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Femtoscopic search for the 1-st order PT

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- Femtoscopic signature of QGP 1-st order PT
- Solving Femtoscopy Puzzle II
- Searching for large scales
- Conclusions

Richard Lednický [email protected]

Rischke & Gyulassy, NPA 608, 479 (1996)

With 1st order

Phase transition

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)

Femto-puzzle II

No signal of a

bump in Rout

near the QGP

threshold

expected at

AGS-SPS

energies !

Cassing – Bratkovskaya: Parton-Hadron-String-Dynamics

Perspectives at FAIR/NICA energies

Solving Femtoscopy Puzzle II

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

Imaging

- 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

This year we have celebrated 90th Anniversary

of the birth of one of the Femtoscopyfathers

M.I. Podgoretsky (22.04.1919-19.04.1995)

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

GGLP’60: enhanced ++, --vs +- at small

opening angles – interpreted as BE enhancement

depending on fireball radius R0

p p 2+ 2 - n0

R0 = 0.75 fm

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

QS symmetrization of production amplitudemomentum correlations of identical particles are sensitive to space-time structure of the source

KP’71-75

total pair spin

CF=1+(-1)Scos qx

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

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 qx=1-½(qx)2+..exp(-Rx2qx2 -Ry2qy2-Rz2qz2-2Rxz2qx qz)

Interferometry or correlation radii:

Rx2 =½ (x-vxt)2 , Ry2 =½ (y)2 , Rz2 =½ (z-vzt)2

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

Csorgo, Pratt’91: LCMS vz = 0

pion

0.73c

0.91c

← 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’2-2vxx’t’+vx2t’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 , Ry0 = tr. flow velocity pt–spectra T = temperature

BW fit of

Au-Au 200 GeV

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

Hydro assuming ideal fluid explains strong collective

() flows at RHIC but not the interferometryresults

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

+ ? initialF

Early Acceleration & FemtoscopyPuzzle I

Scott Pratt

Lattice says:

crossover at µ = 0 but CP location is not clear

CP: T ~ 170 MeV, μB > 200 MeV

Cassing – Bratkovskaya:

Imaging is based on

Conclusions from Imaging