Phenomenology, Constraints and Renormalization of a Light Scalar Singlet η

This study explores the phenomenology and theoretical viability of a hypothetical CP-even scalar boson η with a mass of 75 GeV, weakly mixing with the Standard Model (SM) Higgs boson (sin θ = 0.01). The model introduces a portal interaction and a vacuum expectation value v_η = 5 GeV, enabling the generation of neutrino masses at the level of 0.1 eV, consistent with experimental constraints. We analyze the boson's production via gluon fusion, decay channels (dominantly η → b b̄, τ⁺τ⁻, μ⁺μ⁻), and collider signatures at the High-Luminosity LHC (HL-LHC) and Future Circular Collider (FCC-hh). The model predicts a detectable signal at HL-LHC with a luminosity of 3000 fb⁻¹ (S/√B ≈ 9.5) and at FCC-hh with 300 fb⁻¹. Loop corrections to lepton masses, electroweak precision observables, and the muon's anomalous magnetic moment are calculated, showing consistency with current bounds. Detection strategies leveraging high-p_T muons, tau-ID algorithms, and machine learning for background reduction are proposed. This work offers a testable framework for beyond-SM physics, addressing open questions such as neutrino masses, and provides prospects for future experimental validation.