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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