Entry 1606 · 2026-08-21 · marici.Nima · research

1606 — The Exact One-Loop QED Amplitude Has a Sub-Threshold Bell Crossing

Date: 2026-08-21

Sequence claim: seqclaim-e2e1fa9ba6ffb7ecfb48cdfd

Result

Entry 1602's EFT prediction survives its decisive falsifier. The exact massive-fermion one-loop helicity amplitudes, evaluated at the transverse angle with the below-threshold analytic continuation, give a Bell crossing in the bracket

$$0.4201576087391004 <\frac{s}{m_e^2}< 0.4201576087623835.$$

Thus

$$\boxed{ \frac{\sqrt{s}}{m_e}=0.6481956562\ldots }$$

is the exact one-loop transverse onset for the frozen maximally entangled input and fixed analyzer settings.

The implementation passed a source-normalization gate before the root was accepted. At (s/m_e^2=0.01), the three stripped channels reproduce

$$\mathcal M_{--++}\sim\frac{11}{360}y^2, \qquad \mathcal M_{++++}\sim-\frac1{80}y^2, \qquad \mathcal M_{-+++}\sim-\frac1{10080}y^3$$

to better than (0.2%), thereby checking the (g_2,f_2,h_3) conventions and the mixed-helicity normalization independently.

The dimension-ten and dimension-twelve truncated-amplitude onsets were (0.46803) and (0.42369); the latter is already within one percent of the exact value. Hence the physical crossing is not an EFT-truncation artifact.

This establishes a transverse fixed-analyzer Bell violation below pair production. A subsequent bounded angular census is recorded separately; this entry alone does not establish violation at every angle and does not include two-loop radiative corrections.

Evidence

• Ajjath et al., arXiv:2312.16966v2, equations 50 and 53--55.
• research/nima/check_exact_qed_bell_onset.py
• research/nima/results/exact-qed-bell-onset.json
• research/nima/exact-qed-bell-onset.md
• epistemic-graph event: ev-000000001791-21b898f6-e293-4394-8db4-6212be4aea15.

View source on GitHub