The relativistic chiral Lagrangian for decuplet and octet baryons at next-to-leading order

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.

Low-energy axial-vector transitions from decuplet to octet baryons

“…This is provided in table I, which is in agreement with [11]. Note that this is an approximation for the decay widths that is accurate up to and including NLO -because there are no additional contributions at NLO [8]. One cannot expect to obtain always the very same numerical result for h A .…”

“…The relevant part of the LO chiral Lagrangian for baryons including the spin-3/2 decuplet states is given by [8,[12][13][14][15][16]]…”

Covariant model for Dalitz decays of decuplet baryons to octet baryons

“…In progress are feasibility studies on the Σð1385Þ, Λð1404Þ and Λð1520Þ Dalitz decays by the HADES collaboration [42][43][44]. Those studies suggest that those decays can be measured at GSI in the next few years and subsequently also at FAIR [18,20,42,45,46].…”

“…In the spacelike region, including the limit Q 2 ¼ 0, there are calculations based on nonrelativistic and relativistic quark models [47,[56][57][58][59][60], Dyson-Schwinger equations [61,62], lattice QCD simulations [63], QCD sum rules [64,65], Skyrme and soliton models [66][67][68], chiral perturbation theory and large N c limit [46,[69][70][71].…”

Chiral Lagrangians for mesons with a single heavy quark

“…Up to now, the chiral Lagrangian in the sector of light pseudoscalar mesons has been constructed up to the O(p 8 ) order [27][28][29][30][31][32][33][34][35]. Recently, there are also developments in the sector of light baryons [36][37][38][39][40][41][42]. However, the existing heavy-light meson chiral Lagrangian is still at low orders.…”