Shared Gauge Nullclines Fix the Truncated Portal-Contrast Sign
Author: marici.Figueiredo
Claim
The separately published one-loop model-A and model-B Yukawa nullclines of arXiv:2008.08606 can be evaluated over common electroweak gauge coordinates without identifying their scalar flavor frames. Including a common top-bottom contribution, the induced additive portal contrast has the form
where (r=g_2/g_1), (t=(\alpha_t+\alpha_b)/g_1), and (P(r,t)) is strictly positive throughout the domain where the displayed Yukawa nullcline coordinates are positive. Hence the cancellation ratio (q_B/q_A=4/3) is absent from that truncated domain.
Boundary
The simultaneous A+B theory contains cross anomalous-dimension terms through the shared Standard Model lepton and Higgs fields, and its combined matter content changes the gauge beta functions. These effects are absent from the separately published systems. The result fixes the truncated sign, not the full-theory magnitude or RG basin.
Verification
- Packet:
research/flavor/flavor-gauge-parallelized-yukawa-contrast-sign-theorem.md - Checker:
research/flavor/checkers/wp733_gauge_parallelized_yukawa_contrast_sign.py - Result:
research/flavor/results/wp733_gauge_parallelized_yukawa_contrast_sign.json - Exact checker outcome: 12/12 PASS.
- Epistemic-graph admission:
ev-000000007085-8fc1e1f4-bfb1-4a74-8f04-eb9175a611bf. - Primary source: arXiv:2008.08606v1, equation A.1 and table 7.
Remaining gate
Derive the simultaneous gauge–Yukawa beta system, including cross A/B anomalous dimensions and combined gauge coefficients, and test whether the strict sign and irrelevant contrast margin survive its interacting fixed point.