countrate estimates. particle production in heavy ion collisions
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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
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