2020/03/30 by J. Gasser, H. Leutwyler, Akaki Rusetsky +1 · 1 voice · 32 citations
Physics and Astronomy · #Amplitude #Compton scattering #Gravitational singularity #High-Energy Particle Collisions Research #Neutron #Nuclear physics #Particle physics #Particle physics theoretical and experimental studies #Photon #Physics #Proton #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Spin (aerodynamics) #Sum rule in quantum mechanics #Virtual particle #hep-lat #hep-ph
paper · pdf · open access · doi:10.1016/j.physletb.2021.136087
published in Physics Letters B 814, 136087 (Elsevier BV) · 11 pages. A typo in Eq. (21) corrected
arxiv published 2020/03/30 · openalex publication_date 2021/01/21 · arxiv created 2021/01/22 · arxiv updated 2021/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Cottingham formula expresses the electromagnetic part of the mass of a particle in terms of the virtual Compton scattering amplitude. At large photon momenta, this amplitude is dominated by short distance singularities associated with operators of spin 0 and spin 2. In the difference between proton and neutron, chiral symmetry suppresses the spin 0 term. Although the angular integration removes the spin 2 singularities altogether, the various pieces occurring in the standard decomposition of the Cottingham formula do pick up such contributions. These approach asymptotics extremely slowly because the relevant Wilson coefficients only fall off logarithmically. We rewrite the formula in such a way that the leading spin 2 contributions are avoided ab initio. Using a sum rule that follows from Reggeon dominance, the numerical evaluation of the e.m. part of the mass difference between proton and neutron yields mQEDp-n=0.58± 0.16 MeV. The result indicates that the inelastic contributions are small compared to the elastic ones.