  The fundamental process of neutrinoless double beta decay, $nn\to ppe^-e^-$,
dominated by the exchange of light Majorana neutrinos, is studied in the
framework of chiral effective field theory. Considering neutrinos as virtual
states, we evaluate the contributions of finite nucleon size to the transition
amplitude in a non-perturbative manner, as opposed to expanding these effects
in powers of momentum. Based on the nucleon form factors expressed in terms of
the dipole and Kelly parametrizations, we find that, at the leading order, the
present scheme could renormalize the amplitude in the context of the standard
mechanism and provide predictions consistent with the previous investigations.
Consequently, we argue that the impact of the effects of finite nucleon size on
the amplitude is comparable to that of the leading-order contact term
introduced in [Phys. Rev. Lett.120, 202001(2018)] in a perturbative scheme. Our
results provide not only a benchmark calculation for the transition amplitude
between two schemes but also evidence for the reasonableness of
non-perturbative treatment for the effects of finite nucleon size in
conventional nuclear many-body methods.
