Kˉ- 4 He, Kˉ- 3 He 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 - 4 He and Kˉ - 3 He calculations of the scattering lengths discussion about the bound Kˉ-He states Study of the Kˉ 3 He FSI in the pd  3 He K + K ˉ reaction: model predictions  measurements at COSY-Jülich accelerator Observation of the K 0 d FSI in the pp  dK + K 0 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)= (±0.18)+ i 0.49(±0.37) fm M. Iwasaki et al. (KEK, Japan), PRL 78 (1997) 3067 a(Kˉp)=( ± (stat.) ± (syst.)) + i (0.302 ± (stat.) ± (syst.)) fm G. Beer at al. (DEAR collaboration), PRL 94, (2005)

Kˉp and Kˉn scattering lengths obtained from the KN scattering data a(Kˉp)= 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)= i fm; a(Kˉn) = 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 a 0 (KN) [fm] a 1 (KN) [fm] Reference i i0.57 R.C. Barrett, A. Deloff, Phys. Rev. C 60 (1999) (K-matrix fit close to Martin’s fit) i i0.66 J.A. Oller, U.-G. Meissner, Phys. Lett. B 500 (2001) 263 (Chiral Unitary Approach) i i0.72 J.E. Conboy, Rutherford- Appleton Lab. Report, RAL (1985) (Constant Scattering Length fit) KN (I=0,1) vacuum scattering lengths used in the calculations

Set a 0 (KN) [fm] a 1 (KN) [fm] Reference i0.45 isospin 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) i i 0.30 Y. Akaishi and T. Yamazaki, Phys. Rev. C 65 (2002) (strongly attractive Optical Potential) KN (I=0,1) in-medium scattering lengths used in the calculations

KˉA wave function at fixed coordintes of nucleons (R j = |r K – r j |) KN scattering amplitudes effective wave in each scattering center j KˉA: Multiple Scattering Approach

4 He 3 He This values were used to describe the electromagnetic form-factors of 3 He and 4 He up to momentum transfer q 2 =8 fm -2 (V.N. Boitsov, L.A. Kondratyuk, and V.B. Kopeliovich,Sov. J. Nucl. Phys. 16, 287 (1973)) The 4 He and 3 He density function

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

Kˉ-He scattering length in the Multiple Scattering theory

Set for KN A(Kˉ 4 He) [fm] Mult. Scatt. A(Kˉ 4 He) [fm] Optical Potential A(Kˉ 3 He) [fm] Mult. Scattering i i i i i i i i i I i1.20 − i i i 4.03 Kˉ- 4 He, Kˉ- 3 He scattering lengths In the Multiple Scattering Theory V.Grishina et al., Phys.Rev. C 75, (2007)

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

system parameter Kˉ 3 He Kˉ 4 He E [MeV] ÷ ÷ -6.7  [MeV] 21.6 ÷ ÷ 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 dd  4 He K + Kˉ reaction at Q=39MeV at ANKE-COSY Upper limit is  tot ≤ 14 pb X.Yuan et al., Eur.Phys.J. A (2009) in print It is impossible to study the Kˉ 4 He FSI using this data

The distribution of the T(K 3 He)=1/2(M(Kˉ 3 He)+M(K + 3 He)) – (m K + m He3 ) in pd  3 He K + Kˉ reaction. The data are from the experiment by MOMO at COSY-Jülich, F. Bellemann at al, Phys. Rev. C 75, (2007) The distribution of the T(K 3 He)=1/2(M(Kˉ 3 He)+M(K + 3 He)) – (m K + m He3 ) in pd  3 He K + Kˉ reaction. The data are from the experiment by MOMO at COSY-Jülich, F. Bellemann at al, Phys. Rev. C 75, (2007) Q=40 MeV K 3 He relative energy distribution for pd  3 He K + Kˉ reaction without or with Kˉ 3 He FSI calculated in the Multiple Scattering approach V.Grishina et al., Phys.Rev. C 75, (2007)

K + Kˉ relative energy distribution for the pd  3 He K + Kˉ reaction without or with Kˉ 3 He FSI calculated in the Multiple Scattering approach Contribution of the  meson and resolution effect were included V. Grishina, M. Büscher, L. Kondratyuk, Phys. Rev. C 75, (2007) Q=40 MeV

KK and K 3 He relative energy distributions measured by MOMO-COSY for the pd  3 He K + Kˉ reaction could be described as  -contribution + phase space without FSI The signes of charges on two kaons were not determined in the MOMO vertex detector. The result for K 3 He 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 F. Bellemann at al, Phys. Rev. C 75, (2007) Q=35.1 MeV Q=40.6MeV Q=55.2 MeV

Predictions for the Kˉ 3 He invariant mass distribution for the pd  3 He K + Kˉ reaction without or with Kˉ 3 He FSI We neglected the FSI effect for the kaons produced via the  -meson decaying outside the nucleus Q=40 MeV

Fit with the constant amplitudes Fit with the A(Kd)=(-1+i1.2) fm Evidence of the Kd FSI was found in the recent data on the pp  d K + K 0 reaction measured at ANKE-COSY The data are from A.Dzyuba et al., Eur.Phys. J. A 29, 245 (2006) The fit is from A.Dzyuba et al., Eur.Phys. J. A 38, 1-8 (2008) It was used the restriction on the A(Kd) found within the framework of the low-energy EFT U.-G. Meissner, U. Raha, and A.Rusetsky, Eur. Phys. J. C 47, (2006)

Submitted COSY proposal # 195.1, 2009 It is possible to measure the K 3 A interactions at COSY-Jülich

Simulated Kˉ 3 He mass distribution for the pd  3 He K+Kˉ at Q=25MeV (submitted COSY proposal #195, A.Dzyuba et al. 2009) Phase space Kˉ 3 He FSI with scattering length A (Kˉ 3 He)=1.5 fm Contours of correlations between the determinations of the real and imaginary parts of the A (Kˉ 3 He). The points are the predictions of the multiple scattering model with KˉN parameters from sets 1-3 Set 3 Set 2 Set 1

Calculations of the s-wave Kˉ 3 He and Kˉ  scattering lengths were performed within the Multiple Scattering Approach A possibility of the loosely bound states in the Kˉ  and Kˉ 3 He systems was discussed Kˉ 3 He final state interaction effects were analyzed for the pd  3 He 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 a 0 (KN) = i0.76 fm a 1 (KN) = i0.57 fm Multiple Scattering A(Kd) = i 0.94 fm A. Deloff, Phys. Rev. C 61, (2000) Faddeev Approach A(Kd) = i 0.95 fm A. Deloff, Phys. Rev. C 61, (2000) Multiple Scattering Calculation A(Kd) = i 1.23 fm V. Grishina et al., Eur. Phys.J. A 21, (2004) Note that our result is multiplied by the “reduced mass factor” (1+m K /m N )/ (1+m K /m d ) = 1.18 Set 1