On the convergence of the chiral expansion for the baryon ground-state masses

Abstract

We study the chiral expansion of the baryon octet and decuplet masses in the isospin limit. It is illustrated that a chiral expansion of the one-loop contributions is rapidly converging up to quark masses that generously encompasses the mass of the physical strange quark. We express the successive orders in terms of physical meson and baryon masses. In addition, owing to specific correlations amongst the chiral moments, we suggest a reordering of terms that make the convergence properties more manifest. Explicit expressions up to chiral order five are derived for all baryon masses at the one-loop level. The baryon masses obtained do not depend on the renormalization scale. Our scheme is tested against QCD lattice data, where the low-energy parameters are systematically correlated by large-N c sum rules. A reproduction of the baryon masses from PACS-CS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC is achieved for ensembles with pion and kaon masses smaller than 600 MeV. Predictions for baryon masses on ensembles from CLS as well as all low-energy constants that enter the baryon masses at N 3 LO are made.

Flavor decomposition of the pion-nucleon σ-term

“…Refs. [17,[33][34][35][36][37][38][39][40]. However, there is an unresolved discrepancy between the precise Roy-Steiner determination of σ πN and present lattice QCD calculations, see Ref.…”

Low-energy constants from charmed baryons on QCD lattices

“…From any such ensemble we take its published pion and kaon masses as given in lattice units and derive their associated quark masses. As in our previous works [2,3] only. As emphasized repeatedly the lattice data sets on hadron masses are quite sensitive to the latter and permit an accurate determination of their values [2,3].…”

“…As in our previous works [2,3] only. As emphasized repeatedly the lattice data sets on hadron masses are quite sensitive to the latter and permit an accurate determination of their values [2,3]. Consistent results were obtained from two independent analysis based on distinct lattice data sets on the hadron masses.…”

On the convergence of chiral expansions for charmed meson masses in the up, down and strange quark masses

“…In a realization of this scheme [8,9] all terms proportional to a heavy tadpole I R must be dropped. In addition the renormalized scalar bubble takes the form…”

“…as properly formulated in terms of on-shell meson masses [8]. In (3.9) we use a notation H R requesting H, R ∈ [0 − ] or H, R ∈ [1 − ].…”