Transcript Strangenessproduction at SIS energies

Properties of nuclear matter
from subtheshold
strangeness production
Christoph Hartnack, Helmut Oeschler, Jörg Aichelin
Subatech Nantes and TH Darmstadt
Outline:
●
Subthreshold production, optical potential
●
Spectra, temperatures and KN rescattering
●
Azimuthal distribution and the KN potential
●
Scaling laws and the nuclear equation of state
●
Conclusion
Calculations performed with IQMD, a semiclassical,
microscopic N-body model with quantum features for
the description of HICs on an event-by-event basis
Subthreshold kaon production
•Production of kaons at energies below
the kinetic threshold for K production
in elementary pp collisions
•Fermi momenta may contribute in
energy
•Multistep processes can cumulate the
energy needed for kaon production
•Importance of resonances (especially
the D) for storing energy
•Short livetime of resonance favors
early production at high densities
•Sensitivity to in-medium effects and
nuclear equation of state
Time-evolution
& kaon production
0fm/c
4fm/c
8fm/c
12fm/c
16fm/c
20fm/c
K+: early, multistep induced product. when baryon density is highest
K-: prod. later when pion density is highest, strangeness exchange
In medium effects on kaons
•KN-Rescattering,
absorption for K•Optical potential:
repulsive for K+,
attractive for K-
Penalizes K+ production
at high densities but
favors K- production at
high densities
Effects yields but also
dynamics
Parametrization from
Schaffner-Bielich RMF results
Can we reveal the KN potential from K+ yields?
No Pot
KN pot
Au-data: Foerster et al, KaoS
Ni-data: Uhlig et al., KaoS
Visible difference between calculations with and without KN
potential on a log-scale. KN-pot yields less kaons, but incertainties
on D induced cross sections discourage a preliminary conclusion.
K- production dominated by strangeness exchange
BB
+pY+BY
+pB
BB+pB+pY+BY
Direct channels BB, pB enhanced by K- potential, similar for
exchange channels pY+BY. The K+ potential penalizes hyperon
production and compensates in the dominant channels pY+BY.
Spectra: slopes dominated by KN-rescattering
Rescattering
potential
Collision number
K+
KK+ rescatter
Strong enhancement Slight effects:
of the slope from
enhancement (K+)
initial to final mom. or reduction (K-)
High K+ rescattering
less K- rescattering
Temperatures of K+
IQMD results with KNrescattering are in good
agreement with KaoS data
K+ heated up by coll. with
expanding nucl.medium
KaoS
A.Förster et al.
PRC75(2007) 024906
K- show systematically lower temperatures.
Reason: less rescattering, diff. potentials?
Azimuthal distributions
Azimuthal distributions are
effected by rescattering and by the
optical potential.
While the rescattering acts in the
same direction for K+ and K- the
optical potential gives opposite
effects for K+ and KAzimuthal distribution fitted with
a (1+v1 cos(f) + 2 v2cos(2f))
Ni+Ni 1.93 GeV,
F. Uhlig et al, KaoS
KaoS and FOPI see opposite signs
of v2 for K+ and K-
Excitation function of v2 for K+
Rescattering and optical
potential are needed to
describe the v2 of kaons.
The effects of the optical
potential become dominant
with respect to the effect of
rescattering when going
down in beam energy.
This is in agreement with
calculations of Li&Ko who
found a strong potential
effect for Au+Au 1 GeV/A.
Comparison of v1(y0) to FOPI data
Preliminary data from FOPI (Kim et al. ) favor an optical
potential less strong than implemented by us
The original idea of measuring the eos
•Eos describes the energy needed
to compress nuclear matter
•A hard eos requires more energy
for a given density than a soft one
•For a given density and a given
available energy a soft eos leaves
more thermal energy to the system
than a hard eos
•R.Stock: This thermal energy
could be measured by regarding
pion production
At which density can we
measure the eos?
Different densities are reached for hard
and soft eos. A soft eos yields higher
densities than a hard eos.
The differences in compressional energy
and thus in thermal energy become less.
The pion number is not sensitive enough.
Pions come out late due to reabsorption in
dense matter
Kaons might be an interesting probe.
However the effects of the optical
potential and incertainties of the cross
section do not allow a direct measure of
the eos from kaon yields.
The solution: ratios Au/C
KaoS data support soft eos
Symbols: KaoS data
Lines IQMD
Data: Ch.Sturm et al.
RQMD: Ch. Fuchs
IQMD supports this
Robust against changes of
cross sections, optical potential,
Delta lifetimes, etc.
Au: central versus peripheral
central
peripheral
A soft eos yields higher values than a
hard eos.
Different cross
sections and
potential parameters
may change the
global yield.
However, the
parameter a for the
increase of the kaon
yield N with the
number A of
participating
nucleons (raising
with centrality)
N(K)=N0 Aa
depends on the eos.
Determination of the eos from a
The relation between the
compression modulus
and a is monotonously
falling.
KaoS:Förster et al.
KaoS data (Förster et al.)
favor a value below 200
MeV, i.e. a soft eos.
soft
hard
C.H. et al. PRL 96 (2006) 012302
Same for Au/C ratio
Another scaling systematics: system size
Scaling with system size in
inclusive A+A events
System size, Kaos Data
Apart in Au+Au from
KaoS agrees with that
2 independent observables
( centrality scaling and
system size scaling)
confirm soft eos
Kaons and density isomers
•Could reveal density isomers by a sudden rise in the
excitation function of kaons - KaoS might measure it
A 2ndminimum
would yield a
sudden factor of
10 in the kaon
yield
Effect related to subthreshold prod.
C.H. et al. PRL 72 (1994) 3767
Density
isomers
yield up to
800
600 MeV factors of
10 in K+
production
KaoS DATA: no
isomer up to 3r0
A density isomer would
have needed the strong
raise indicated by the
arrows.
IQMD calculations using a
KN optical potential and a
soft eos are consistent with
KaoS data on Au+Au and
C+C of Sturm et al.
For higher densities/beam
energies we need other
particles produced below
threshold
Conclusions
•
Kaon spectra reveal strong rescattering of kaons with
the surrounding nuclear matter
•
Comparison of flow variables supports the existence
of KN optical potential
•
Scaling laws of the kaon production claim strongly
for a soft equation of state
•
The KaoS measurements (which can be continued by
eos data) contradict the existence of density isomers
at moderate densities
Effect of the potential: penalty
reimbursed
•Initial distributions show a
difference of calculations with
KN-pot and without pot at all
energies. This is due to the
penalty paid at the production.
•In the final state the kaons
regain the paid penalty and the
curves of both calculations
become rather close
Only at small energies a lack
remains stemming from those
Kaons with did not undergo collisions: kaons which failed to be
produced due to the penalty.
No KN potential : final=initial
KN collisions change the spectra
Most kaons underwent many
collisions before leaving.
They show a significant
enhancement of the slope.
initial
At the time before the freeze
out of the kaons (about 12-20
fm/c) the nucleonic system is
still hot and expanding. The
kaons carry the temperature
of that expansion phase.
Comparison to data for K-
Less rescattering for the K- yield smaller temperature than for K+
Comparison of spectra for K+
Temperature: centrality dependence
Temperature and collisions
Maxwellian Demon
Au+Au 1.5 GeV azimuthal distribution
For Au+Au at 1.5 GeV we
needed both potential and
rescattering to reproduce
the results of Foerster et
al.
Influence on v2(pT) at midrapidity
Again opposite effect on K+ an Kuseful for balancing the effect of rescattering
FOPI and KaoS see opposite signs of v2 for K+ and K-
V2:pT dependence
Polar distributions
Polar distribution: rescattering and
potential
Excitation function of K+
A observation which is robust
sNDTsushima
sND=.75 sNN
versus effects of production cross sections, KN-potential, D-lifetime
Going down in beam energy
A soft eos yields a 1.4 at E=0.8 AGeV, a hard eos yields a 1.2
Limits for lower E: no asymptotic yield for peripheral collisions
System size dependence
Einc
A soft eos obtains higher kaon
yields for heavy systems
1.8
1.5
KaoS: PRC in preparation
1.2
1.0
0.8
0.6
A mixture of both
NC=0 has a visible fraction to the yield, shows a taller rapidity
distribution and strongly negative flow.
For NC>2 a positive flow and a wider y-distribution is observed
The potential shifts to negative flow
Initial vs final
Pot vs. NoPot
NC=0: initial shadowing boosted by potential to strong neg. flow
NC>2: initial bias, enhanced by scattering, reduced by potential
Final flow a superposition of different flows
Initial flow: bias for having collisions or not
Final flow: visible shift from the potential
Rescattering enhances potential effect
For NC=0 the initial flow is inverted
Rescattering adds up more positive flow