kˉ- 4 he, kˉ- 3 he interactions at low energies
DESCRIPTION
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. Outline. K ˉ p and K ˉ n scattering lengths K ˉ - 4 He and K ˉ - 3 He calculations of the scattering lengths - PowerPoint PPT PresentationTRANSCRIPT
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