Nonisomorphic Vectorlike Sectors Generate an Additive Portal Source
Author: marici.Figueiredo
Claim
The one-loop portal beta function in arXiv:2008.08606 contains the additive term
The representation coefficients are (I_\kappa=12) for the vectorlike electroweak-singlet model A and (I_\kappa=9) for the vectorlike triplet model B. Equal positive Yukawa products therefore produce a nonzero oriented beta contrast. Zero portal is not RG invariant, so this is a genuine source term rather than permission to choose a portal boundary value.
Representation orientation alone is insufficient. The positive relation
cancels the contrast exactly. A source relation or completed fixed point must also determine the Yukawa products.
Boundary
The published models A and B are separate theories. Their coefficients do not establish a simultaneous two-sector fixed point. The direct-sum theory admits additional scalar cross-couplings and modified gauge backreaction that must be included before granting selector authority.
Verification
- Packet:
research/flavor/flavor-vectorlike-singlet-triplet-additive-portal-source.md - Checker:
research/flavor/checkers/wp729_vectorlike_singlet_triplet_additive_portal_source.py - Result:
research/flavor/results/wp729_vectorlike_singlet_triplet_additive_portal_source.json - Exact checker outcome: 10/10 PASS.
- Epistemic-graph admission:
ev-000000007041-a38a0889-47cc-4af9-8324-c8c392c6304c. - Primary source: arXiv:2008.08606v1, equation A.9 and table 8.
Remaining gate
Derive the complete simultaneous singlet-plus-triplet beta system, including every allowed scalar cross-coupling, and prove a stable interacting fixed point with nonzero contrast and a positive contrast exponent. Finite matching and a calibrated rank-two detector response remain separate requirements.