Kˉ-4He, Kˉ-3He interactions at low energies

Vera Grishina (INR RAS, Moscow, Russia)

University of Bonn, Germany

August 31 – September 5, 2009

• Kˉp and Kˉn scattering lengths• Kˉ -4He and Kˉ -3He calculations of the scattering lengths discussion about the bound Kˉ-He states• Study of the Kˉ 3He FSI in the pd 3He K+Kˉ reaction: model predictions measurements at COSY-Jülich accelerator Observation of the K0d FSI in the ppdK+K0 reaction measured at COSY-Jülich accelerator

Kˉp scattering length from experiment

it is negative from the data on the strong-interaction 1s level shift of the kaonic hydrogen atom

a(Kˉp)= - 0.78(±0.18)+ i 0.49(±0.37) fmM. Iwasaki et al. (KEK, Japan), PRL 78 (1997) 3067

a(Kˉp)=(- 0.468 ± 0.090 (stat.) ± 0.015 (syst.))+ i (0.302 ± 0.135 (stat.) ± 0.036 (syst.)) fmG. Beer at al. (DEAR collaboration), PRL 94, (2005) 212302

Kˉp and Kˉn scattering lengths

obtained from the KN scattering data

a(Kˉp)= - 0.7+ i 0.64 fm;

a(Kˉn)=0.26+ i 0.57 fm A.D. Martin, Nucl. Phys. B 179, 33 (1981),

K-matrix solution

a(Kˉp)= - 0.045 + i 0.835 fm;

a(Kˉn) = 0.94+ i 0.72 fm

J. Conboy (1985), fit S1

Kˉp and Kˉn elementary amplitudes expressed in term

of the isospin I=0,1 KN amplitudes

Set a0 (KN)

[fm]

a1 (KN)

[fm]

Reference

1 -1.59 +i0.76 0.26 + i0.57 R.C. Barrett, A. Deloff,

Phys. Rev. C 60 (1999) 025201

(K-matrix fit close to Martin’s fit)

2 -1.31 +i1.24 0.26 + i0.66 J.A. Oller, U.-G. Meissner,

Phys. Lett. B 500 (2001) 263

(Chiral Unitary Approach)

3 -1.03 +i0.95 0.94 + i0.72 J.E. Conboy, Rutherford-Appleton Lab. Report,

RAL-85-091 (1985)

(Constant Scattering Length fit)

KN (I=0,1) vacuum scattering lengths used in the calculations

Set a0 (KN)

[fm]

a1 (KN)

[fm]

Reference

4 0.33 +i0.45

isospin

0.33 +i0.45

averaged

A. Ramos and E. Oset,

Nucl. Phys. A 671 (2000) 481

(self-consistent microscopic theory based on chiral

approach; corresponds to KˉA Optical Potential with

a depth -50 MeV)

5 +2.9 + i 1.1 0.43 + i 0.30 Y. Akaishi and T. Yamazaki,

Phys. Rev. C 65 (2002) 044005

(strongly attractive Optical Potential)

KN (I=0,1) in-medium scattering lengths used in the calculations

KˉA wave function at fixed coordintes of nucleons (Rj = |rK – rj|)

KN scattering amplitudes

effective wave in each scattering center j

KˉA: Multiple Scattering Approach

4He 3HeThis values were used to describe the electromagnetic form-factors of 3He and 4He up to momentum transfer q2 =8 fm-2

(V.N. Boitsov, L.A. Kondratyuk, and V.B. Kopeliovich,Sov. J. Nucl. Phys. 16, 287 (1973))

The 4He and 3He density function

Kˉ -He FSI factor in the Multiple Scattering (MS) Approach

Kˉ-He scattering length inthe Multiple Scattering theory

Set

for KN

A(Kˉ 4He) [fm]

Mult. Scatt.

A(Kˉ 4He) [fm] Optical Potential

A(Kˉ 3He) [fm] Mult. Scattering

1 -1.80 + i 0.90 - 1.26 + i0.60 -1.50 + i 0.83

2 -1.98 + i 1.08 - 1.39 + i0.65 -1.66 + i 1.10

3 -2.24 + i 1.58 -1.59 + i0.88 -1.52 + i 1.80

4 -1.47 + I 2.22 -1.51 + i1.20 −

5 - 3.49 + i 1.80 -1.57 + i0.74 -3.93 + i 4.03

Kˉ-4He, Kˉ-3He scattering lengths In the Multiple Scattering Theory

V.Grishina et al., Phys.Rev. C 75, 015208 (2007)

Pole positions of the Kˉ 4He and Kˉ 3He scattering amplitudes

system

parameter Kˉ 3He Kˉ 4He

E [MeV] - 4.5 ÷ -8.4 - 4.8 ÷ -6.7

[MeV] 21.6 ÷ 26.8 14.9 ÷ 18

Poles of the unitarized amplitudes found in the case of the sets 1-2(candidates to the KA bound states)

Recent measurement of the isospin-filtering

dd4He K+Kˉ reaction at Q=39MeV

at ANKE-COSY

Upper limit is tot ≤ 14 pbX.Yuan et al., Eur.Phys.J. A (2009) in print

It is impossible to study the Kˉ 4He FSI

using this data

The distribution of the

T(K 3He)=1/2(M(Kˉ 3He)+M(K+ 3He))– (mK + mHe3)

in pd 3He K+ Kˉ reaction.The data are from the experiment

by MOMO at COSY-Jülich,F. Bellemann at al,

Phys. Rev. C 75, 015204(2007)

The distribution of the

T(K 3He)=1/2(M(Kˉ 3He)+M(K+ 3He))– (mK + mHe3)

in pd 3He K+ Kˉ reaction.The data are from the experiment

by MOMO at COSY-Jülich,F. Bellemann at al,

Phys. Rev. C 75, 015204(2007)

Q=40 MeV

K 3He relative energy distribution for pd 3He K+Kˉ reaction without or with Kˉ 3He FSI calculated in the Multiple Scattering approach V.Grishina et al., Phys.Rev. C 75, 015208 (2007)

K+Kˉ relative energy distribution for

the pd 3He K+Kˉ reaction without or with Kˉ 3He FSI calculated in the

Multiple Scattering approach

Contributionof the meson and

resolution effectwere included

V. Grishina, M. Büscher,L. Kondratyuk,

Phys. Rev. C 75, 015208(2007)

Q=40 MeV

KK and K 3He relative energy distributions measured by MOMO-COSY for the pd 3He K+Kˉ reaction could be described as -contribution + phase space without FSI

The signes ofcharges on two kaonswere not determinedin the MOMO vertex detector.The resultfor K 3He relativeenergy distributionIs averaged overthe two charge statesof kaons.

Measurements to becarried out withidentification of allthree final state particles

F. Bellemann at al, Phys. Rev. C 75, 015204 (2007)

Q=35.1 MeV

Q=40.6MeV

Q=55.2 MeV

Predictions for the Kˉ 3He invariant massdistribution for the pd 3He K+Kˉ reaction without or with Kˉ 3He FSI

We neglected the FSI effect for the kaons produced via the -meson decayingoutside the nucleus

Q=40 MeV

Fit with the constantamplitudes

Fit with the A(Kd)=(-1+i1.2) fm

Evidence of the Kd FSI was found in the recent data on the ppd K+K0 reaction measured at ANKE-COSY

The data are fromThe data are fromA.Dzyuba et al., Eur.Phys. J. A A.Dzyuba et al., Eur.Phys. J. A 29, 29, 245 (2006)245 (2006)

The fit is fromThe fit is fromA.Dzyuba et al., Eur.Phys. J. A A.Dzyuba et al., Eur.Phys. J. A 38, 38, 1-8 (2008)1-8 (2008)

It was used the restriction on the A(Kd) found within the framework of the low-energy EFTU.-G. Meissner, U. Raha, and A. Rusetsky, Eur. Phys. J. C 47,473-480 (2006)

Submitted COSY proposal# 195.1, 2009

It is possible to measure the K 3A interactions at COSY-Jülich

Simulated Kˉ 3He mass distribution for the pd 3He K+Kˉ at Q=25MeV (submitted COSY proposal #195, A.Dzyuba et al. 2009)

Phasespace

Kˉ 3He FSI with scattering length A (Kˉ 3He)=1.5 fm

Contours of correlations between thedeterminations of the real and imaginary parts of the A (Kˉ 3He). The pointsare the predictions of the multiplescattering model with KˉN parametersfrom sets 1-3

Set 3

Set 2

Set 1

• Calculations of the s-wave Kˉ 3He and

Kˉ scattering lengths were performed within the Multiple Scattering Approach

A possibility of the loosely bound states

in the Kˉ and Kˉ 3He systems was discussed • Kˉ 3He final state interaction effects were

analyzed for the pd 3He K+ Kˉ reaction• New measurements of the Kˉ -light nucleus

interactions could be performed at COSY-Jülich

Kˉd scattering length was calculated in Multiple Scattering and Faddeev Approaches

a0 (KN) = -1.59 +i0.76 fm

a1 (KN) = 0.26 + i0.57 fm

Multiple ScatteringA(Kd) = -0.72 + i 0.94 fm A. Deloff, Phys. Rev. C 61, 024004 (2000)

Faddeev ApproachA(Kd) = -0.84 + i 0.95 fm A. Deloff, Phys. Rev. C 61, 024004 (2000)

Multiple Scattering CalculationA(Kd) = -0.78 + i 1.23 fm V. Grishina et al., Eur. Phys.J. A 21, 507-520 (2004)

Note that our result is multiplied by the “reduced mass factor”

(1+mK/mN )/ (1+mK/md) = 1.18

Set

1