Absence of a zero-point ambiguity

We study in this work the ambiguity between the two definitions of vacuum energy, namely, the energy of the zero-point fields and the minimum of the effective potential. We name their difference the zero-point ambiguity (ZPA) and show that for a self-interacting mass scalar field in the geometry of Casimir plates and in N = m + 1 space-time dimensions the renormalized ZPA vanishes. So, it is undetectable via Casimir forces.