Reinhard Stock

together with F. Beca4ni, J. Steinheimer and M. Bleicher

Erice School of Nuclear Physics September 2016

Hadron Forma*on and the Sta*s*cal Model at low Energy

(SPS, NICA, FAIR)

1

2

State of the art: SHM Data Analysis with UrQMD ModificaNon

Data2−10 1−10 1 10 210 310

Stat

. Mod

el w

ith M

odif.

Fac

tor

2−10

1−10

1

10

210

310

3 MeV±T = 162 6 MeV± = 244

Bµ

0.03 MeV± = 0.88 Sγ

/DOF = 9.1/92χ

+π -π

+K-K0K

Λφ

Ξ

Ξ ΛΩ

Ω

p

158 AGeV central Pb+Pb NA49

Data2−10 1−10 1 10 210 310

Stat

. Mod

el

2−10

1−10

1

10

210

310

4 MeV±T = 150 10 MeV± = 265

Bµ

0.05 MeV± = 0.91 Sγ

/DOF = 26.9/92χ

+π-π

+K-K

0KΛ

φΞ

ΞΛ

Ω

Ω

p

158 AGeV central Pb+Pb NA49

Example: Pb+Pb central NA49 at SPS T increases by 12 MeV chi2/dof decreases

+π-

π +K-

K p p Λ Λ Ξ Ξ Ω Ω

((H

ydro

+A

ft)

- H

ydro

)/H

ydro

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1158 AGeV Pb+Pb central

3

Modification factors for hadronic Multiplicities Baryon-Antibaryon annihilation effects

Bulk Hadrons nearly unaffected

CorrecNons to SHM

Revisit the hadronic-expansions stage: UrQMD study of afterburner effects

4

State of the art. F. Becattini et al. arXiv: 1605.09694

The Phase Boundary from StaNsNcal Model Analysis

5

The QCD Phase Boundary : AGS, SPS, LHC •  low curvature up to mu(B)= 400MeV •  in agreement with lattice predictions

O. Kaczmarek et al. , PRD 83 (2011) P. Hedge et al. , arXiv: 1511.03378 G. Enrodi et al. , JHEP 1104 (2011)

Abrupt drop-off beyond mu(B)=400MeV see also A.Andronic et al. , Nucl. Phys. A772 (2006)

arXiv:1605.09694

6

StaNsNcal Model Results down to SIS

Abrupt drop-off beyond mu(B)=400MeV A.Andronic et al. , Nucl. Phys. A772 (2006)

•  not compatible with smooth interpolations

7

High Baryochemical PotenNal

Specific high µB phenomena:

•  canonical strangeness suppression

•  critical point

•  purely hadronic dynamics below „onset of deconfinement“

8

Canonical Suppression of Strangeness

ncaniS = nGC

iS · iSs = ±1,±2,±3

iS Is(xi)

I0(xi)! 1 for large xi

A.Andronic et al. , Nucl. Phys. A772 (2006)

1/S

A. Tounsi and K. Redlich J. Phys. G28 (2002) 2095

9

Search for the CriNcal Point of QCD

10

State of the art: µB vs. √s A.Andronic et al. , Nucl. Phys. A772 (2006)

Inadequate for our purpose!

11

Dynamics below the „onset of deconfinement“

J. Steinheimer et al. arXiv: 1603.02051

•  subthreshold for all strange particles! •  all yields are essentially resonance decays •  recall hadronization theory!

12

SHM Analysis of SIS Data J. Steinheimer et al. arXiv: 1603.02051

•  T, γS, and µB constant after interpenetration time •  are the data canonic or grand canonic?

13

UrQMD at 6 AGeV

•  similar pattern above thresholds •  wait for FAIR and NICA

14

Backup

15

Combining UrQMD with the Stat. Model

•  drastic chi2/dof improvement •  T rises above traditional SHM

Hydro

-210 -110 1 10 2103

10S

tat.

Mo

de

l Fit

-210

-110

1

10

210

310

(a) UrQMD 158 AGeV Pb+Pb central

2 MeV±T = 160

6 MeV±=246 B

µ

0.03±=0.90 S

γ

/DOF=4.7/82χ

+π-π

+K-

K

p

p

Λ

ΛΞ

ΞΩ

Ω

+π-π +K

-K p p Λ Λ Ξ Ξ Ω Ω

(fit-

mo

de

l)/e

rro

r

-5

0

5

Hydro+Aft

-210 -110 1 10 2103

10

Sta

t. M

od

el F

it

-210

-110

1

10

210

310

(b) UrQMD 158 AGeV Pb+Pb central

1 MeV±T = 151

7 MeV±=277 B

µ

0.04±=1.00 S

γ

/DOF=28.2/82χ

+π-π

+K-

K

p

p

Λ

Λ

Ξ

Ξ Ω

Ω

+π-π +K

-K p p Λ Λ Ξ Ξ Ω Ω

(fit-

mo

de

l)/e

rro

r

-5

0

5

16

Tensions concerning Tc •  We report T(c)=163MeV, similar to e+e- -> hadrons

•  Lattice matching to Hadron Gas (HRG) reports T(c)=150MeV

A. Bazavov et al. , PRD 90 (2014)

A. Bazavov et al. , PRL 113 (2014)

Open Question!