Femtoscopic search for the 1-st order PT

1. Femtoscopic search for the 1-st order PT • Femtoscopic signature of QGP 1-st order PT • Solving Femtoscopy Puzzle II • Searching for large scales • Conclusions Richard Lednický Physics@NICA’09

2. Rischke & Gyulassy, NPA 608, 479 (1996) With 1st order Phase transition Femtoscopic signature of QGP 3D 1-fluid Hydrodynamics Initial energy density 0 • Long-standing signature of QGP: • 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)

3. Femto-puzzle II No signal of a bump in Rout near the QGP threshold expected at AGS-SPS energies !

4. Cassing – Bratkovskaya: Parton-Hadron-String-Dynamics Perspectives at FAIR/NICA energies  Solving Femtoscopy Puzzle II

5. r Radii vs fraction of the large scale r1 Input: 1, 2=1-1, r1=15, r2=5 fm 1-G Fit: r ,  2-G Fit: 1, 2, r1,r2 r2  2 1 1 1 Typical stat. errors in 1-G (3d) fit  (r1)/0.06 fm e.g., NA49 central Pb+Pb 158 AGeV Y=0-05, pt=0.25 GeV/c Rout=5.29±.08±.42 Rside=4.66±.06±.14 Rlong=5.19±.08±.24 =0.52±.01±.09  (1)/0.01 1

6. Imaging

7. Conclusions • Femtoscopic Puzzle I – Small time scales at SPS-RHIC energies – basically solved due to initial acceleration • Femtoscopic Puzzle II – No clear signal of a bump in Rout near the QGP threshold expected at AGS-SPS energies – basically solved due to a dramatic decrease of partonic phase with decreasing energy • Femtoscopic search for the effects of QGP threshold and CP can be successful only in dedicated high statistics and precise experiments allowing for a multidimensional multiparameter or imaging correlation analysis

8. This year we have celebrated 90th Anniversary of the birth of one of the Femtoscopyfathers M.I. Podgoretsky (22.04.1919-19.04.1995)

9. Spare Slides

10. Introduction to Femtoscopy 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

11. 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

12. 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 of γγmomentum correlations (BE enhancement) & differences (orthogonality) Grishin, KP’71 & KP’75 with space-time correlations (HBT effect) in Astronomy HBT’56 intensity-correlation spectroscopy Goldberger,Lewis,Watson’63-66

13. 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 

14. “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;often called cartesian or BP’95 parameterization Csorgo, Pratt’91: LCMS vz = 0

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

16. 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

17. Hydro assuming ideal fluid explains strong collective () flows at RHIC but not the interferometryresults 2005 Femtoscopy Puzzle I 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

18. Early Acceleration & FemtoscopyPuzzle I Scott Pratt

21. Lattice says: crossover at µ = 0 but CP location is not clear CP: T ~ 170 MeV, μB > 200 MeV

22. Cassing – Bratkovskaya:

23. Imaging is based on

25. Conclusions from Imaging  