On proton charge radius definition

¹ Department of Physics, Technical University of Denmark - Fysikvej bld. 307, DK-2800 Kongens Lyngby, Denmark, EU
² Department of Chemical and Biochemical Engineering, Technical University of Denmark Søltofts Plads, bld. 229, DK-2800 Kongens Lyngby, Denmark, EU

Received: 16 June 2019
Accepted: 14 October 2019

Abstract

We find a relation for the proton charge radius in closed form. The result 0.841235641(10) fm agrees with determinations from muonic hydrogen. Our relation is based on a mapping from an intrinsic configuration space for the proton to the observed size in laboratory experiments. The torus of the configuration space leads to periodic potentials in dynamical toroidal angles with the proton charge radius as a scale parameter in the mapping to laboratory space. The periodic potentials allow the introduction of Bloch phase factors which open for period doublings in the wave function. The opening of Bloch degrees of freedom is mediated by the Higgs mechanism. Thus, we find that pi times the proton charge radius equals twice the proton Compton wavelength.