Countrate estimates. Particle production in heavy ion collisions.
-
Upload
samuel-goodman -
Category
Documents
-
view
225 -
download
0
Transcript of Countrate estimates. Particle production in heavy ion collisions.
![Page 1: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/1.jpg)
Countrate estimates
![Page 2: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/2.jpg)
Particle production in heavy ion collisions
![Page 3: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/3.jpg)
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- - -
![Page 4: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/4.jpg)
ObservablesU+U 23 AGeV
![Page 5: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/5.jpg)
Pion multiplicities per participating nucleons
RHIC
![Page 6: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/6.jpg)
meson-baryon interaction
![Page 7: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/7.jpg)
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
![Page 8: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/8.jpg)
GSI
Meson production in central Au+Au collisionsW. Cassing, E. Bratkovskaya, A. Sibirtsev, Nucl. Phys. A 691 (2001) 745
![Page 9: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/9.jpg)
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
![Page 10: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/10.jpg)
Particle yields in midrapidity from central A+A collisions
![Page 11: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/11.jpg)
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
![Page 12: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/12.jpg)
E = 10.7 AGeV
E = 40 AGeV E = 80 AGeV
Central Au+Au collisions (midrapidity): statistical model results
![Page 13: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/13.jpg)
E = 158 AGeV
Central Au+Au collisions (midrapidity): Statistical model results
![Page 14: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/14.jpg)
Central Au+Au collisions (midrapidity): Statistical model results
![Page 15: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/15.jpg)
Central Au+Au collisions (midrapidity): Statistical model results
![Page 16: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/16.jpg)
Central Au+Au collisions (midrapidity): Statistical model results
![Page 17: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/17.jpg)
Central Au+Au collisions (midrapidity): Statistical model results
![Page 18: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/18.jpg)
Central Au+Au collisions (midrapidity): Statistical model results
![Page 19: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/19.jpg)
Strangeness/pion ratios
Decrease of baryon-chemicalpotential: transition frombaryon-dominatedto meson-dominatedmatter
?
C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692
![Page 20: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/20.jpg)
Strangeness = 2 × (K+ + K−) + 1.54 × (Λ + Λ¯)Entropy = 1.5 × (π+ + π−) + 2 × p¯
![Page 21: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/21.jpg)
The freeze-out curve in the QCD phase diagramA. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199
![Page 22: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/22.jpg)
J. Randrup and J. Cleymans, hep-ph/0607065
![Page 23: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/23.jpg)
![Page 24: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/24.jpg)
Pion production in Au + Au collisions at 1.5 AGeV
Data: T. Schuck, Dipl. Thesis 2003, GSI/Uni Frankfurt
![Page 25: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/25.jpg)
"Boltzmann" parameterisation:
d3/dp3 = C1 exp(-E/T1) + C2 exp(-E/T2)
![Page 26: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/26.jpg)
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
![Page 27: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/27.jpg)
N. Xu, Int. J. Mod. Phys. E16 (2007) 715
![Page 28: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/28.jpg)
![Page 29: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/29.jpg)
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)
![Page 30: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/30.jpg)
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
![Page 31: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/31.jpg)
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
![Page 32: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/32.jpg)
![Page 33: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/33.jpg)
Dense baryonic matter up to 3 ρ0:
Probing the nuclear equation-of-state with heavy ions
![Page 34: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/34.jpg)
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
![Page 35: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/35.jpg)
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)
![Page 36: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/36.jpg)
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
![Page 37: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/37.jpg)
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
![Page 38: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/38.jpg)
![Page 39: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/39.jpg)
Dynamics of a semi-central Au+Au collision at 2 AGeV(BUU calculation, P. Danielewicz, MSU)
![Page 40: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/40.jpg)
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
![Page 41: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/41.jpg)
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
![Page 42: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/42.jpg)
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
![Page 43: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/43.jpg)
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
![Page 44: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/44.jpg)
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
![Page 45: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/45.jpg)
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
![Page 46: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/46.jpg)
![Page 47: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/47.jpg)
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+ + +.
![Page 48: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/48.jpg)
The in-medium properties of strange mesons
![Page 49: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/49.jpg)
(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
![Page 50: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/50.jpg)
B 3-80 , T 130 MeV
![Page 51: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/51.jpg)
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
![Page 52: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/52.jpg)
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
![Page 53: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/53.jpg)
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
![Page 54: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/54.jpg)
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.
![Page 55: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/55.jpg)
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
![Page 56: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/56.jpg)
Antikaon spectral function in nuclear matter
self-consistent coupled channel calculation with mean field (s,p,d waves)
(1405)
K- K-
N-1
![Page 57: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/57.jpg)
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
![Page 58: Countrate estimates. Particle production in heavy ion collisions.](https://reader035.fdocuments.net/reader035/viewer/2022062323/56649ece5503460f94bdb427/html5/thumbnails/58.jpg)
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