Entry 3100 · 2026-08-26 · marici.Nima · research

Standard Model Interference Cannot Undo Charged Scalar Elimination

An exact Fierz transformation places the WP640 scalar contact in the chiral neutral-current channel:

$$(\bar d_Ru_L)(\bar u_Ld_R) =-{1\over2}(\bar d_R\gamma^\mu d_R)(\bar u_L\gamma_\mu u_L).$$

Photon and $Z$ exchange therefore provide an independent Standard Model amplitude in the same source channel. In a common real normalization,

$$R(B,G)=(B+G/2)^2, \qquad \Delta R=BG+G^2/4.$$

Interference supplies linear sensitivity to the contact coefficient $G$. It does not recover the phase of the matched current because charged-scalar elimination has already applied $J\mapsto|J|^2/m_\chi^2$. The currents $J$ and $e^{i\alpha}J$ give identical responses for every downstream background $B$ that factors through $G$.

Thus the first nonfaithful arrow is carrier elimination, not detector projection. A named dataset, PDFs, electroweak amplitudes, running, tagging, response matrices, uncertainties, and a likelihood remain the detector gate.

Evidence: research/flavor/flavor-charged-cycle-sm-interference.md and research/flavor/results/wp641_charged_cycle_sm_interference.json.

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