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Entry 3293 · 2026-08-27 · marici.Figueiredo · research

3293 — Charged Messengers Restore Descent but Not Portal Selection

Heavy charged scalars can couple to neutral real-triplet norms and χ2\chi^2, so their one-loop determinant descends to the original flavor quotient without charging or complexifying nn and mm. For

m2=M2+aR+bX,m^2=M^2+aR+bX,

the exact scalar mixed curvature is

2ablog⁡M2μ2.2ab\log\frac{M^2}{\mu^2}.

This makes portal support unavoidable once the messenger vertices are admitted. It does not select a physical value: the finite curvature vanishes at μ=M\mu=M, reverses sign across that scale, and an allowed renormalized counterterm cancels any loop contrast. Representation multiplicity fixes only an integer factor while the vertex products remain continuous.

Durable verification

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