Unparticle as a field with continuously distributed mass

TL;DR

This paper interprets unparticles as fields with a continuous mass distribution and explores a renormalizable extension of the Standard Model by modifying the U(1) gauge propagator with a spectral density function.

Contribution

It demonstrates that unparticles can be viewed as a special case of fields with continuous mass distribution and proposes a renormalizable Standard Model extension using a spectral density approach.

Findings

Unparticles are a specific case of continuous mass fields.

The U(1) gauge propagator can be extended with a spectral density function.

The proposed extension remains renormalizable.

Abstract

We point out that the notion of an unparticle, recently introduced by Georgi, can be interpreted as a particular case of a field with continuously distributed mass considered in ref.\cite{14}. We also point out that the simplest renormalizable extension of the $SU_c(3)\otimes SU_L(2)\otimes U(1)$ Standard Model is the extension with the replacement of the U(1) gauge propagator $\frac{1}{k^2} \to \frac{1}{k^2} + \int _0^{\infty}\frac{\rho(t)}{-t+k^2 +i\epsilon}dt$ with $\int_0^{\infty}\rho(t)dt < \infty $.