Composite Z'

TL;DR

This paper explores the theoretical possibility of a composite Z' boson arising from fermion interactions, showing how low-energy effective models and fixed points determine its properties and mass ratios.

Contribution

It demonstrates how the Stueckelberg model emerges from NJL-type interactions and how compositeness conditions fix the mass ratios and include a possible high-energy remnant mass term.

Findings

The Stueckelberg model is effectively induced via fermion loops.

Mass ratios of scalar and neutrino are fixed by infrared fixed points.

The Z' mass includes a contribution from a high-energy strongly interacting theory.

Abstract

We investigate a possibility of a composite Z' vector boson. For the compositeness, the required gauge coupling g in low energy is not so big, g^2/(4\pi) > 0.015 in the case of the U(1)_{B-L} model. We show that the Stueckelberg model is effectively induced in low energy via the fermion loop from the Nambu-Jona-Lasinio (NJL) model having the vectorial four-fermion interaction. In terms of the renormalization group equations (RGE's), this situation is expressed by the compositeness conditions. We find that the solutions of the RGE's with the compositeness conditions are determined by the infrared fixed points. As a result, the ratio of the masses of the extra electroweak singlet scalar and the right-handed neutrino is fixed. The mass of the composite Z' boson contains the contribution \Delta of the Stueckelberg mass term. This nonzero \Delta might be a remnant of a strongly interacting theory in high energy.