Absence of fifth-order contributions to the nucleon mass in heavy-baryon chiral perturbation theory

We have calculated the contribution of order Mπ5 in the chiral expansion of the nucleon mass in two-flavour heavy-baryon chiral perturbation theory. Only one irreducible two-loop integral enters, and this vanishes. All other corrections in the heavy-baryon limit can be absorbed in the physical pion-nucleon coupling constant which enters in the Mπ3, term, and so there are no contributions at Mπ5. Including finite nucleon mass corrections, the only contribution agrees with the expansion of the relativistic one-loop graph in powers of Mπ/mN, and is only 0.3% of the Mπ3 term. This is an encouraging result for the convergence of two-flavour heavy-baryon chiral perturbation theory.