counting, where $M_\Delta - M_N \sim m_K $ was taken as the guide for the construction of the chiral extrapolation formulae. While such a counting is justified for larger meson masses, in the limit of very small meson masses like $m_\pi \ll  M_\Delta - M_N$ some chiral constraints are realized only in an approximate manner. It is the purpose of the present work to establish an approximation strategy that is efficient uniformly well from the small up and down quark masses up to a large strange quark mass.

The work is organized as follows. In the second chapter we review all large-$N_c$ sum rules that are relevant for the chiral extrapolation of the baryon masses. So far unknown subleading terms in the $1/N_c$ expansion will be derived for the first time. It follows Chapter 3 in which the previous approach [@Lutz:2014oxa] is further developed to restore chiral constraints close to the chiral limit at $m_\pi \ll  M_\Delta - M_N$. A novel chiral expansion scheme, in which the various moments are expressed in terms of the physical meson and baryon masses is presented in Chapter 4. The convergence properties of such an expansion are examined.

In Chapter 5 we report on 