sigma_nu_weak_ref_cm2
plain-language theorem explainer
sigma_nu_weak_ref_cm2 supplies the absolute reference cross-section for the weak neutrino channel at 1 GeV in cm² units. Dark-matter normalization studies cite it to fix the expected interval 5.2e-38 to 5.4e-38 cm² before scaling by the J(φ) ratio. The definition is a direct product of the squared Fermi prediction, the reference energy squared, and the GeV^{-2} to cm² conversion.
Claim. The reference weak neutrino cross-section is given by $G_F^2 E^2_{ref} (0.3894×10^{-27})$ cm², where $G_F$ is the predicted Fermi constant in GeV^{-2} and $E_{ref}=1$ GeV.
background
The P0-A6 module defines the weak neutrino reference channel used to normalize dark-matter cross-section predictions. row_fermi_pred supplies the Fermi constant prediction $1/ (√2 vev_canonical²)$ in GeV^{-2}. E_ref_GeV fixes the reference energy at 1 GeV and gev2_to_cm2 supplies the conversion factor 0.3894×10^{-27} cm²/GeV^{-2}.
proof idea
The definition is a one-line arithmetic product that squares row_fermi_pred, multiplies by E_ref_GeV squared, and scales by gev2_to_cm2.
why it matters
This definition anchors the P0-A6 weak-reference row and supplies the input to DarkMatterWeakReferenceCrossSectionScoreCardCert together with row_weak_ref_cross_section_band and row_sigma_DM_weak_ref_band. It converts the Fermi constant prediction into an absolute cross-section, producing the derived dark-matter band 5.7e-39 < σ_DM < 7.1e-39 cm². The 1 GeV reference choice remains a protocol normalization inside the Recognition framework.
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