Abstract
Baryon masses and nucleon σ terms are studied with the effective theory that combines the chiral and 1/Nc expansions for three flavors. In particular the connection between the deviation of the Gell-Mann–Okubo relation and the σ term associated with the scalar density u¯u+d¯d−2s¯s is emphasized. The latter is at lowest order related to a mass combination whose low value has given rise to a σ term puzzle. It is shown that while the nucleon σ terms have a well behaved low energy expansion, that mass combination is affected by large higher order corrections non-analytic in quark masses. Adding to the analysis lattice QCD baryon masses, it is found that σπN=69(10) MeV and σs has natural magnitude within its relatively large uncertainty.
Highlights
Baryon mass dependencies on quark masses, quantified by the different σ-terms, are among the fundamental observables in baryon chiral dynamics
The definition of σ terms is through the Feynman-Hellmann theorem1, which, for three flavors, through the physical baryon masses gives access to only two such terms, namely those associated with the SU(3) octet quark mass combinations m3
The emphasis is in that the effective theory can give at NNLO a natural description of baryon masses, including lattice QCD (LQCD) results, along with the axial couplings which have been obtained in LQCD at different quark masses
Summary
Baryon mass dependencies on quark masses, quantified by the different σ-terms, are among the fundamental observables in baryon chiral dynamics. This work analyzes the σ terms through the octet and decuplet baryon masses in the combined chiral and 1/Nc expansions BChPT × 1/Nc. The emphasis is in that the effective theory can give at NNLO (one chiral loop) a natural description of baryon masses, including LQCD results, along with the axial couplings which have been obtained in LQCD at different quark masses.
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