Breakdown of regularization scheme equivalence in massive $\lambda\phi^4$ theory

Through a two loop self-energy diagram in massive $\lambda\phi^4$ theory, we demonstrated that the equivalence between dimensional regularization (DR) and cut-off regularization yield \emph{broke down} in contrast to the conventional expectation. Then we employed a differential equation approach to aid the analysis and the result obtained in this approach also showed disagreement with DR. The disagreement or in-equivalence between DR and cut-off like regularization schemes were shown to be not removable in any consistent use of DR in massive $\lambda\phi^4$ theory. The applicability of DR in gauge field theories like QCD and QED was argued to be guaranteed by gauge invariance