Lorentz Contracted Proton

2014/10/15 by D. Bedoya Fierro, Fierro, D. Bedoya, N. G. Kelkar +3
Engineering · Physics and Astronomy · #Atomic and Molecular Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Nuclear Theory (nucl-th) #Particle Accelerators and Free-Electron Lasers #Quantum and Classical Electrodynamics

paper · pdf · doi:10.48550/arxiv.1410.4228

openalex publication_date 2014/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The proton charge and magnetization density distributions can be related to the well known Sachs electromagnetic form factors G_E,M(\bm q²) 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 to the form factors 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/c² expansion. We find that the inclusion of the above corrections reduces the size of the proton determined from electron proton scattering data. Indeed the central value of the latest proton radius of r_p = 0.879 fm as determined from e-p scattering changes to r_p = 0.8404 fm after applying corrections.

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