Unparticle self-interactions

TL;DR

This paper develops techniques to analyze unparticle self-interactions within conformal field theories, enabling a better understanding of the production and scattering of unparticle stuff through conformal partial wave expansion.

Contribution

It introduces methods for studying unparticle self-interactions using conformal partial wave expansion, applicable to inclusive and exclusive processes, and exemplifies these in a solvable 2D model.

Findings

Unparticle self-interactions can be decomposed into contributions from various conformal operators.

The methods provide a framework analogous to particle scattering in quantum field theory.

Application to a 2D solvable model demonstrates the approach's effectiveness.

Abstract

We develop techniques for studying the effects of self-interactions in the conformal sector of an unparticle model. Their physics is encoded in the higher n-point functions of the conformal theory. We study inclusive processes and argue that the inclusive production of unparticle stuff in standard model processes due to the unparticle self-interactions can be decomposed using the conformal partial wave expansion and its generalizations into a sum over contributions from the production of various kinds of unparticle stuff, corresponding to different primary conformal operators. Such processes typically involve the production of unparticle stuff associated with operators other than those to which the standard model couples directly. Thus just as interactions between particles allow scattering processes to produce new particles in the final state, so unparticle self-interactions cause the production of various kinds of unparticle stuff. We discuss both inclusive and exclusive methods for computing these processes. The resulting picture, we believe, is a step towards understanding what unparticle stuff "looks like" because it is quite analogous to way we describe the production and scattering of ordinary particles in quantum field theory, with the primary conformal operators playing the role of particles and the coefficients in the conformal partial wave expansion (and its generalization to include more fields) playing the role of amplitudes. We exemplify our methods in the 2D toy model that we discussed previously in which the Banks-Zaks theory is exactly solvable.