Comment about the vanishing of the vacuum energy in the Wess-Zumino model

We check the cancellation of the vacuum energy in the Wess-Zumino model at the two-loop order in the component field formalisms with and without auxiliary fields. We show that in both cases the vacuum energy is equal to zero. However, in the formalism where the auxiliary fields are excluded, the vanishing of the vacuum energy arises due to the cancellation between the potential and kinetic energies, while in the formalism with the auxiliary fields, both terms vanish separately.