Baryon masses at second order in large-N chiral perturbation theory

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We consider flavor breaking in the the octet and decuplet baryon masses at second order in large-N chiral perturbation theory, where N is the number of QCD colors. We assume that 1/N 1/NF mₛ / Λ≫ mᵤ,d/Λ, αEM, where NF is the number of light quark flavors, and mᵤ,d,ₛ / Λ are the parameters controlling SU(NF) flavor breaking in chiral perturbation theory. We consistently include non-analytic contributions to the baryon masses at orders mq³/², mq² mq, and (mq mq) / N. The mq³/² corrections are small for the relations that follow from SU(NF) symmetry alone, but the corrections to the large-N relations are large and have the wrong sign. Chiral power-counting and large-N consistency allow a 2-loop contribution at order mq² mq, and a non-trivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are non-trivial consequences of the 1/N expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is 7 for the I = 0 mass differences and 0.35 for the I ≠ 0 mass differences, consistent with the expectation that the error is of order 1/N² 10%.