Are the Chiral Based $$\bar{\varvec{K}}\varvec{N}$$ K ¯ N

Importance of chiral constraints for the pole content of the K¯N scattering amplitude

“…In addition, we constrain the fitted meson decay constants by fixing their mutual ratio adopting either F K = F π or F K = 1.193 F π , the second ratio complying with the PDG [39] as well as lattice results [40] reviews. This leaves us with just 4 fitted parameters (F π and three β's) while 7 parameters were used in [1].…”

“…As a different dataset and fitting approach was used in [5] the χ 2 /dof taken from this earlier publication cannot be compared directly with the χ 2 /dof obtained for our current models. We also note that no χ 2 /dof was provided in [1] but the same author presented χ 2 /dof in more extendend fits performed later in [20]. Table 1: The fitted meson decay constants and inverse ranges, both in MeV, obtained in fits of low energy K − p data.…”

“…where the channel matrices K rel , K are real in the physical region, and specify the chosen model parameterization. In [1], a Lippmann-Schwinger equation (LSE) in the form…”

“…The debated on-shell factorisation corresponds to replacing the loop momentum q in the argument of T and V by its on-shell value k, and subsequently pulling T and V out of the integral to arrive at an algebraic (matrix) equation. This procedure is not applied in [1], and so the solution there is somewhat more elaborate.…”

“…If one can construct an improved model, which is more reconcilable with chiral symmetry and does not introduce additional shortcomings, there is no reason to stick to the old model. In the following section, we attempt to devise an improved model with the same cutoff function u(q) as used in [1], but with a softened effective interaction kernel of O(m) at threshold. As we will see, obeying this chiral SU(3) constraint is quite relevant for the pole content of the amplitude.…”