Upper bounds on the fine structure constant and on nucleon magnetic moments in terms of Compton scattering cross-sections

Abstract

We derive and compare with experimental data the bound α≤−λm_p-m_pν₁²/2π²∫^∞_ν0dν'σ_tot(ν')/(ν'²+ν₁²)+2πm_p[∫^∞_ν0ν'²dν'σ_tot(ν')/(ν'²+ν₁²){ν'²(dσ/dt)₀+πλ²+2ν'|λ|√π√(dσ/dt)₀−σ²_tot/16π}]⁻¹, where α is the fine-structure constant, m_p the proton mass, ν₀ the photo-pion production threshold, σ_tot and (dσ/dt)₀ are the unpolarized total hadronic photo-absorption cross section on protons and the unpolarized forward differential cross section for proton Compton scattering at photon-lab energy ν', and λ and ν₁ are any real numbers. We derive similar bounds on proton and neutron magnetic moments.