Three-body approach to theK−dscattering length in particle basis

Abstract

We report on the first calculation of the scattering length A K − d based on a relativistic three-body approach where the two-body input amplitudes coupled to the KN channels have been obtained with the chiral SU (3) constraint, but with isospin symmetry breaking effects taken into account.Results are compared with a recent calculation applying a similar set of two-body amplitudes, based on the fixed center approximation, considered as a good approximation for a loosely bound target, and for which we find significant deviations from the exact three-body results. Effects of the hyperon-nucleon interaction, and deuteron D-wave component are also evaluated.

Low energyK¯Ninteractions and Faddeev calculation of theK−dscattering length in isospin and particle

“…In conjunction with the observation in Section II A just mentioned above, we conclude here that it is important to retain these ηY channels for A K − d . Before ending this subsection we should mention that, as shown in our previous publication [1], we have also tested the KN amplitude from Ref. [5] in the three-body equation, and the result turned out to be very close to the one with OS1, as expected.…”

“…In fact, these quantities are very sensitive to the value of the threshold at which they are calculated, which is then reflected in the values obtained for the A K − d scattering length. These aspects have been discussed in our previous paper [1], and will be revisited at beginning of Sec. IV.…”

“…they are evaluated with the values of the parameters reached at the end of minimization (these values can be found in Ref. [1]). The branching ratios and the a K − p scattering length obtained in this model are comparable to the values from the Oset-Ramos model, see Table II. The same conclusion holds when we compare the total cross sections and the πΣ mass spectrum given in Figs.…”

Faddeev-chiral unitary approach to theK−dscattering length

“…Following recent findings, in the present paper we revisit our previous work [3,4] within an improved χP T for the coupled channel KN amplitudes, using them to obtain…”

“…Since the nucleon-nucleon (NN) two-body interaction that we have adopted in the present work is the same as that used in Refs. [3,4], this section is devoted to the coupledKN channel interactions that are the primary two-body ingredient to the three-body approach.…”