Aspects of the Stueckelberg Extension

TL;DR

This work develops a Stueckelberg extension of the electroweak sector by adding a U(1)_X factor that generates a massive Z' through a non-Higgs Stueckelberg coupling to a pseudo-scalar, with the photon remaining massless. It extends both the Standard Model and MSSM (StMSSM), deriving the neutral-boson mass matrix, modified neutral currents, and an expanded neutralino/CP-even scalar sector that includes a new scalar ρ and Stueckelberg fermions; a hidden sector may couple to Z' via mixing, potentially yielding a large invisible width for Z'. The paper analyzes signatures at a linear collider, showing sharp Z' resonances and modified forward-backward asymmetries near the Z' pole, and discusses strategies to detect these signals and disentangle hidden-sector contributions. It also generalizes to an arbitrary number of extra U(1) factors, outlining how axions and gauge fields combine to yield multiple massive directions while preserving a massless photon in generic cases. Overall, the results provide a concrete framework for testing Stueckelberg mass generation, its collider phenomenology, and the possible existence of hidden sectors in future experiments.

Abstract

A detailed analysis of a Stueckelberg extension of the electro-weak gauge group with an extra U(1) factor is presented for the Standard Model as well as for the MSSM. The extra gauge boson gets massive through a Stueckelberg type coupling to a pseudo-scalar, instead of a Higgs effect. This new massive neutral gauge boson Z' has vector and axial vector couplings uniquely different from those of conventional extra abelian gauge bosons, such as appear e.g. in GUT models. The extended MSSM furthermore contains two extra neutralinos and one extra neutral CP-even scalar, the latter with a mass larger than that of the Z'. One interesting scenario that emerges is an LSP that is dominantly composed out of the new neutralinos, leading to a possible new superweak candidate for dark matter. We investigate signatures of the Stueckelberg extension at a linear collider and discuss techniques for the detection of the expected sharp Z' resonance. It turns out that the substantially modified forward-backward asymmetry around the Z' pole provides an important signal. Furthermore, we also elaborate on generalizations of the minimal Stueckelberg extension to an arbitrary number of extra U(1) gauge factors.

Figures (7)

• Figure 1: Plot of the neutralino mass spectrum as a function of $M$ (left), for values $\tan(\beta)=3$, $\mu = 500$, $m_2 = 400$, $m_1 = 300$, $m_S = 500$, $\delta = 0.029$ and of the (squared) components of the LSP also as a function of $M$ (right).
• Figure 2: The mass of the LSP as function of $M$ and $\delta$. Plot of the lowest eigenvalues of the neutralino mass matrix for values $\tan(\beta)=3$, $\mu = 500$, $m_2 = 400$, $m_1 = 300$, $m_S = 500$ as a function of $M$ and $\delta$.
• Figure 3: Plot of the total cross-section $\sigma(e^+e^-\rightarrow \mu^+\mu^-)$ (left) and the forward-backward asymmetry $A_{fb}$ in $e^+e^-\rightarrow \mu^+\mu^-$ (right) in the vicinity of the Z$'$ resonance for $M_{{\rm Z}'}=250\,{\rm GeV}$, $\phi= 0.029$. The values of $\Gamma_{{\rm Z}'}$ are $3\, {\rm GeV}$ (black line), $0.5\, {\rm GeV}$ (blue line), $0.2\, {\rm GeV}$ (green line), $0.08\, {\rm GeV}$ (red line).
• Figure 4: Plot of the total cross-section $\sigma(e^+e^-\rightarrow \mu^+\mu^-)$ (left) and the forward-backward asymmetry $A_{fb}$ in $e^+e^-\rightarrow \mu^+\mu^-$ (right) in the vicinity of the Z$'$ resonance for $M_{{\rm Z}'}=250\,{\rm GeV}$. The values of $\delta$ are $0.1$ (black line), $0.05$ (blue line), $0.01$ (green line), $0.001$ (red line).
• Figure 5: Plot of the total cross-section $\sigma(e^+e^-\rightarrow u\bar{u})$ (left) and the forward-backward asymmetry $A_{fb}$ in $e^+e^-\rightarrow u\bar{u}$ (right) in the vicinity of the Z$'$ resonance for $M_{{\rm Z}'}=250\,{\rm GeV}$, $\phi= 0.029$. The values of $\Gamma_{{\rm Z}'}$ are $3\, {\rm GeV}$ (black line), $0.5\, {\rm GeV}$ (blue line), $0.2\, {\rm GeV}$ (green line), $0.08\, {\rm GeV}$ (red line).