K

1
K-4He, K-3He interactions at low
energies
Vera Grishina (INR RAS, Moscow, Russia)

University of Bonn, Germany August 31 September
5, 2009
2
Outline

• Kp and Kn scattering lengths
• K -4He and K -3He
• calculations of the scattering lengths
• discussion about the bound K-He states
• Study of the K 3He FSI in the pd ? 3He KK
  reaction
• model predictions ? measurements
• at COSY-Jülich accelerator
• Observation of the K0d FSI in the
• pp?dKK0 reaction measured
• at COSY-Jülich accelerator

3
Kp scattering length from experiment

• it is negative from the data on the
  strong-interaction 1s level shift of the kaonic
  hydrogen atom
• a(Kp) - 0.78(0.18) i 0.49(0.37) fm
• M. Iwasaki et al. (KEK, Japan), PRL 78 (1997)
  3067
• a(Kp)(- 0.468 0.090 (stat.) 0.015 (syst.))
• i (0.302 0.135 (stat.) 0.036 (syst.)) fm
• G. Beer at al. (DEAR collaboration), PRL 94,
• (2005) 212302

4
Kp and Kn scattering lengths

• obtained from the KN scattering data

a(Kp) - 0.7 i 0.64 fm a(Kn)0.26 i 0.57 fm A.D. Martin, Nucl. Phys. B 179, 33 (1981), K-matrix solution
a(Kp) - 0.045 i 0.835 fm a(Kn) 0.94 i 0.72 fm J. Conboy (1985), fit S1
5
Kp and Kn elementary amplitudes expressed in
termof the isospin I0,1 KN amplitudes
6
KN (I0,1) vacuum scattering lengths used in
the calculations
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 Martins 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)
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KN (I0,1) in-medium 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 KA 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)
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KA Multiple Scattering Approach
KA wave function at fixed coordintes of nucleons
(Rj rK rj)
KN scattering amplitudes
effective wave in each scattering center j
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The 4He and 3He density function
4He
3He
This 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))
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K -He FSI factor in the Multiple Scattering (MS)
Approach
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K-He scattering length inthe Multiple
Scattering theory
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K-4He, K-3He scattering lengths In the Multiple
Scattering Theory
V.Grishina et al., Phys.Rev. C 75, 015208 (2007)
Set for KN A(K 4He) fm Mult. Scatt. A(K 4He) fm Optical Potential A(K 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
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Pole positions of the K 4He and K 3He
scattering amplitudes
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Poles of the unitarized amplitudes found in the
case of the sets 1-2(candidates to the KA bound
states)
system parameter K 3He K 4He
E MeV - 4.5 -8.4 - 4.8 -6.7
G MeV 21.6 26.8 14.9 18
15

• Recent measurement of the isospin-filtering
• dd?4He KK reaction at Q39MeV
• at ANKE-COSY
• Upper limit is stot 14 pb
• X.Yuan et al., Eur.Phys.J. A (2009) in print
• It is impossible to study the K 4He FSI
• using this data

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K 3He relative energy distribution for pd ? 3He
KK reaction without or with K 3He FSI
calculated in the Multiple Scattering approach
V.Grishina et al., Phys.Rev. C 75, 015208 (2007)
The distribution of the T(K 3He)1/2(M(K
3He)M(K 3He)) (mK mHe3) in pd ? 3He K
K reaction. The data are from the experiment by
MOMO at COSY-Jülich, F. Bellemann at al, Phys.
Rev. C 75, 015204 (2007)
Q40 MeV
17
KK relative energy
distribution for the pd ? 3He KK reaction
without or with K 3He FSI calculated in
the Multiple Scattering approach
Q40 MeV
Contribution of the f meson and resolution
effect were included V. Grishina, M. Büscher, L.
Kondratyuk, Phys. Rev. C 75, 015208 (2007)
18
KK and K 3He relative energy distributions
measured by MOMO-COSY for the pd ? 3He KK
reaction could be described as f-contribution
phase space without FSI
The signes of charges on two kaons were not
determined in the MOMO vertex detector. The
result for K 3He relative energy distribution Is
averaged over the two charge states of
kaons. Measurements to be carried out
with identification of all three final state
particles
Q35.1 MeV
Q40.6MeV
Q55.2 MeV
F. Bellemann at al, Phys. Rev. C 75, 015204
(2007)
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Predictions for the K 3He invariant
mass distribution for the pd ? 3He KK reaction
without or with K 3He FSI
Q40 MeV
We neglected the FSI effect for the kaons
produced via the f(1020)-meson decaying outside
the nucleus
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Evidence of the Kd FSI was found in the recent
data on the pp?d KK0 reaction measured at
ANKE-COSY
The data are from A.Dzyuba et al., Eur.Phys. J. A
29, 245 (2006)
Fit with the A(Kd)(-1i1.2) fm
The fit is from A.Dzyuba et al., Eur.Phys. J. A
38, 1-8 (2008)
Fit with the constant amplitudes

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

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It is possible to measure the K 3A interactions
at COSY-Jülich
Submitted COSY proposal 195.1, 2009
22
K 3He FSI with scattering length A (K 3He)1.5
fm
Set 3
Phase space
Set 2
Set 1
Simulated K 3He mass distribution for the pd ?
3He KK at Q25MeV (submitted COSY proposal
195, A.Dzyuba et al. 2009)
Contours of correlations between
the determinations of the real and imaginary
parts of the A (K 3He). The points are the
predictions of the multiple scattering model with
KN parameters from sets 1-3
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Conclusions

• Calculations of the s-wave K 3He and
• K a scattering lengths were performed within
  the Multiple Scattering Approach
• A possibility of the loosely bound states
• in the K a and K 3He systems was discussed
  
• K 3He final state interaction effects were
  analyzed for the pd ? 3He K K reaction
• New measurements of the K -light nucleus
  interactions could be performed at COSY-Jülich

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Kd 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 Scattering
• A(Kd) -0.72 i 0.94 fm A. Deloff, Phys. Rev.
  C 61, 024004 (2000)
• Faddeev Approach
• A(Kd) -0.84 i 0.95 fm A. Deloff, Phys. Rev.
  C 61, 024004 (2000)
• Multiple Scattering Calculation
• A(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
• (1mK/mN )/ (1mK/md) 1.18

Set 1