Leading logarithms for the nucleon mass

Abstract

Within the heavy baryon chiral perturbation theory approach, we have studied the leading logarithm behaviour of the nucleon mass up to four-loop order exactly and we present some results up to six-loop order as well as an all-order conjecture. The same methods allow to calculate the main logarithm multiplying the terms with fractional powers of the quark mass. We calculate thus the coefficients of $m^{2n+1}{\log }^{(n-1)}({\mu }^2/m^2)$ and $m^{2n+2}{\log }^n({\mu }^2/m^2)$, with $m$ the lowest-order pion mass. A side result is the leading divergence for a general heavy baryon loop integral.

Comments: 24p, misprints corrected, some minor reformulations