K^+

phy

sics

wit

h he

avy

ions

Aman Sood, Christoph Hartnack, Elena Bratkovskaya

Strangeness production at threshold:

The nucleus can act as detector Strangeness can probe nuclear properties

K+

and the nuclear Eq.of

state

What strange particles can tell us about hadronic matter and

what hadronic matter tells us about strange particles

K^+

phy

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h he

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2

For the physics one needs comparison with theory:One simulates the complete heavy ion reaction on the computerusing

different eqs. of statedifferent KN potentials (+ other unknown quantities)

and compares the results with experiment

-> One has to assure that the results are robustThis requires

a lot of systematics

(different

AA, different

energies)

10-10

10-8

10-6

10-4

10-2

1

10 2

0 0.2 0.4 0.6 0.8

mt - m0 (GeV/c2)

1/m

t 2 d2 N

/(dm

tdy c.

m.)

((G

eV/c

2 )-3)

-0.05<yc.m.<0.05(x100)-0.15<yc.m.<-0.05(x10-1)-0.25<yc.m.<-0.15(x10-2)-0.35<yc.m.<-0.25(x10-3)-0.45<yc.m.<-0.35(x10-4)-0.55<yc.m.<-0.45(x10-5)

HADESHSD w potHSD wo pot

Not directly: one measures spectra butno observablegives direct information on cross sections, potentials, equation of state ….

How one can solve physics questions with HI experiments ?

K^+

phy

sics

wit

h he

avy

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3

-

Semiclassical

dynamical N(1)-body model -

with quantum features -

based on 2-

and 3-body interactions

-

-

Microscopic calculation of heavy ion collisions on an event-by-event-basis

- includes N,Δ,p with isospin

d.o.f.

-

-

strange particles treated virtually

The tools:

Isospin-Quantum Molecular

Dynamics

(IQMD)

Hadron String Model (HSD)

(Differences

here

not important)

Allows

for a «

photo

»

of the high

density

phase

and for a look inside

…

K^+

phy

sics

wit

h he

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Strangeness

is

complicated: Many combinations

are possible -

Many channels

have to be

implemented

•Each

channel

contains

isospin subdivisions

•Only

few channels

(like

pppΛK+) are measured

by experiment

(even

incomplete

infos)

•Significant

incertainties

from parametrization

of unknown channels

or isospin subdivisions

K^+

phy

sics

wit

h he

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•Production of kaons

at energies below the kinetic threshold for K production in elementary pp collisions

•Fermi momenta

may contribute to

of the collisions

•Multi-step processes (especially with a Δ) can cumulate the energy needed for kaon

production. Short Δ

lifetime

enhances production at high densities

•Repulsive KN potential cause a

penalty factor at high density

The ρ

dependence

of both

yields

a sensitivity

to the eq. of state

and KN potential

Subthreshold

kaon production

K^+

phy

sics

wit

h he

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Multistep

processes

require

high

densities, but medium effects

of kaons penalize

the high

density

production

Effect of repulsive KN potential

and multistep

processes compensate to a large extend but sensitivity to the eos

still survives. However,

the absolute yield depends on many details and is not conclusive.

soft

hard

Incl. KN potentialNo KNpotential

Condition: The yield

depends

of the EOS

Soft : K =200 MeVHard: K=380 MeV

K= compressibilitymodulus at ρ0

K^+

phy

sics

wit

h he

avy

ions

7Robust

versus effects

of production cross sections, KN-potential, less

stopping

(reduced

σNN

) , lifetime

of the Δ, …

Variation ofσNΔ

Variation ofUKN

Ratio K+

in Au/C yields

robust

observables

σND

TsushimaσND

=.75 σNN

K^+

phy

sics

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Different cross sections and potential parameters may change the global yield.

However, the parameter α

for the increase of the kaon

yield

N with the number A of participating nucleons (raising with centrality)

N(K)=N0

Apartα

depends on the eos. A soft eos

yields

higher values than a hard eos.centralperipheral

Verification

by second independent

observable:Centrality

dependence

of the K+

yield

Experimental value: >1.19

K^+

phy

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Three independent variables

Centrality dependence

of the K+

yield

Energy dependence

of the K+ yield(A dependence

of the K+ yield)

allow for the conclusion that

hadronic

equation of state is soft

K at ρ0

around 200 MeV

or even smaller

K^+

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According

to the theoreticalcalculations

the spectral form

at

low

mt is

the only

observablewhich

depends

exclusively

on

the KN interaction ( and noton the σ(NN(Δ) K+ΛN))

IQMDIQMD HSDHSD

What nuclei tell us about K+

properties

K^+

phy

sics

wit

h he

avy

ions

1111

transversetransverse

momentummomentum

spectraspectra

in in A+A,dependA+A,depend

on Kon K++N potentialN potential

IQMD and HSD IQMD and HSD modelsmodels

describedescribe

thethe

HADES HADES Ar+KClAr+KCl

at 1.75 at 1.75 AGeVAGeV

datadata

withwith

aa

repulsiverepulsive

KK++N potentialN potential

UU

KK

~ 40 MeV at ~ 40 MeV at ρρ00

. .

ShapeShape

of of thethe

ppTT

--spectraspectra

isis

sensitive to sensitive to thethe

inin--mediummedium potential!potential!

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.00

0.01

0.02

0.03

0.04

0.05

0.06

HADES: K0

S=(K0+K0bar)/2 HSD: K0/2

U()=0

U()=+20 MeV

U()=+40 MeV

pt [GeV/c]

Ar+KCl, 1.75 A GeV, b< 6 fm , |ycm|<0.07 )

dN/(d

p tdycm

) [(G

eV/c

)-1]

U(ρ0) = α40MeV

U(ρ0) = α 40MeV

K^+

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Transverse momentum spectrum of K+

is compatible

with a linear K+ -

nucleus potential of

as predicted by nuclear matter calculation (nucl-th/0404088)

ConclusionsHI reactions can measure K+propertiesK+

can measure nuclear matter properties

K+

are presently the best tool to measure the

nuclear equation of stateCompressibility modulus K around 200 MeV

K+ -

nucleus potential is close to that predicted bytheory (around 40 MeV

at ρ0 )

Independent models (HSD and IQMD) agree

U(ρ/ρ0) = 40ρ/ρ0 · [MeV ]