Countrate estimates

Particle production in heavy ion collisions

Particle multiplicities for central Au+Au collisionsfrom UrQMD calculations

Au+Au 6 AGeV central minimum bias 0.00072 0.00018

Example Ω production

Direct production:NN + - NN (Ethr = 12.7 GeV)

Production via multiple collisions:

NN K+ΛN, NN K+K-NN, ΛK- - 0, -K- - -

ObservablesU+U 23 AGeV

Pion multiplicities per participating nucleons

RHIC

meson-baryon interaction

SIS: KaoS AGS: E802,E866 SPS: NA49

Production of K+ und K- mesons in central AuAu/PbPb collisions

NN K+N: Elab 1.6 GeVNN K+K-NN: Elab 2.5

GeV

RHIC RHIC

GSI

Meson production in central Au+Au collisionsW. Cassing, E. Bratkovskaya, A. Sibirtsev, Nucl. Phys. A 691 (2001) 745

Rapidity distributions

Rapidity: y(0) = y-ym with y =0.5 ln [(E+pz)/(E-pz)]

Central Pb+Pb collisions at SPS energies C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

Particle yields in midrapidity from central A+A collisions

Central Au+Au collisions (midrapidity): statistical model results

E = 2 AGeV E = 4 AGeV

E = 6 AGeVE = 8 AGeV

A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

E = 10.7 AGeV

E = 40 AGeV E = 80 AGeV

Central Au+Au collisions (midrapidity): statistical model results

E = 158 AGeV

Central Au+Au collisions (midrapidity): Statistical model results

Central Au+Au collisions (midrapidity): Statistical model results

Central Au+Au collisions (midrapidity): Statistical model results

Central Au+Au collisions (midrapidity): Statistical model results

Central Au+Au collisions (midrapidity): Statistical model results

Central Au+Au collisions (midrapidity): Statistical model results

Strangeness/pion ratios

Decrease of baryon-chemicalpotential: transition frombaryon-dominatedto meson-dominatedmatter

?

C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

Strangeness = 2 × (K+ + K−) + 1.54 × (Λ + Λ¯)Entropy = 1.5 × (π+ + π−) + 2 × p¯

The freeze-out curve in the QCD phase diagramA. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

J. Randrup and J. Cleymans, hep-ph/0607065

Pion production in Au + Au collisions at 1.5 AGeV

Data: T. Schuck, Dipl. Thesis 2003, GSI/Uni Frankfurt

"Boltzmann" parameterisation:

d3/dp3 = C1 exp(-E/T1) + C2 exp(-E/T2)

Kinetic energy of a particle:Ek = Eth + Eflow = 3/2 kT + m/2flow2

The explosion of the fireball

Blast wave model: isotropically expanding System with temperature T P.J. Siemens and J.O. Rasmussen, Phys. Rev. Lett. 42 (1979) 880

dotted line: f = const. solid line: Hubble expansion f = rH

N. Xu, Int. J. Mod. Phys. E16 (2007) 715

Participants

Spectators

Determination of collision centrality

Number of participating nucleons in A+A collisions : Apart = 2 x A/Z x (Z – Zspec)

or Zero Degree Calorimeter: EZDC= Ebeam APro-Spec and Apart = 2 ( A - EZDC/Ebeam)

Determination of the reaction plane

Transverse Momentum Method: P. Danielewicz & G. Odyniec, Phys. Lett. 157 B (1985) 146

Q = p

= 1 für y>ycm

R = arctan(Qy/Qx)

Dispersion of the reaction plane:

Sub-Event-Method: = 1 - 2

s/

P ²

Expect Large Pressure Gradients Hydro FlowExpect Large Pressure Gradients Hydro Flow

...])φ[2(2φcos211

2122

3

3

RRT

vvdydp

Nd

pd

NdE

])φ[2cos(2 Rv

The Flow ProbeThe Flow ProbeThe Flow ProbeThe Flow Probe

Dense baryonic matter up to 3 ρ0:

Probing the nuclear equation-of-state with heavy ions

Observable in HI collisions: collective flow (driven by pressure)

The equation-of-state of (symmetric) nuclear matter

E/A() = -16 MeV

(E/A)()/

Compressibility:

(E/A)/

= 200 MeV: "soft" EOS = 380 MeV: "stiff" EOS

C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1Equation of state:

PV T E P E/V E/A

Definition of the potentials in transport codes

Bethe Weizsaecker –mass formula:

Volume term

(with eos)

+Surface term +Coulomb term +symmetry term

(+pairing term not included)

2 and 3 body interactions (no equilibrium required)

The eos in IQMDafter the convolution of the Skyrme type potentials supplemented by momentum dependent interactions (mdi) for infinite nuclear matter at equilibrium

hard

soft

Baryon/energy density in central cell (Au+Au, b=0 fm):Transport code HSD: mean field, hadrons + resonances + strings

E. Bratkovskaya, W. Cassing

Baryon and energy densities at FAIR energies

Dynamics of a semi-central Au+Au collision at 2 AGeV(BUU calculation, P. Danielewicz, MSU)

Azimuthal angle distribution:dN/d1 + 2v1cos + 2v2 cos2

C.Pinkenburg et al., (E895), Phys. Rev. Lett. 83 (1999) 1295

Azimuthal angular distribution of protons measured

in Au+Au collisions at 1.15, 2, 4, 6, 8 AGeV

Rapidity: y(0) = y-ym with y = 0.5 ln [(E+pz)/(E-pz)]

AGeV

dN/d1 + 2v1cos + 2v2 cos2

P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592

Probing the nuclear equation-of-state: proton collective flow

Transverse in-plane flow: Elliptic flow:

F = d(px/A)/d(y/ycm)

K = 170 – 210 MeV K = 170 – 380 MeV

P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592

pressure P = ρ2 · ( δ(ε/ρ) / δρ )with nuclear density ρ and energy density ε

Pressure as function of density

Independent observable ? particle production

Within microscopic transport models the collective flow is sensitive to:

The nuclear matter equation of state

In-medium nucleon-nucleon cross sections

Momentum dependent interactions

Probing the equation-of-state of symmetric nuclear matter:

Kaon production in Au+Au collisions at 1 AGeV

K+ mesons probe high densities

udsn

du

udd

su

K+

pp → K+Λp (Ethres= 1.6 GeV)

K+ reabsorption negligible

Probing the nuclear equation-of-state (ρ = 1 – 3 ρ0) by K+ meson production in C+C and Au+Au collisions

Transport model (RBUU)Au+Au at 1 AGeV:κ = 200 MeV ρmax 2.9 ρ0

K+κ = 380 MeV ρmax 2.4 ρ0

K+Reference system C+C: K+ yield not sensitive to EOS

Idea: K+ yield baryon density ρ compressibility κ

Experiment: C. Sturm et al., (KaoS Collaboration), Phys. Rev. Lett. 86 (2001) 39Theory: Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

The compressibility of nuclear matterExperiment: C. Sturm et al., (KaoS Collaboration) Phys. Rev. Lett. 86 (2001) 39

Theory: QMD Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 IQMD Ch. Hartnack, J. Aichelin, J. Phys. G 28 (2002) 1649

soft equation-of-state:≤ 200 MeVAu/C ratio: cancellation of systematic errors both in experiment and theory

Exploring the "nuclear" EOS at 3ρ0 < ρ < 7ρ0

Measure excitation function of (multi-strange) hyperon production in heavy-ion collisions from 2 - 15 AGeV (no data yet):

Direct production:

NN Λ0Λ0 NN (Ethr = 7.1 GeV)NN + - NN (Ethr = 9.0 GeV) NN + - NN (Ethr = 12.7 GeV)

Production via multiple collisions:

NN K+Λ0N, NN K+K-NN, Λ0K- - 0, -K- - - Λ0 K+ +0 , + K+ + +.

The in-medium properties of strange mesons

(1232)

(1600)

k,

p,n

N(1440)

N(1520)

M[GeV]

0

1

a1

Vakuum<qq> 0

Mesonen

BaryonenChiral Symmetry of QCD:

Quarks are massless.

In natur chiral symmetry is broken:Spontaneous: Parity-Doubletts are not degenerated Explicit: small pion mass (Goldstone Boson)

Explicit breaking: mu 5 MeV, md 10 MeV, ms 150

MeV Spontaneos/dynamical breaking:quarks couple to the virtual quark-antiquark pairs of the chiral

condensate

B 3-80 , T 130 MeV

K mesons in dense matter

G.E Brown, C.H. Lee, M. Rho, V. Thorsson, Nucl. Phys. A 567 (1994) 937 T. Waas, N. Kaiser, W. Weise, Phys. Lett. B 379 (1996) 34

J. Schaffner-Bielich, J. Bondorf, I. Mishustin ,Nucl. Phys. A 625 (1997)

How to measure in-medium modifications of kaons in heavy-ion collisions?

yield at subthreshold beam energies

repulsive K+N and attractive K-N potential: angular distributions

In-medium modifications of K+ mesons

Data: M. Menzel et al., (KaoS Collab.), Phys. Lett. B 495 (2000) 26 K. Wisniewski et al., ( FOPI Collab.), Eur. Phys. J A 9 (2000) 515

Reduced K+ yield due to increased in-medium K+ mass

Data: Y. Shin et al., (KaoS Collaboration), Phys. Rev. Lett. 81 (1998) 1576 F. Uhlig et al., (KaoS Collaboration), Phys. Rev. Lett. 95 (2005) 012301 Calculations see A. Larionov, U. Mosel, nucl-th/0504023

Data show evidence for repulsive K+N interaction !

K+ azimuthal emission pattern from A+A collisions

K+ mean free path in nuclear matter at ρ0: λ ~ 5 fm

F. Uhlig et al., (KaoS Collaboration), Phys. Rev. Lett. 95 (2005) 012301

Ni+Ni at 1.93 AGeV: π, K+ and K- azimuthal distributions

3.8 fm < b < 6.4 fm 0.4 < y/ybeam <0.6 0.2 GeV < p┴< 0.8 GeV IQMD Calculation:

C. Hartnack et al.

dN(φ)/φ 1 + 2v1cos(φ) + 2v2cos(2φ) + ...

Au+Au 1.5 AGeV semi-central collisions (b > 6.4 fm)K+ and K- azimuthal angular distributions

M. Płoskon, PhD Thesis 2005

Antikaon spectral function in nuclear matter

self-consistent coupled channel calculation with mean field (s,p,d waves)

(1405)

K- K-

N-1

dN(φ)/φ 1 + 2v1cos(φ) + 2v2cos(2φ) + ...

Elliptic flow of K+ and K- mesons:Comparison to off-shell transport calculations

and in-medium spectral functionsData: M. Płoskon, PhD Thesis, Univ. Frankfurt 2005Off-shell transport calculations: W. Cassing et al., NPA 727 (2003) 59, E. Bratkovskaya, priv. com.Coupled channel G-Matrix approach (K- spectral functions): L. Tolos et al., NPA 690 (2001) 547

Summary Kaon production

Excitation function of K+ production in A+A collisions (ρ = 1–3 ρ0): The nuclear matter equation-of-state is soft ( K 200 MeV) Yield and elliptic flow of K+ mesons in A+A collisions: The in-medium potential of K+ mesons is repulsive (i.e. the effective K+ mass is increased) Yield and elliptic flow of K- mesons in A+A collisions: Quantitative interpretation of data requires off-shell transport calculations and in-medium spectral functions