Pornrad SrisawadDepartment of Physics, Naresuan University, Thailand

Yu-Ming Zheng Yu-Ming Zheng China Institute of Atomic Energy, Beijing China Institute of Atomic Energy, Beijing ChinaChina

Yupeng YanYupeng YanSuranaree University of Technology, Nakhon Ratchasima Suranaree University of Technology, Nakhon Ratchasima ThailandThailand

Influence of the in-medium Kaons Potential on Kaons Production in Heavy Ion

Collisions

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OutlineOutline

The Kaon properties in dense The Kaon properties in dense mattermatterProbing in-medium kaon Probing in-medium kaon potentialpotential and EOSand EOSResults and DiscussionResults and DiscussionSummarySummary

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How much energy is needed to compress hadronic matter?

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Good probes for dense matter

Kaons:

: 1.58

: 2.5

thr

thr

K us NN N K E GeV

N K

K us NN NNK K E GeV

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2 *2

* 22

*2 *2

0

0

K K

KNK K s

K K

iV m

m m V Vf

k m

Dispersion relation :

*2 *20Kk m V

in-medium energy”

• Do kaons change their properties in dense matter?

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Density dependence of the in-medium kaon potential at zero momentum. IA: the impulse approximation [NPA 567 (1994) 937],

0 30KU MeV

0 5KU MeV

BR potential

KL potential

*2 2 *2 2

450

0.6 ;

KN MeV

f f f f

*2 2

350KN MeV

f f

0

2 2 20 0*2

2 2

, ,

KNK s

K

U

m V Vf

m

k k k

k

k

SkyrmeSkyrme forces in the QMDforces in the QMD modelmodel Skyrme forces are easy to handle,Skyrme forces are easy to handle, cover the rangecover the rangeof uncertainty concerning the EOS for isospin of uncertainty concerning the EOS for isospin symmetric nuclear matter symmetric nuclear matter and and therefore widely used therefore widely used in transport calculations for heavy ion collisions. in transport calculations for heavy ion collisions. The QMD N-particle Hamiltonian is given by The QMD N-particle Hamiltonian is given by (1)(1)

2 2

,( )

1

2Sk Yuk Coul

i i ij ij iji i j

j i

H k m V V V

23 3 1 2 31 2 3 ln 1Sk

ijV t t t q q q q q k k q q

4Yuk e

V t

q q

q q

2 2coul Z e

VA

q q

The individual nucleons are described by Gaussian The individual nucleons are described by Gaussian

wave packets with fixed width 2Lwave packets with fixed width 2L1/21/2. . This leads to a This leads to a

One-particle Wigner density One-particle Wigner density

(2)(2)

(3)(3)

Where is an interaction densityWhere is an interaction density

2 22/ /23

1, i it t

if t e e

q-q k-kL Lq,k

3 3 3 3

22

0 0 0

, ; ,

ln 1

Sk Skij i j

ij ij iji j

V d qd q d kd k f t V f t

k k

q,k q,k q,k q ,k

ij

2 /4

3/2

1

4i jq q L

ij eL

30 0.16 , 16Bfm E MeV

The parameters in Eq. (3) are fitted to The parameters in Eq. (3) are fitted to the saturation point and the the saturation point and the momentum dependence of the real part of the nucleon-momentum dependence of the real part of the nucleon-nucleon optical potential. nucleon optical potential.

With this Hamiltonian Eq. (1) With this Hamiltonian Eq. (1) the EOS of the EOS of isospin isospin

saturated nuclear mattersaturated nuclear matter , i.e. the binding energy , i.e. the binding energy per per

Particle, Particle, is of the simple formis of the simple form

(4) (4)

, , , , 3

0 0.16 , 16Bfm E MeV

222

0 0 0 0

3ln 1

10 2 1 2F

bind

kEE

A M

We can see that We can see that

below 3below 3ρρ00,, the the

DBHF EOS with DBHF EOS with

K=200MeVK=200MeV is is

close to close to the soft the soft

Skyrme EOS, Skyrme EOS,

But becomes But becomes

significantly stiffersignificantly stiffer

at higher density.at higher density.

The nuclear EOS The nuclear EOS from soft and hard Skyrme forces are compared to from soft and hard Skyrme forces are compared to the Predictions fromthe Predictions from microscopic ab inito calculationsmicroscopic ab inito calculations, i.e. , i.e. relativistic DBHF[Nucl. Phys. A648 (1999)105]relativistic DBHF[Nucl. Phys. A648 (1999)105], , non- relativistic non- relativistic BHF [Nucl. Phys. A706 (2002)418]BHF [Nucl. Phys. A706 (2002)418] and variantional [Phys. Rev. and variantional [Phys. Rev. C58 (1998)1804] calculationsC58 (1998)1804] calculations..

How can we measure the eos?How can we measure the eos?

The nuclear EOS is studied by particle (Δ, N*, π, K, Λ, Σ, η, ρ,…) production in heavy ion collisions ---- pion and kaon production in HIC

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The Influence of K+N by (BR)

The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

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The Influence of K+N by (BR)

The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

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The Influence of EOS

The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

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The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

The Influence of K+N by (BR)

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The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

The Influence of K+N by (BR)

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The Influence of EOS

The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

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The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

The Influence of K+N by (BR)

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The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

The Influence of K+N by (BR)

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The cross sections of K+ at difference polar angle distributions, Data are from KaoS [Phys.Rev,C75,024906(2007)].

The Influence of EOS

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The Influence of K+N by (BR)

The transverse mass spectra K+ of Ni + Ni 1.93 A GeV,Data are from KaoS [Senger, P., et al.: Nucl. Instr. Meth. Phys. Res. A. 327, 393 (1993)].

−0.69 < yc.m. < −0.54,

−0.54 < yc.m. < −0.39

−0.39 < yc.m. < −0.24.

The scaling factors 102, 101 and 100 are applied to the spectra from top to bottom

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The Influence of K+N by (BR)

The transverse mass spectra K+ of Ni + Ni 1.93 A GeV,Data are from KaoS [Senger, P., et al.: Nucl. Instr. Meth. Phys. Res. A. 327, 393 (1993)].

−0.69 < yc.m. < −0.54,

−0.54 < yc.m. < −0.39

−0.39 < yc.m. < −0.24.

The scaling factors 102, 101 and 100 are applied to the spectra from top to bottom

04/22/2304/22/2323

The Influence of EOS

The transverse mass spectra K+ of Ni + Ni 1.93 A GeV,Data are from KaoS [Senger, P., et al.: Nucl. Instr. Meth. Phys. Res. A. 327, 393 (1993)].

−0.69 < yc.m. < −0.54,

−0.54 < yc.m. < −0.39

−0.39 < yc.m. < −0.24.

The scaling factors 102, 101 and 100 are applied to the spectra from top to bottom

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The influence of K+N by (BR) & EOS

The invariant cross section K+, Data are from KaoS [A. Forster,et al., Phys ReV, C75,024906 (2007)].

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The invariant cross section K+, Data are from KaoS [A. Forster,et al., Phys ReV, C75,024906 (2007)].

The influence of K+N by (BR) & EOS

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The invariant cross section K+, Data are from KaoS [A. Forster,et al., Phys ReV, C75,024906 (2007)].

The influence of K+N by (BR) & EOS

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The polar angle distribution of K+

The influence of K+N by (BR),Data are from KaoS [A. Forster,et al., Phys ReV, C75,024906 (2007)].

The distributions are normalized to 1 for cos θc.m. = 0

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The polar angle distribution of K+

The influence of K+N by (BR),Data are from KaoS [A. Forster,et al., Phys ReV, C75,024906 (2007)].

The distributions are normalized to 1 for cos θc.m. = 0

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The directed transverse momentum of K+

The influence of K+N by (BR),Data are from KaoS [J. Ritman, private communication]

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Summary

Most transport simulations reproduce corresponding data only when in-medium potentials are included The BR parametrization of kaon mean field pvovides the best overall description of the K+ observables at SIS energies. Calculated results with a in-medium K+N potential can reasonably describe the features of KaoS and Fopi data.This indicates that production cross section, transverse mass spectra are sensitive probes to extract information on in-medium properties of K+ and prefer soft equation of state.

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Summary

However K+ the polar distribution and the directed transverse momentum are not sensitive observes in kaon nucleus potential and equation of state.Details concerning the interplay between density and momentum dependence have still to be settled and require future efforts. More experimental measurements with improved errors, theoretical innovations, and detailed analyses are needed.

It is also needed to study the EOS at the FAIR/GSI energies between 20 -30 A GeV ( ～ 8 )

max

0

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