  In the framework of heavy-baryon chiral perturbation theory, we investigate
the fixed point structure of renormalization group equations (RGE) for the
ratios of the renormalized low energy constants (LECs) that feature in the
pion-nucleon chiral Lagrangian. The ratios of the LECs deduced from our RGE
analysis are found to be in semi-quantitative agreement with those obtained
from direct fit to the experimental data. The naturalness of this agreement is
discussed using a simple dimensional analysis combined with Wilsonian RGEs.
