  Recently, we have worked out the axial two-nucleon current operator to
leading one-loop order in chiral effective field theory using the method of
unitary transformation. Our final expressions, however, differ from the ones
derived by the JLab-Pisa group using time-ordered perturbation theory (Phys.
Rev. C 93, no. 1, 015501 (2016) Erratum: [Phys. Rev. C 93, no. 4, 049902
(2016)] Erratum: [Phys. Rev. C 95, no. 5, 059901 (2017)]). In this paper we
consider the box diagram contribution to the axial current and demonstrate that
the results obtained using the two methods are unitary equivalent at the
Fock-space level. We adjust the unitary phases by matching the corresponding
two-pion exchange nucleon-nucleon potentials and rederive the box diagram
contribution to the axial current operator following the approach of the
JLab-Pisa group, thereby reproducing our original result. We provide a detailed
information on the calculation including the relevant intermediate steps in
order to facilitate a clarification of this disagreement.
