Renormalizability of the leading order operator for neutrinoless double- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> decay incorporating the effects of finite nucleon size

The fundamental process of neutrinoless double \ensuremath{\beta} decay, $nn\ensuremath{\rightarrow}pp{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$, dominated by the exchange of light Majorana neutrinos, is studied in a quasiphenomenological framework based on chiral effective field theory. In the current calculation, we evaluate the contributions of finite nucleon size to the transition amplitude in a nonperturbative manner by incorporating the nucleon form factors. We find that the present approach could renormalize the amplitude in the context of the standard mechanism and provide predictions consistent with the previous investigations. Consequently, we argue that the physics parametrized by the form factors is related to that of the leading-order contact term introduced in [V. Cirigliano et al., Phys. Rev. Lett. 120, 202001 (2018)]. in a perturbative scheme. To solidify our calculation, we also perform nuclear many-body calculations for finite nuclei $^{76}\mathrm{Ge}$ and $^{136}\mathrm{Xe}$. Our results provide not only a benchmark calculation for the transition amplitude between two frameworks but also evidence for the reasonableness of nonperturbative treatment for the effects of finite nucleon size in conventional nuclear many-body methods.