Up- vs down-squark exchange: rate ratio roughly 100
ProvedGoodmanWitten.odd_nucleus_rate_ratiodark-mattermathematical-physicsparticle-physics
With , the ratio of the squared single-nucleon matrix elements of Eq. (4) for the favoured and unfavoured quark flavour satisfies
Since rates are proportional to squared matrix elements, the rate for up-squark exchange on odd- nuclei (or down-squark exchange on odd- nuclei) is roughly 100 times the rate for the opposite flavour.
Formalization Note "Roughly 100 times" is read as order of magnitude .
Preamble
import Mathlib import Definitions.Def_GoodmanWitten_basic
Formal statement
namespace GoodmanWitten
theorem odd_nucleus_rate_ratio :
(100 : ℝ) ≤ ((1 + 1.2) / (1 - 1.2)) ^ 2 ∧ ((1 + 1.2) / (1 - 1.2)) ^ 2 < (1000 : ℝ) := by sorry
end GoodmanWitten
Source
M. W. Goodman and E. Witten, Detectability of certain dark-matter candidates, Phys. Rev. D 31, 3059-3063 (1985), https://doi.org/10.1103/PhysRevD.31.3059, p. 3061, left column, paragraph 'From Eq. (4) we expect...' and g_A = 1.2 below the isovector relation
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.