Abstract: The amplitude of the two-loop level in N-N(nucleon-nucleon) scattering is calculated using covariant chiral effective theory. Based on the skeleton of the box diagram, the two-loop diagram results from the correction of pion self-energy. Two subtraction schemes will be employed for comparison: $\overline {{\rm{MS}}}$ and ${\rm{E}}\overline {{\rm{MS}}}$. The loop amplitude obtained with $\overline {{\rm{MS}}}$ contains terms that violate chiral power counting rules; with ${\rm{E}}\overline {{\rm{MS}}}$, the results are entirely chiral contributions with the exception of non-local “anomalous” ones that must be retained.

Key words: covariant chiral effective field theory, $\scriptstyle\overline {{\rm{MS}}}$ scheme, $\scriptstyle{\rm{E}}\overline {{\rm{MS}}}$ scheme, chiral power counting rules