Some Issues in a Gauge Model of Unparticles

TL;DR

This paper examines a gauge model of unparticles, highlighting issues with unitarity, Ward identities, and singularities, and suggests the model's limitations in mimicking dynamical gauge boson effects.

Contribution

It identifies fundamental inconsistencies in a gauge unparticle model, including violations of Ward identities and non-integrable singularities, questioning its viability.

Findings

Non-integrable singularities in physical quantities

Violation of Ward identity due to lack of dispersion relation

Extension of the (2-d) rule to triple gauge boson Green functions

Abstract

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and Ward identity of physical amplitudes. We find that non-integrable singularities arise in physical quantities like cross section and decay rate from gauge interactions of unparticles. We also show that Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward-Takahashi identity for general Green functions is incorporated in the model. A previous observation that the unparticle's (with scaling dimension d) contribution to the gauge boson self-energy is a factor (2-d) of the particle's has been extended to the Green function of triple gauge bosons. This (2-d) rule may be generally true for any point Green functions of gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.