A Note on Unparticle Decays

TL;DR

This paper investigates the decay properties of scalar unparticles coupled to Standard Model particles, analyzing their propagator's pole structure and spectral function to understand stability and decay rates.

Contribution

It provides a detailed analysis of the unparticle propagator's pole structure with a mass gap, revealing conditions for stability and decay into Standard Model particles.

Findings

A scalar unparticle with a mass gap develops an isolated pole below the continuum.

The pole's position determines whether the unparticle is stable or decays.

Decay widths are related to the pole's proximity to the decay threshold.

Abstract

The coupling of an unparticle operator O_U to Standard Model particles opens up the possibility of unparticle decays into standard model fields. We study this issue by analyzing the pole structure (and spectral function) of the unparticle propagator, corrected to account for one-loop polarization effects from virtual SM particles. We find that the propagator of a scalar unparticle (of scaling dimension 1 < d_U < 2) with a mass gap m_g develops an isolated pole, m_p^2-i m_p Gamma_p, with m_p^2 < m_g^2 below the unparticle continuum that extends above m_g (showing that the theory would be unstable without a mass gap). If that pole lies below the threshold for decay into two standard model particles the pole corresponds to a stable unparticle state (and its width Gamma_p is zero). For m_p^2 above threshold the width is non zero and related to the unparticle decay rate into Standard Model particles. This picture is valid for any value of d_U in the considered range.