Lorentz contracted proton

Abstract

Abstract:The proton charge and magnetization density distributions can be related to the well known Sachs electromagnetic form factors G E,M (q 2 ) through Fourier transforms, only in the Breit frame. The Breit frame however moves with relativistic velocities in the Lab and a Lorentz boost must be applied before extracting the static properties of the proton from the corresponding densities. Apart from this, the Fourier transform relating the densities and form factors is inherently a non-relativistic expression. We show that the relativistic corrections to it can be obtained by extending the standard Breit equation to higher orders in its 1/c 2 expansion. We find that the inclusion of the above corrections reduces the size of the proton as determined from electron proton scattering data by about 4%.

Update on the impact of the proton radius on the neutron star radius

“…Applying the relativistic correction explained in Ref. [11], the radius decreases to 0.844 fm [12], which is very close to the recent muonic hydrogen atom measurement [3].…”

Short range interactions in the hydrogen atom

“…One of the application of this principle is the Breit equation which starting from the elastic electron proton scattering amplitude gives us some well known interaction terms (like the Coulomb, electron Darwin, fine and hyperfine structure [15]) and some new input in the non-relativistic picture (like the proton Darwin and retardation terms [6,15]). Finally, it is possible to include in the Breit equation, the finite size corrections in an elegant way by using the most general current of the proton and replacing…”

“…This implies that we will not take into account terms with spins or momentum dependent interactions. We are then left with the ep interaction potential given by [6],…”

“…Today it has become a laboratory for precision physics (especially from the experimental point of view) where several areas of physics are combined to explain the intricacies of this rather simple system. The inputs required are taken from particle physics [1] (as such the hydrogen atom constitutes also a testing ground for fundamental theories like Quantum Electrodynamics (QED) and its electroweak extension [2]), quantum field theories which provide the necessary formalism (the two body Breit equation [3,4], the one-body Dirac equation or the Bethe-Salpeter equation [5]) and nuclear (or hadronic) physics contributing to the physics of the finite extension of the central nucleus [6,7]. Indeed, latest efforts in the field tend to extract the static properties of the proton from hydrogen transitions [6,8,9].…”

“…Finally, the scalar interaction potential V ep which includes now the electron Darwin term [6] has a large repulsive core close to the center. By reversing the sign of the electron charge we arrive at the interaction Hamiltonian of the positron-proton system.…”