Beyond the standard model with sum rules

TL;DR

This paper explores the implications of sum rules derived from zero point energy regularization on extensions of the standard model, finding that most simple extensions are incompatible unless supersymmetry is unbroken.

Contribution

It introduces sum rules from zero point energy regularization that constrain possible extensions of the standard model, highlighting supersymmetry as a unique consistent extension.

Findings

Simple extensions like two Higgs doublet model are incompatible with sum rules.

Unbroken supersymmetry can satisfy the sum rules.

Different regularization schemes yield Lorentz-invariant stress-energy tensors with varying interpretations.

Abstract

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 is 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 can not be complete extensions in their current forms. The only exception is unbroken supersymmetry and maybe 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.