Pornrad SrisawadDepartment of Physics, Naresuan

University, Thailand

Yu-Ming ZhengYu-Ming ZhengChina Institute of Atomic Energy, China Institute of Atomic Energy,

Beijing Beijing ChinaChina

Azimuthal distributions of K+ Azimuthal distributions of K+

mesons in heavy-ion collisionsmesons in heavy-ion collisions

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IntroductionIntroduction

Kaons in dense matterKaons in dense matter

Kaon production in transport modelKaon production in transport model

Probing in-medium kaon potentialProbing in-medium kaon potential

SummarySummary

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IntroductionIntroduction

Kaons in dense hadronic matter are important Kaons in dense hadronic matter are important a possible restoration of chiral symmetry a possible restoration of chiral symmetry the properties of nuclear matter at high the properties of nuclear matter at high

densities and temperatures. densities and temperatures. Extensive experimental efforts to search for Extensive experimental efforts to search for

the kaon in-medium potential in heavy ion the kaon in-medium potential in heavy ion collisions. collisions.

The azimuthal distributionThe azimuthal distribution is one of sensitive is one of sensitive

observes to extract information on in-medium observes to extract information on in-medium properties at high densities.properties at high densities.

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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

Subthreshold Kaon production (ELab< Ethr):

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The azimuthal distribution

1tan ( )y

x

p

p

1 21 2 cos 2 cos 2 ...dN

v vd

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2 2t x yp p p

1 cos x

t

pv

p

2 2

2 2 2cos 2 x y

x y

p pv

p p

Off plane : v2 < 0

In – plane : v2 > 0

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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

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Ratio of (p+Au/p+C ) at Tp = 2.3 GeV

RBUU transport_ _ without Coulomb._._ only Coulomb…. Coulomb + 20 MeV_.._.. Coulomb + 40 MeV

o data__ Coulomb + 20 MeV

Eur. Phy. J. A 22 (2004) 301.Phys. Lett. B 540 (2002) 207.

0 20KU MeV

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K+ In-plane Flow

Transverse K+ flow in 1.93 AGeV Ni + Ni reactions at impact parameter b≤4 fm. Data are from FOPI [Z. Phys. A352(95)355 (old) and Prog. Part. Nucl. Phys. 42 (99) 187(new)].

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Probing in-medium kaon Probing in-medium kaon potentialpotential

Influence of in-medium KInfluence of in-medium K++ potential on the potential on the kaon yields kaon yields

for central (b=0) Au +Au and C + C for central (b=0) Au +Au and C + C reactionsreactions.. [PPNP56(1)1] [PPNP56(1)1]

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The KThe K++ excitation functions in Au + Au (scaled by 10-1)and C + C reactions excitation functions in Au + Au (scaled by 10-1)and C + C reactions are compared to data from KaoS [PRL 82 (99) 1640); PRC 66 (02) 054604].are compared to data from KaoS [PRL 82 (99) 1640); PRC 66 (02) 054604].

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KK++ rapidity distributions in Ni + Ni reactions rapidity distributions in Ni + Ni reactions at 1.93 AGeV.at 1.93 AGeV.

Data are from FOPI Data are from FOPI [NPA625 (97) 307][NPA625 (97) 307] and KaoS and KaoS [PLB 495 [PLB 495

(2000) 26](2000) 26]. .

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Au+Au at 1.5 A GeV

data

The azimuthal distribution

K+ Out of-plane Flow

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197 197Au+ Au

   ExperimentExperiment

datadata

CalculationCalculation

with Kwith K++NN

CalculationCalculation

without Kwithout K++NN

transverse transverse flow (vflow (v11))

0.04±0.010.04±0.01 -0.015±0.0016-0.015±0.0016 -0.006±0.0013-0.006±0.0013

Elliptic flowElliptic flow

vv22

-0.09±0.03-0.09±0.03 -0.043±0.0016-0.043±0.0016 -0.03±0.0013-0.03±0.0013

197 197Au Au+

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Ni+Ni at 1.93 A GeV

data

The azimuthal distribution

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   ExperimetExperimet

DataData

CalculationCalculation

with Kwith K++NN

CalculationCalculation

without Kwithout K++NN

transverse transverse flow (vflow (v11))

-0.01±0.01-0.01±0.01 --0.013±0.00150.013±0.0015

-0.006±0.0014-0.006±0.0014

Elliptic-flow Elliptic-flow (v(v22))

-0.05±0.03-0.05±0.03 --0.040±0.00160.040±0.0016

-0.02±0.0014-0.02±0.0014

58 58Ni + Ni

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Summary K+ production can be used to probe the in-medium kaon potential, and consequently to probe an expected partial restoration of chiral symmetry at supra-normal nuclear densities.

Most transport simulations reproduce corresponding data only when in-medium potentials are included

• The azimuthal distribution is one of sensitive observes to extract information on in-medium properties at high densities.

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We have analyzed the azimuthal distributions of K+ mesons produced in Au+Au reactions at 1.5 A GeV and in Ni + Ni reactions at 1.93 A GeV within the QMD model.

Calculated results with a in-medium K+N potential can reasonably describe the features of KaoS data.This indicates that the azimuthal distribution is one of sensitive probes to extract information on in-medium properties of K+ mesons at high densitis.

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