pSPSS signal properties at GAIA-ee with ILC and FCC-ee benchmarks

Abstract

The phenomenological symmetry protected seesaw scenario (pSPSS) provides a framework for incorporating heavy neutrinos into extensions of the Standard Model, yielding potentially observable signatures at high-energy colliders. In this paper, we investigate the properties of pSPSS signals at a hypothetical electron-positron collider that possesses a circumference the same as of the Earth, the Global Accelerator for Interactions and Anomalies (GAIA), conceived as the upper limit of how large of a collider can be built on Earth and what energy is achievable using current technology. The performance of this particle collider is reviewed alongside proposed collider designs, namely the International Linear Collider (ILC) and the electron-positron Future Circular Collider (FCC-ee). Monte Carlo simulations were done for identical pSPSS processes at center-of-mass energies corresponding to each collider design. Key observables, including hadronic jets, missing transverse energy, and muons, were analyzed through superimposed histograms to assess variations in signal behavior across energy scales. The results show an inverse relationship between the cross section and center-of-mass energy. GAIA-ee exhibits a statistically limited performance for the pSPSS signal, while the FCC-ee yields the highest event rates. These findings suggest that the high-luminosity Z pole environment is the optimal condition for discovering the pSPSS signal and illustrate the role of collider scale in probing Beyond the Standard Model scenarios. This study positions GAIA-ee as a conceptual upper bound limit for Earth-based collider designs and provides insight into how extreme energy scales may influence the observability of heavy neutrino signatures within the pSPSS framework.