The possibility of physics beyond the Standard Model is studied. The requirement of finiteness of the zero-point energy density and pressure or the requirement of the Lorentz invariance of the zero-point stress-energy tensor in Minkowski space-time, implies regularization sum rules on the number of degrees of freedom and mass of fundamental particles spectrum. The consequences of these sum rules on the existence of particles beyond the Standard Model are studied. If these sum rules are to be satisfied, it is shown that some simple and minimal extensions of the Standard Model such as the two-Higgs-doublet model, right-handed neutrinos, mirror symmetry cannot be complete extensions in their current forms. The only exception is unbroken supersymmetry and may be broken supersymmetry. A comparison between different regularization schemes is also done. It is shown that while all considered regularization schemes give a Lorentz invariant expression for the zero-point stress-energy tensor in Minkowski space, their physical interpretations are quite different.