10.09.2009 Richard Lednický Physics@NICA’09 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

Femtoscopic signature of QGP3D 1-fluid Hydrodynamics

Rischke & Gyulassy, NPA 608, 479 (1996)

With 1st order

Phase transition

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 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 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

Input: 1, 2=1-1, r1=15, r2=5 fm

1-G Fit: r ,

1

2-G Fit: 1, 2, r1,r2

r1

r2

21 1

1

(r1)/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 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

7

8

This year we have celebrated 90th Anniversary

of the birth of one of the Femtoscopy fathers

M.I. Podgoretsky (22.04.1919-19.04.1995)

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

2xGoldhaber, Lee & PaisGGLP’60: enhanced ++ , -- vs +- at small

opening angles – interpreted as BE enhancement

depending on fireball radius R0

R0 = 0.75 fm

p p 2+ 2 - n0

12

Kopylov & Podgoretsky

KP’71-75: settled basics of correlation femtoscopyin > 20 papers

• proposed CF= Ncorr /Nuncorr & mixing techniques to construct Nuncorr

• 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)Scos qx

p1

p2

x1

x2

q = p1- p2 → {0,2k*} x = x1 - x2 → {t*,r*}

nnt , t

, nns , s

2

1

0 |q|

1/R0

total pair spin

2R0

KP’71-75

exp(-ip1x1)

CF → |S-k*(r*)|2 = | [ e-ik*r* +(-1)S eik*r*]/√2 |2

PRF

“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}

Rx2 =½ (x-vxt)2 , Ry

2 =½ (y)2 , Rz2 =½ (z-vzt)2

q0 = qp/p0 qv = qxvx+ qzvz

y side

x out transverse pair velocity vt

z long beam

Podgoretsky’83; often called cartesian or BP’95 parameterization

Interferometry or correlation radii:

cos qx=1-½(qx)2+.. exp(-Rx2qx

2 -Ry2qy

2 -Rz

2qz2

-2Rxz2qx qz)

Grassberger’77RL’78

Csorgo, Pratt’91: LCMS vz = 0

pion

Kaon

Proton

, , Flow & Radii ← Emission points at a given tr. velocity

px = 0.15 GeV/c 0.3 GeV/c

px = 0.53 GeV/c 1.07 GeV/c

px = 1.01 GeV/c 2.02 GeV/c

For a Gaussian density profile with a radius RG and linear flow velocity profile F (r) = 0 r/ RG:

0.73c 0.91c

Rz2 2 (T/mt)

Rx2= x’2-2vxx’t’+vx

2t’2

Rz = evolution time Rx = emission duration

Ry2 = y’2

Ry2 = RG

2 / [1+ 02 mt /T]

Rx , Ry 0 = tr. flow velocity pt–spectra T = temperature

t’2 (-)2 ()2

BW: Retiere@LBL’05

BW fit ofAu-Au 200 GeV

T=106 ± 1 MeV<bInPlane> = 0.571 ± 0.004 c<bOutOfPlane> = 0.540 ± 0.004 cRInPlane = 11.1 ± 0.2 fmROutOfPlane = 12.1 ± 0.2 fmLife time (t) = 8.4 ± 0.2 fm/cEmission duration = 1.9 ± 0.2 fm/cc2/dof = 120 / 86

Retiere@LBL’05

R

βz ≈ z/τβx ≈ β0 (r/R)

17

2005 Femtoscopy Puzzle I

3D Hydro

2+1D Hydro

1+1D Hydro+UrQMD

(resonances ?)

But comparing1+1D H+UrQMDwith 2+1D Hydro

kinetic evolution

at small pt

& increases Rside

~ conserves Rout,Rlong

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

19

20

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

24

25

Conclusions from Imaging