No-Go Bounds on Electromagnetic-Topology-to-Higgs Coupling via Einstein-Cartan Torsion: Planck Suppression and Alternative Coupling Paths

Abstract

We investigate whether electromagnetic fields with non-trivial topological structure — specifically, non-zero magnetic helicity in Hopf-fibration configurations — can couple to the Higgs sector through spacetime torsion in Einstein-Cartan gravity. We derive the torsion-Higgs coupling Lagrangian LST = -(ξ/4)Sµνρ Sµνρ|φ|2 from the Einstein-Cartan-Sciama-Kibble action via explicit variational procedure (Appendix A) and establish the phase transition threshold ε ≥ 2λv2 ≈ 15,734 GeV2. Our central result is a set of no-go bounds. The standard EC torsion channel is suppressed by ~10129 orders relative to threshold for laboratory fields (B ~ 20 T). Three alternative paths are quantitatively analyzed: Chern-Simons coupling to a BSM pseudoscalar (deficit: ~45 orders), axion-like particle mixing (deficit: ~53 orders with optimistic astrophysical bounds), and Nieh-Yan topological density (deficit: ≥ 40 orders under generous assumptions). We show these bounds are frame-invariant under Jordan-to-Einstein conformal transformation. The minimum deficit of ~40 orders across all analyzed paths establishes a rigorous benchmark for any future theory proposing EM-topology-to-scalar coupling. Null-result experimental protocols are proposed that would independently constrain torsion-scalar coupling constants.

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