Richard Lednický 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

Femtoscopic signature of QGP 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: 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)

3 Femto-puzzle II No signal of a bump in R out 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 Input: 1, 2 =1- 1, r 1 =15, r 2 =5 fm 1-G Fit: r, 1 2-G Fit: 1, 2, r 1,r 2 r1r1 r2r  (r 1 )/0.06 fm  ( 1 )/0.01 Typical stat. errors 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 in 1-G (3d) fit Radii vs fraction of the large scale

6 Imaging

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 R out 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 7

8 This year we have celebrated 90 th Anniversary of the birth of one of the Femtoscopy fathers M.I. Podgoretsky ( )

Spare Slides 9

10 Introduction to Femtoscopy 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

11 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

12 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 of γγ momentum correlations (BE enhancement) with space-time correlations (HBT effect) in Astronomy HBT’56 & differences (orthogonality) Grishin, KP’71 & KP’75 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 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 |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

“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 -2R xz 2 q x q z ) Grassberger’77 RL’78 Csorgo, Pratt’91: LCMS v z = 0

pion Kaon Proton , , Flow & Radii ← 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:

BW fit of Au-Au 200 GeV T=106 ± 1 MeV = ± c = ± 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 R β z ≈ z/τ β x ≈ β 0 (r/R)

Femtoscopy Puzzle I 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

18 Early Acceleration & Femtoscopy Puzzle I Scott Pratt

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

22 Cassing – Bratkovskaya:

23 Imaging is based on

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25   Conclusions from Imaging