Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Abstract

The relativistic chiral SU (3) Lagrangian is used to describe kaon-nucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel BetheSalpeter equation with the interaction kernel truncated at chiral order Q 3 where we include only those terms which are leading in the large N c limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large N c baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU(3) symmetry-breaking effects are well controlled by the combined chiral and large N c expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of p lab ≃ 500 MeV.

Quark-mass dependence of baryon resonances

“…The task to construct a systematic effective field theory for the meson-baryon scattering processes in the resonance region is closely linked to the fundamental question as to what is the 'nature' of baryon resonances. Here we support the conjecture [1,2,3,4] that baryon resonances not belonging to the large-N c ground states are generated dynamically by coupled-channel dynamics [5,6,7,8,9,10]. For a comprehensive discussion of this issue we refer to [4].…”

“…The chiral symmetry breaking scale is Λ χ ≃ 4πf ≃ 1.13 GeV , with the parameter f ≃ 90 MeV determined by the pion decay process. Once the available energy is sufficiently high to permit elastic two-body scattering a further typical dimensionless parameter m 2 K /(8 πf 2 ) ∼ 1 arises [12,1,2]. Since this ratio is uniquely linked to two-particle reducible diagrams it is sufficient to sum those diagrams keeping the perturbative expansion of all irreducible diagrams, i.e.…”

“…The perturbative nature of subthreshold amplitudes, a crucial assumption of the χ-BS(3) approach proposed in [12,1,2], is not necessarily true in phenomenological coupledchannel schemes in [24,19,20,25,26,16]. Using the subtraction scales as free parameters, as advocated in [25,26,16], may be viewed as promoting the counter terms of chiral order Q 3 to be unnaturally large.…”

“…Moreover, if the scheme advocated in [25,26,16] were applied in all eleven isospin strangeness sectors with J P = 1 2 − a total number of 26 subtraction parameters arise. This should be compared with the only ten counter terms of chiral order Q 3 contributing to the on-shell scattering amplitude at that order [2]. Selecting only the operators that are leading in the large-N c limit of QCD out of the ten Q 3 operators only four survive [2].…”

Estimation of the Spatial Structure of \(\Lambda \)(1405) with Energy-Dependent Complex \(\bar{K}N\) Potential

“…One of the candidates is the Λ(1405) [1], which is too light to be described by the usual three-quark model [2]. Instead, the interpretation as theKN quasibound state [3,4] has been supported, and in particular the approaches respecting chiral SU(3) symmetry of QCD do work well [1,[5][6][7][8]. For the confirmation of the dominance of such aKN molecular component in the Λ(1405), the concept of the compositeness has been used in recent works [9,10].…”