Generalized Dalitz Plot analysisGeneralized Dalitz Plot analysis

of the near threshof the near threshold pp old pp →→ ppKppK++KK-- reaction reaction

in view of thein view of the KK++KK-- interactioninteraction

Excited QCD, Stara Lesna, 4th February 2010

Michał Silarski

Jagiellonian University

OutlineOutline

Physical motivation Measurements of the pp→ppK+K- reaction with COSY-11 Study of the proton-kaon and kaon-antikaon interactions

differential cross sections at excess energy Q = 10 MeV

and Q = 28 MeV Generalization of the Dalitz Plot Analysis of the K+K- final state interaction

Summary

Physical motivationPhysical motivation

a0 and f0 mesons as a K+K- molecules

Nature of (1405) – K-p bound state (?)

Mechanism of the pp→ppK+K- reaction

Physics of heavy ion collisions

Physics of neutron stars: kaon condensates

COoler SYnchrotron COSY

WASA

• Polarised and unpolarised proton and deuteron beams

• momentum range: 600 – 3700 MeV/c• stochastic and electron cooling• meson production up to (1020)

COSY-11cluster target

drift chambers

scintillator

scintillator

COSY-11: C. Quentmeier et al., Phys.Lett. B 515 (2001) 276-282

COSY-11: P. Winter et al., Phys. Lett. B 635 (2006) 23-29

COSY-11: M. Wolke, PhD thesis

DISTO: F. Balestra et al.., Phys. Rev. C 63, 024004 (2001)

ANKE: Y.Maeda et al. Phys., Rev. C 77, 01524 (2008)

22

0

2

FSIKppKppFMM

fm 5.10

1

1

)(sin 01)( 0

1

ia

ikakF

qC

SeqF

pK

ppSi

pp

pp

2121

kFkFqFFKpKpppFSI

σtot = 0.95 ± 0.17 nb

Differential cross sections for the ppDifferential cross sections for the pp→→ppKppK++KK-- reaction at Q = 10 MeVreaction at Q = 10 MeV

ppK

ppKppK

pK

pKpK dMd

dMdR

dMd

dMdR

;

σtot = 6.5 ± 1.1 nb

ppK

ppKppK

pK

pKpK dMd

dMdR

dMd

dMdR

;

Differential cross sections for the ppDifferential cross sections for the pp→→ppKppK++KK-- reaction at Q = 28 MeVreaction at Q = 28 MeV

Generalization of the Dalitz PlotGeneralization of the Dalitz Plot

Event representation: interior of a equilateral triangle

222

22

4

1

kjkjjk

kijkji

ppEEM

dMdMs

dEdE

Final state interaction: modification of the homogeneous event distribution

321 EEEs

Probability of reaction yielding a state with the i-th particle in momentum range dp

i ( in CM):

23

43214

33

32

31

312

16

1fsEp

EEEEpdpdpdpdRd

jj

jj

Assuming that f depends only on invariant masses of the particles one obtains (Nyborg et al. Phys. Rev. 140 922 (1965 ) ):

smmmmMMMMMBB

dMdMdMdMdMBs

fRd

,,,,,,,,,

824

23

22

21

2134

2124

234

214

212

2134

2124

234

214

212

225

Generalization of the Dalitz PlotGeneralization of the Dalitz Plot

Analysis of the KAnalysis of the K++KK-- final state interaction final state interaction

32

1

22

0

2

2

1

kFkF

kFqFF

FMM

KKKp

KpppFSI

FSIKppKpp

KKKK aik

kF3

3 1

1

isi

eie

iei

siKK N

NNNNa

ln2,2

fm 335.0 45.0

iaKK

Phys. Rev. C 80, 045202 (2009)

Analysis of the KAnalysis of the K++KK-- final state interaction final state interaction

SummarySummary

Shape of the excitation function for the near threshold pp→ppK+K- reaction reveal a significant enhancement which may be plausibly assigned to the influence of the pK- or K+K- interaction

Calculations which take into account the proton-proton and proton-kaon interactions underestimate experimental data very close to threshold

Ansatz proposed by ANKE collaboration reproduces the experimental ratios RpK RppK also at significantly lower enegies

The estimated K+K-scattering length amounts to:

fm 335.0 45.0

iaKK

Thank You for attention

BACKUPProdukcja kaonów w zderzeniach nukleon-nukleon

KppKpKpp

KppKpKpp

1405

13850

Produkcja stowarzyszona:

KppKpppp

KdKdpn

Produkcja mezonu rozpadającego się na parę K+K- :

Zderzenia proton-proton blisko progu na produkcję pary K+K-

( COSY-11, ANKE ):

KppKpKpp

KppKfppapp

KppKpp

1385/1405

?

/

lub

0

00

Produkcja kaonów w zderzeniach nukleon-nukleon