100TeV Grand Unification Micro-Mechanisms: Heavy Boson Spectrum and FCC Detection

Grand Unified Theories (GUTs) face critical challenges in addressing the fine-tuning problem of the Higgs mass term, where enormous contributions proportional to the GUT scale (over 13 orders of magnitude larger than the weak scale) must be canceled order by order in perturbation theory. This paper focuses on the micro-mechanisms of grand unification at the 100TeV energy scale, a regime validated by recent observations of ultra-high-energy gamma rays (exceeding 100TeV) from astrophysical sources like supernova remnants. We investigate the heavy gauge boson spectrum generated through torsion-induced spontaneous symmetry breaking, a key interaction mechanism that underpins symmetry breaking in quantum systems. The study systematically analyzes the decay characteristics of these heavy bosons and evaluates their detectability at the Future Circular Collider (FCC), particularly focusing on compatibility with existing experimental constraints and collider phenomenology frameworks. By bridging theoretical GUT frameworks with high-energy experimental prospects, this work provides insights into resolving longstanding unification challenges and offers testable predictions for next-generation collider experiments targeting the 100TeV energy frontier.