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Register a new userFaddeev calculation of 6 He Lambda Lambda using SU_6 quark-model baryon-baryon interactions
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Authors
Y. Fujiwara
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Quark-model hyperon-nucleon and hyperon-hyperon interactions by the Kyoto-Niigata group are applied to the two-Lambda plus alpha system in a new three-cluster Faddeev formalism using two-cluster resonating-group method kernels. The model fss2 gives a reasonable two-Lambda separation energy Delta B_{Lambda Lambda}=1.41 MeV, which is consistent with the recent empirical value, Delta B^{exp}_{Lambda Lambda}=1.01 +/- 0.20 MeV, deduced from the Nagara event. Some important effects that are not taken into account in the present calculation are discussed.
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The previous Faddeev calculation of the two-alpha plus Lambda system for 9 Lambda Be is extended to incorporate the spin-orbit components of the SU_6 quark-model baryon-baryon interactions. We employ the Born kernel of the quark-model Lambda N LS interaction, and generate the spin-orbit component of the Lambda alpha potential by the alpha-cluster folding. The Faddeev calculation in the jj-coupling scheme implies that the direct use of the quark-model Born kernel for the Lambda N LS component is not good enough to reproduce the small experimental value Delta E^exp_{ls}=43 +- 5 keV for the 5/2^+ - 3/2^+ splitting. This procedure predicts three to five times larger values in the model FSS and fss2. The spin-orbit contribution from the effective meson-exchange potentials in fss2 is argued to be unfavorable to the small ls splitting, through the analysis of the Scheerbaum factors for the single-particle spin-orbit potentials calculated in the G-matrix formalism.
Previously we calculated the binding energies of the triton and hypertriton, using an SU_6 quark-model interaction derived from a resonating-group method of two baryon clusters. In contrast to the previous calculations employing the energy-dependent interaction kernel, we present new results using a renormalized interaction, which is now energy independent and reserves all the two-baryon data. The new binding energies are slightly smaller than the previous values. In particular the triton binding energy turns out to be 8.14 MeV with a charge-dependence correction of the two-nucleon force, 190 keV, being included. This indicates that about 350 keV is left for the energy which is to be accounted for by three-body forces.
Quark-model nucleon-nucleon and hyperon-nucleon interactions by the Kyoto- Niigata group are applied to the hypertriton calculation in a new three-cluster Faddeev formalism using the two-cluster resonating-group method kernels. The most recent model, fss2, gives a reasonable result similar to the Nijmegen soft-core model NSC89, except for an appreciable contributions of higher partial waves.
We calculate Lambda alpha, Sigma alpha and Xi alpha potentials from the nuclear-matter G-matrices of the SU6 quark-model baryon-baryon interaction. The alpha-cluster wave function is assumed to be a simple harmonic-oscillator shell-model wave function. A new method is proposed to derive the direct and knock-on terms of the interaction Born kernel from the hyperon-nucleon G-matrices, with explicit treatments of the nonlocality and the center-of-mass motion between the hyperon and alpha. We find that the SU6 quark-model baryon-baryon interactions, FSS and fss2, yield a reasonable bound-state energy for 5 He Lambda, -3.18 -- -3.62 MeV, in spite of the fact that they give relatively large depths for the Lambda single-particle potentials, 46 -- 48 MeV, in symmetric nuclear matter. An equivalent local potential derived from the Wigner transform of the nonlocal Lambda alpha kernel shows a strong energy dependence for the incident Lambda-particle, indicating the importance of the strangeness-exchange process in the original hyperon-nucleon interaction. The Sigma alpha and Xi alpha potentials are repulsive with the attractive isospin I=1/2 (Sigma alpha) and I=0 (Xi alpha) components and the repulsive I=3/2 (Sigma alpha) and I=1 (Xi alpha) components.
We calculate the lambda-nucleon scattering phase shifts and mixing angles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. Scattering amplitudes are obtained by solving the corresponding coupled-channel integral equations that have a milder ultraviolet behavior compared to their non-relativistic analogs. This allows us to consider the removed cutoff limit in our leading-order calculations also in the $^3P_0$ and $^3P_1$ partial waves. We find that, in the framework we are using, at least some part of the higher-order contributions to the baryon-baryon potential in these channels needs to be treated nonperturbatively and demonstrate how this can be achieved in a way consistent with quantum field theoretical renormalization for the leading contact interactions. We compare our results with the ones of the non-relativistic approach and lattice QCD phase shifts obtained for non-physical pion masses.
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