction  R peak (STAR)  0.025 ----------- ---- - --------------------- r 0 = 5 fm no r-k correlation

52. References related to resonance formation in final state: R. Lednicky, V.L. Lyuboshitz, SJNP 35 (1982) 770 R. Lednicky, V.L. Lyuboshitz, V.V. Lyuboshitz, Phys.At.Nucl. 61 (1998) 2050 S. Pratt, S. Petriconi, PRC 68 (2003) 054901 S. Petriconi, PhD Thesis, MSU, 2003 S. Bekele, R. Lednicky, Braz.J.Phys. 37 (2007) 994 B. Kerbikov, R. Lednicky, L.V. Malinina, P. Chaloupka, M. Sumbera, arXiv:0907.061v2 B. Kerbikov, L.V. Malinina, PRC 81 (2010) 034901 R. Lednicky, Phys. Part. Nucl. Lett. 8 (2011) 965 R. Lednicky, P. Chaloupka, M. Sumbera, in preparation

53. 53  Discrete spectrum: A 2   n0 (r * ) =  c n0 (0) [1- r * /|a|+f(0)/r * + O(f(0)/a) + O(r *2 /a 2 )]  n0 (r * )  exp(-r * /|na|)  0 at r * >> |na|  -k* (r * )   A c [1 - r * (1+cos  * )/|a| + f(0)/r * + O(f(0)/a) + O(r *2 /a 2 )]  p-wave |  -k* (r * )|  1 at r * >> |a| k *  0  Continuum:  +  - Universal dependence of the WF on r * and scattering amplitude f RL’04 in continuum (at k *  0) and discrete spectrum at a given orbital angular momentum and r * <<  -1  =(2  b ) 1/2 = virtual momentum (k * =i  ),  b (r * )  exp(-  r * ) at r * >  -1 Particularly, for  +  - atom with the main q.n. n:  n =|na| -1, |a|=387 fm

54. 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 = 1.09  0.22 r 0 = 4.66  0.46 fm 5.86  0.67 fm KK (~50% K s K s )  f 0 (980) & a 0 (980) RL-Lyuboshitz’82 couplings from Martin or Achasov t Achasov’01,03 Martin’77 no FSI Lyuboshitz-Podgoretsky’79: K s K s from KK also show BE enhancement r 0 ↓ M t  Universal expansion !

55. 55 NA49 central Pb+Pb 158 AGeV vs RQMD: FSI theory OK 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  

56. 56 Correlation study of particle interaction -  +   scattering length f 0 from NA49 CF Fit CF(  +   ) by RQMD with SI scale: f 0  sisca f 0 input f 0 input = 0.232 fm sisca = 0.6  0.1 Compare with ~0.8 from S  PT & BNL E765 K  e  ++ CF=Norm [ Purity RQMD(r*  Scale  r*)+1-Purity]

57. 57 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 

58. 58 ad hoc time shift  t = –10 fm/c CF + /CF  Sensitivity test for ALICE a, fm   84  226  249 CF + /CF   1+2  x*  /a k*  0 Here  x*  = -  v  t   CF-asymmetry scales as -  t  /a Erazmus et al.’95 Delays of several fm/c can be easily detected

59. 59 Large lifetimes evaporation or phase transition x || v |  x|  |  t|  CF-asymmetry yields time delay Ghisalberti’95 GANIL Pb+Nb  p+d+X CF + (pd) CF  (pd) CF + /CF  < 1 Deuterons earlier than protons in agreement with coalescence e -t p /  e -t n /   e -t d /(  /2) since t p  t n  t d Two-phase thermodynamic model CF + /CF  < 1 123 1 2 3 Strangeness distillation : K  earlier than K  in baryon rich QGP Ardouin et al.’99

60. 60 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 ? problem