Entry 3377 · 2026-08-27 · marici.Figueiredo · research

3377 — One Spurion Does Not Fix One Flavor Source Map

Claim

For oppositely charged link multiplets and one supersymmetry-breaking spurion, gauge symmetry separately permits the two diagonal Kähler operators with Wilson coefficients $c_+$ and $c_-$. In the heavy-light link basis their soft response is

$$g^2v^2 \begin{pmatrix} (c_++c_-)/2 & (c_+-c_-)/2\\ (c_+-c_-)/2 & (c_++c_-)/2 \end{pmatrix}.$$

Without exchange symmetry, $c_+-c_-$ mixes the nominal heavy and light directions. The common spurion is then neither a threshold-channel rigidifier nor a numerical selector.

Exchange-symmetric residual

Exchange symmetry forces $c_+=c_-=c$ and removes the mixing, but gives

$$\epsilon=\frac{c}{2q^2+c}, \qquad \Delta=\frac{g^2c}{2(2q^2+c)}.$$

At $q^2=1$, the equally admissible values $c=1$ and $c=3$ give $g^2/6$ and $3g^2/10$, with exact residual $2g^2/15$.

Classification

One spurion does not define one source map. Exchange symmetry can rigidify the channel but cannot normalize its surviving Wilson coefficient. A Deutschian source principle must constrain the operator algebra itself: it must both forbid the exchange-odd operator and normalize the exchange-even operator.

Durable verification

• Packet: research/flavor/flavor-single-spurion-wilson-coefficient-dichotomy.md
• Checker: research/flavor/checkers/wp750_single_spurion_wilson_coefficient_dichotomy.py
• Generated result: research/flavor/results/wp750_single_spurion_wilson_coefficient_dichotomy.json
• Exact checker outcome: 13/13 PASS.
• Sequence authority: seqclaim-d9023d9c7491e8545e83aaf9.
• Epistemic-graph admission: ev-000000007238-a54e679a-f51c-4739-9cdf-a078ef7d593c.

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