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

1. Kˉ-4He, Kˉ-3Heinteractions at low energies Vera Grishina (INR RAS, Moscow, Russia) University of Bonn, Germany August 31 – September 5, 2009

2. Outline • 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 Kˉ3He FSI in the pd  3He K+Kˉ reaction: model predictions  measurements at COSY-Jülich accelerator Observation of the K0d FSI in the ppdK+K0 reaction measured at COSY-Jülich accelerator

3. Kˉp scattering length from experiment it is negative from the data on thestrong-interaction 1s level shift of the kaonic hydrogen atom a(Kˉp)= - 0.78(±0.18)+ i 0.49(±0.37) fm M. 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.)) fm G. Beer at al. (DEAR collaboration), PRL 94, (2005) 212302

4. Kˉp and Kˉn scattering lengths obtained from the KN scattering data

5. Kˉp and Kˉn elementary amplitudes expressed in termof the isospin I=0,1 KN amplitudes

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

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

8. KˉA: Multiple Scattering Approach KˉA wave function at fixed coordintes of nucleons (Rj = |rK – rj|) KN scattering amplitudes effective wave in each scattering center j

9. 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))

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

11. Kˉ-He scattering length inthe Multiple Scattering theory

12. Kˉ-4He, Kˉ-3He scattering lengths In the Multiple Scattering Theory V.Grishina et al., Phys.Rev. C 75, 015208 (2007)

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

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

15. Recent measurement of the isospin-filtering dd4He K+Kˉ reaction at Q=39MeV 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 Kˉ 4He FSI using this data

16. K 3He relative energy distribution for pd  3He K+Kˉ reaction without or with Kˉ 3HeFSI calculated in the Multiple Scattering approachV.Grishina et al., Phys.Rev. C 75, 015208 (2007) The distribution of the T(K 3He)=1/2(M(Kˉ3He)+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

17. K+Kˉ relative energy distribution for the pd  3He K+Kˉ reactionwithout or with Kˉ 3HeFSI calculated in the Multiple Scattering approach Q=40 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 K+Kˉ 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 Q=35.1 MeV Q=40.6MeV Q=55.2 MeV F. Bellemann at al, Phys. Rev. C 75, 015204 (2007)

19. Predictions for the Kˉ 3He invariant mass distribution for the pd  3He K+Kˉ reaction without or with Kˉ 3HeFSI Q=40 MeV We neglected the FSI effect for the kaons produced via the f(1020)-meson decaying outside the nucleus

20. Evidence of the Kd FSI was found in the recent data on the ppd K+K0 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)=(-1+i1.2) 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)

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

22. Kˉ 3He FSI with scattering length A (Kˉ 3He)=1.5 fm Set 3 Phase space Set 2 Set 1 Simulated Kˉ3He mass distribution for the pd  3He K+Kˉ at Q=25MeV (submitted COSY proposal #195, A.Dzyuba et al. 2009) Contours of correlations between the determinations of the real and imaginary parts of the A (Kˉ 3He). The points are the predictions of the multiple scattering model with KˉN parameters from sets 1-3

23. Conclusions • Calculations of the s-wave Kˉ3He and Kˉa scattering lengths were performed within the Multiple Scattering Approach A possibility of the loosely bound states in the Kˉ a 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

24. Kˉd scattering length was calculatedin 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” (1+mK/mN )/ (1+mK/md) = 1.18 Set 1