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Correlation Femtoscopy – status & prospects

Correlation Femtoscopy – status & prospects. In memory of V.L.Lyuboshitz (19.3.1937-4.5.2013) R. Lednický @ JINR Dubna & IP ASCR Prague. History QS correlations FSI correlations Correlation study of particle interaction Correlation asymmetries Summary. History.

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Correlation Femtoscopy – status & prospects

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  1. Correlation Femtoscopy – status & prospects In memory of V.L.Lyuboshitz (19.3.1937-4.5.2013) R. Lednický@ JINR Dubna & IP ASCR Prague • History • QS correlations • FSI correlations • Correlation study of particle interaction • Correlation asymmetries • Summary NTHEP, Crimea, September 23-29, 2013I

  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) function F(k,Z,R) is sensitive to Nucleusradius R if charge Z » 1 of particle production using particle correlations

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

  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. Modern correlation femtoscopy formulated by Kopylov & Podgoretsky KP’71-75: settled basics of correlation femtoscopy in > 20 papers (for non-interacting identical particles)‏ • proposed CF= Ncorr /Nuncorr& mixing techniques to construct Nuncorr •showed that sufficientlysmooth momentum spectrum allows one to neglect space-time coherence at small q* |∫d4x1d4x2p1p2(x1,x2)...|2 →∫d4x1d4x2p1p2(x1,x2)|2... •clarified role of space-time characteristics in various models

  6. QS symmetrization of production amplitudemomentum correlations of identical particles 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 PRF q =p1- p2 → {0,2k*} x = x1 - x2 → {t*,r*} |q| 0 CF →|S-k*(r*)|2  =| [ e-ik*r* +(-1)S eik*r*]/√2 |2 

  7. 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

  8. 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

  9. “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 or correlation radii: Rx2 =½  (x-vxt)2 , Ry2 =½  (y)2 , Rz2 =½  (z-vzt)2  Podgoretsky’83, Bertsch, Pratt’95;so called out-side-long parameterization Csorgo, Pratt’91: LCMS vz = 0

  10. 3-dim fit: CF=1+exp(-Rx2qx2 –Ry2qy2-Rz2qz2-2Rxz2qxqz) Examples of NA49 & STAR data Correlation strength or chaoticity Interferometry or correlation radii STAR  KK NA49 Coulomb corrected z x y

  11. 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

  12. 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 Pt=160MeV/c Pt=380 MeV/c Makhlin-Sinyukov’87 Bertch, Gong, Tohyama’88 Hama, Padula’88 Rout Rside Pratt, Csörgö, Zimanyi’90 Rout Rside Mayer, Schnedermann, Heinz’92 ….. Collective transverse flow F RsideR/(1+mt F2/T)½ 1 in LCMS Longitudinal boost invariant expansion } Rlong(T/mt)½/coshy during proper freeze-out (evolution) time 

  13. BW: Retiere@LBL’05 pion 0.73c 0.91c , , Flow & Radiiin Blast Wave model ← Emission points at a given tr. velocity px = 0.15 GeV/c 0.3 GeV/c Rz2 2 (T/mt) Ry2 = y’2 Rx2= x’2-2vxx’t’+vx2t’2 Kaon t’2  (-)2  ()2 For a Gaussian density profile with a radius RG and linear flow velocity profile F (r) = 0r/ RG: px = 0.53 GeV/c 1.07 GeV/c Ry2 = RG2 / [1+ 02 mt /T] Proton x = RG bx0/[02+T/mt] px = 1.01 GeV/c 2.02 GeV/c  x(p) < x(K) < x(p) Rz  = evolution time Rx  = emission duration Rx , Ry 0 = tr. flow velocity pt–spectra  T = temperature

  14. 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 βx≈β0(r/R) βz≈ z/τ

  15. Femto-puzzle I Contradiction with transport and simple hydro calcul. • - small space-time scales • - their weak energy dep. • - Rout/Rside ~ 1 • Basicallysolveddue to the initial flow increasing with energy (likely related to the increase of the initial energy density and partonic energy fraction)

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

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

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

  19. Femto-puzzle II No signal of a bump in Rout near the QGP threshold (expected at AGS-SPS energies) !? likely solved due to a dramatic decrease of partonic phase with decreasing energy

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

  21. Dense matter (collective flows) also in pp collisions at LHC (for high Nch) ? - pt increases with nch and particle mass - BE CF vs nch and pt points to expansion at high nch - Ridge effect observed in angular correlations at high nch CMS Ridge effect R(kt)  at large Nch  expansion

  22. |-k(r)|2 Similar to Coulomb distortion of -decay Fermi’34: Final State Interaction Migdal, Watson, Sakharov, … Koonin, GKW, LL, ... 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

  23. Assumptions to derive “Fermi-like” 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 OK(usually, to several % even for pions) fig. - tFSI = dd/dE >tprod tFSI (s-wave) = µf0/k*  |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, ...

  24. Effect of nonequal times in pair cms → RL, Lyuboshitz SJNP 35 (82) 770; RL nucl-th/0501065 Applicability condition of equal-time approximation: |t*| m1,2r*2 r0=2 fm 0=2 fm/c r0=2 fm v=0.1 |k*t*| m1,2r*  OK for heavy particles & small k* OK within 5% even for pions if 0 ~r0 or lower

  25. Resonance contribution to CF vs r-k correl. b WP(r,k) ~ exp[-r2/4r02 + bkrcos];  = angle between r and k CF suppressed by a factor WP(0,k) ~ exp[-b2r02k2] 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=126 MeV/c), r0=5 fm *(k=146 MeV/c), r0=5 fm ----------- Rpeak(NA49) ----------  0.10 0.14 Smoothness assumption: WP(r,½(k-kn))  WP(r,-kn)  WP(r,k) Rpeak(STAR) -----------  0.025 Exact  

  26. 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 or Achasov l = 1.09  0.22 R = 4.66 0.46 fm 5.86  0.67 fm no FSI Martin’77 Achasov’01,03 t R↓ Mt  Universal expansion !

  27. Long tails in RQMD: r* = 21 fm for r* < 50 fm NA49 central Pb+Pb 158 AGeV vs RQMD: FSI theory OK 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

  28. 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 & mt scaling STAR AGS SPS =0.50.2 R=4.50.7 fm R=3.10.30.2 fm

  29. Pair purity problem for CF(p)@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. 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 But R(p) < R(p) ? Residual correlations  - 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

  31. scattering lengths f0 from NA49 correlation data Correlation study of particle interaction Fit using RL-Lyuboshitz (82) with fixed PairPurity =0.16 from feed-down and PID Data prefer|f0| «f0(NN) ~ 20 fm  - - CF=1+[CFFSI+SS(-1)Sexp(-r02Q2)] 0= ¼(1-P2) 1= ¼(3+P2) P=Polariz.=0 CFFSI = 20[½|f0(k)/r0|2(1-d00/(2r0)) +2Re(f0(k)/(r0))F1(r0Q) - 2Im(f0(k)/r0)F2(r0Q)] fS(k)=(1/f0S+½d0Sk2 - ik)-1 k=Q/2 F1(z)=0z dx exp(x2-z2)/z F2(z)=[1-exp(-z2)]/z - 

  32. N  r0 fm B f00 fm d00 fm CF=N{1+[CFFSI -½exp(-r02Q2)]}

  33. 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

  34. 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

  35. 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

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

  37. 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

  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. 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 ? problem ~1

  40. 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 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 • LHC femtoscopic data vs nch and mt point to a universal fireball freeze-out density settled at RHIC energies and indicate collective expansion in high-multiplicity pp-collisions • Absence of femtoscopic signals of QGP 1-st order PT (onset and CEP) at √sNN < 10 GeV is likely due to a dramatic decrease of partonic phase with decreasing energy  dedicated high statistics, precise experiments (like planned at NICA and FAIR) are required • 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).

  41. Clear centrality & mt dependence AGSSPSRHIC: radii Weak energy dependence STAR Au+Au at 200 AGeV 0-5% central Pb+Pb or Au+Au R ↑ with centrality &  with mt only Rlong slightly ↑ with energy Rside R/(1+mt F2/T)½  tr. collective flow velocity F Rlong (T/mt)½  Evolution (freeze-out) time

  42. 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

  43. Even stronger effect of KK-bar FSI on KsKs correlations in pp-collisions at LHC ALICE: PLB 717 (2012) 151 e.g. for kt < 0.85 GeV/c, Nch=1-11 the neglect of FSI increases  by ~100% and Rinv by ~40%  = 0.64  0.07  1.36  0.15 > 1 ! Rinv= 0.96  0.04  1.35  0.07 fm

  44. Correlation study of particle interaction CF=Norm[Purity RQMD(r* Scaler*)+1-Purity] +scattering length f0 from NA49 CF + Fit CF(+) by RQMD with SI scale: f0siscaf0input f0input = 0.232 fm - sisca = 0.60.1 Compare with ~0.8 from SPT & BNL E765 K  e

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

  46. 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

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