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

We consider flavor breaking in 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~1NF~mₛΛmu,dΛ, αEM, where NF is the number of light quark flavors, and mu,d,sΛ are the parameters controlling SU(NF) flavor breaking in chiral perturbation theory. We consistently include nonanalytic contributions to the baryon masses at orders mq3/2, mq²lnmq, and (mqlnmq)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 two-loop contribution at order mq²lnmq, and a nontrivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are nontrivial consequences of the 1/N expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is 7 MeV for the ΔI=0 mass differences and 0.35 MeV for the ΔI≠0 mass differences, consistent with the expectation that the error is of order 1N²~10%.