A Complete Diagrammatic Implementation of the KinoshitaLeeNauenberg Theorem at NexttoLeading Order
Abstract
We show for the first time in over 50 years how to correctly apply the KinoshitaLeeNauenberg theorem diagrammatically in a nexttoleading order scattering process. We improve on previous works by including all initial and final state soft radiative processes, including absorption and an infinite sum of partially disconnected amplitudes. Crucially, we exploit the Monotone Convergence Theorem to prove that our delicate rearrangement of this formally divergent series is correct. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons that then cancels in the physically observable cross section. We derive the first complete nexttoleading order, highenergy Rutherford elastic scattering cross section in the $\overline{\mathrm{MS}}$ renormalization scheme as an explicit example of our procedure.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.00763
 Bibcode:
 2017arXiv170100763K
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Nuclear Theory
 EPrint:
 5 pages, 2 figures