On the mass difference between proton and neutron
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 pro...
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doaj-10451abf024846f19ffba1487e0959ff2021-02-25T04:16:42ZengElsevierPhysics Letters B0370-26932021-03-01814136087On the mass difference between proton and neutronJ. Gasser0H. Leutwyler1A. Rusetsky2Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, SwitzerlandAlbert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, SwitzerlandHelmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, Nussallee 14-16, D-53115 Bonn, Germany; Tbilisi State University, 0186 Tbilisi, Georgia; Corresponding author.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 mQED=0.58±0.16MeV. The result indicates that the inelastic contributions are small compared to the elastic ones.http://www.sciencedirect.com/science/article/pii/S0370269321000277Electromagnetic mass differencesDispersion relationsRegge behaviourStructure functionsProtons and neutronsCottingham formula |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
J. Gasser H. Leutwyler A. Rusetsky |
spellingShingle |
J. Gasser H. Leutwyler A. Rusetsky On the mass difference between proton and neutron Physics Letters B Electromagnetic mass differences Dispersion relations Regge behaviour Structure functions Protons and neutrons Cottingham formula |
author_facet |
J. Gasser H. Leutwyler A. Rusetsky |
author_sort |
J. Gasser |
title |
On the mass difference between proton and neutron |
title_short |
On the mass difference between proton and neutron |
title_full |
On the mass difference between proton and neutron |
title_fullStr |
On the mass difference between proton and neutron |
title_full_unstemmed |
On the mass difference between proton and neutron |
title_sort |
on the mass difference between proton and neutron |
publisher |
Elsevier |
series |
Physics Letters B |
issn |
0370-2693 |
publishDate |
2021-03-01 |
description |
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 mQED=0.58±0.16MeV. The result indicates that the inelastic contributions are small compared to the elastic ones. |
topic |
Electromagnetic mass differences Dispersion relations Regge behaviour Structure functions Protons and neutrons Cottingham formula |
url |
http://www.sciencedirect.com/science/article/pii/S0370269321000277 |
work_keys_str_mv |
AT jgasser onthemassdifferencebetweenprotonandneutron AT hleutwyler onthemassdifferencebetweenprotonandneutron AT arusetsky onthemassdifferencebetweenprotonandneutron |
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