Abstract
.A complete and minimal relativistic Lagrangian is constructed at next-to-leading order for SU(3) chiral perturbation theory in the presence of baryon octet and baryon decuplet states. The Lagrangian has 13 terms for the pure decuplet sector, 6 terms for the transition sector from baryon octet to decuplet and (as already known from the literature) 16 terms for the pure octet sector. The minimal field content of 25 of these terms is meson-baryon four-point interactions. 3 terms give rise to the mass splitting for baryon octet and decuplet states, respectively. 2 terms give rise to overall mass shifts. 4 terms provide anomalous magnetic moments and a decuplet-to-octet magnetic transition moment. 1 term leads to an axial vector transition moment. It is shown that meson-baryon three-point coupling constants come in at leading order whereas no additional one appears in the minimal Lagrangian at next-to-leading order. Those low-energy constants that give rise to mass splitting and magnetic moments, respectively, are determined. Predictions are provided for radiative decays of decuplet to octet baryons.
Highlights
Introduction and summaryOne of the research challenges within the framework of the standard model of particle physics [1] is to understand the non-perturbative confinement regime of quantum chromodynamics (QCD)
For the octet and for the decuplet the flavor breaking terms that appear at next-to-leading order (NLO) are capable of splitting up the baryon masses such that they are sufficiently close to the physical masses
The NLO Lagrangian contains all independent terms of order p2 where p denotes a small momentum or Goldstone boson mass
Summary
One of the research challenges within the framework of the standard model of particle physics [1] is to understand the non-perturbative confinement regime of quantum chromodynamics (QCD). In the present work we will construct a complete relativistic next-to-leading order (NLO) Lagrangian for the one-baryon three-flavor sector including the lowest-lying octet and decuplet states. The actual challenge is to provide a minimal Lagrangian, i.e. independent interaction terms that do not lead to the very same observables; see the corresponding discussions in [27,28,29,30] This task has been carried out up to (including) next-to-next-to-. At NLO there are 14 meson-baryon four-point interactions that involve the decuplet states, in line with the findings of [18]. The leading-order (LO) Lagrangian provides meson-baryon three-point interactions. For the three-point interaction of pseudoscalar mesons with baryon decuplets one can have a por an f-wave The latter, must be of order O(p3) which is only NNLO.
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