Is the Standard Model Renormalizable?

TL;DR

This paper demonstrates that the Standard Model cannot be fully renormalized because its physical parameters cannot all be made finite while maintaining Ward-Takahashi identities.

Contribution

It provides a proof that the Standard Model's quantum theory is non-renormalizable under the conditions studied.

Findings

Physical masses and couplings cannot all be finite.

Ward-Takahashi identities are incompatible with renormalizability.

Standard Model is non-renormalizable in the Landau gauge.

Abstract

In this paper, we study the renormalizability of the Standard Model in the Landau gauge. On the basis of the Ward-Takahashi identities, we derive exact expressions for the physical masses of the W and Z as well as the renormalized coupling constants in the theory. We show that it is impossible to make all these renormalized quantities finite. Thus the quantum theory of the Standard Model with the divergent amplitudes obeying the Ward-Takahashi identities is not renormalizable.