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The nucleon and Delta-resonance masses in relativistic chiral effective-field theory

We study the chiral behavior of the nucleon and $Δ$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $πN$ and $πΔ$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $πN$-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and $Δ$ masses, while inclusion of the $πΔ$ loops tends to spoil this agreement.