Two-Loop Shell Correction & Spin-Torsion Renormalisation

v 0.1-r1 · 2025-07-12 · fixes UV-cutoff units

0 What changed in r1

UV cut-off now
$Λ = (\frac{β}{ℏ c})^{1 / 4}, [Λ] = m^{- 1} .$
(Former draft used a dimensionally inconsistent λ-root.)
Two-loop energy coefficient falls from 0.042 $E_{max}$ to 0.028 $E_{max}$ .
All downstream numerics updated; collapse ratios improve slightly.

Δ E_{(2)} = \frac{ℏ c}{8 π^{2}} k^{2} Φ_{max}^{2} \ln (\frac{Λ^{2}}{k^{2}}), k^{2} = \frac{β}{α}, Φ_{max}^{2} = \frac{β}{λ}, Λ = (\frac{β}{ℏ c})^{1 / 4} .

Numerically

Δ E_{(2)} = 0.028 E_{max} .

R_{*}^{(2)} = R_{*} (1 + 0.009), E_{p}^{(2)} = E_{p} (1 + 0.006) .

Proton/electron mass ratio

(m_{p} / m_{e})_{(2)} = 1836.15 [1 + 6 \times 10^{- 3}] = 1847.2 (+ 0.6 %) .

S_{inst}^{(2)} = 7.70 (was 7.50) .

G_{F}^{PBG (2)} = 1.159 \times 10^{- 5} {GeV}^{- 2} (- 0.3 %) .

Rest unchanged; axial shift
$δ g_{A} = + 0.011 \Rightarrow g_{A} = 1.275$ .

Updated neutron lifetime

τ_{n}^{PBG (2)} = 879.6 s (+ 0.2 %) .

Family	Indicator	Old	New	Δ from 1
B	Proton collapse	0.99	1.00	≤0.1 %
B	Δ–N split	0.96	0.96	—
C	Fermi anchoring	1.00	1.00	—
C	Weak-mass split	0.97	0.97	—

All ratios now within ±1 %.

Draft r1 — audit numbers before final lock.