Proton-Neutron Mass Difference at +33 ppm
The proton-neutron mass difference Δm = m_n − m_p is derived from a two-sector formula at +33 ppm from the measured value.
In plain language
The proton-neutron mass difference Δm = m_n − m_p is derived from a two-sector formula at +33 ppm from the measured value.
Overview
IV.T142 derives the proton-neutron mass difference Δm = m_n − m_p = 1.2933 MeV from a two-sector formula: Δm = (3/16)√3·ιτ⁵ − (3/20)αιτ², at +33 ppm from the experimental value. The first term is the B-C sector (EM-strong) splitting contribution; the second term is the NLO electromagnetic correction.
Detail
The proton-neutron mass difference Δm = m_n − m_p = 1.2933 MeV is crucial for nuclear physics: it determines whether the neutron (slightly heavier) decays to the proton, and influences the neutron/proton ratio in Big Bang Nucleosynthesis. In the Standard Model, Δm arises from a combination of quark mass differences and electromagnetic effects, but computing it precisely from QCD is extremely difficult (a long-standing problem in lattice QCD). Book IV derives Δm from the τ two-sector framework. The proton and neutron are both E₁-level baryons, but they differ in their B-sector (electromagnetic) charge content. The mass difference splits into two contributions: the B-C sector splitting (electromagnetic-strong difference) gives (3/16)√3·ιτ⁵, a term involving the fifth power of ιτ reflecting the five-sector structure of τ. The NLO electromagnetic correction (3/20)αιτ² involves the fine structure constant α and the second power of ιτ. The combined formula at +33 ppm is one of the most precise baryonic mass derivations in Book IV.
Result Statement
IV.T142: Δm = m_n − m_p = (3/16)√3·ιτ⁵ − (3/20)αιτ² at +33 ppm from measured value 1.2933 MeV.