The $m^4 \ln m\,$ Contribution to the Nucleon Mass in CHPT

Abstract

In CHPT the hadron masses obtain loop corrections from the pseudoscalar mesons which are identified with the Goldstone bosons of broken chiral symmetry. An expansion of the baryon mass in the quark masses therefore includes non-analytic terms. We calculate the nucleon mass in the one-loop approximation to order $m^4 \sim m_q^2$. We compare the result in the relativistic and in the heavy mass formulation of the theory and derive matching relations between corresponding low-energy constants. We calculate the pion-nucleon loop in old-fashioned perturbation theory and find a contribution to the $m^4 \ln m$ term from an intermediate state which does not occur in the heavy baryon theory.