The ρ-Higgs Portal in Twistorial Spectral Quantum Vacuum Theory: Predictions for TeV-Scale Collider Searches

We derive a unique scalar collective mode ρ as the spectral condensation order parameter ofthe Twistorial Spectral Quantum Vacuum Theory (TSQVT). From the heat-kernel expansionof the twistorial spectral action we derive the portal interaction β ρ|H|2 and compute thecoefficients α,β,γ in terms of spectral moments f0,f2,f4 and finite internal Dirac data. Weshow that ⟨ρ⟩ ̸ = 0 is a natural outcome of the spectral potential and that electroweak symmetrybreaking is induced without introducing ad hoc scalar parameters. We compute the full massmatrix and mixing angle tan2θ = 2δm2/(m2ρ − m2h) with all entries expressed in TSQVTparameters, leaving at most one phenomenological scale to be fixed by data after adopting amatching scheme for quantum corrections (parametrized by κspec with a theoretically boundedrange). We show how this signature is distinguishable from a generic singlet, radion, or dilatonby production mode ratios and decay branching patterns. This work provides a falsifiable,parameter-economic realization of a spectral Higgs portal