Lower bound on the proton charge radius from electron scattering data

Franziska Hagelstein,Vladimir Pascalutsa

doi:10.1016/j.physletb.2019.134825

Franziska Hagelstein, Vladimir Pascalutsa

Open Access

https://doi.org/10.1016/j.physletb.2019.134825

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Abstract

The proton charge-radius determinations from the electromagnetic form-factor measurements in electron-proton (ep) scattering require an extrapolation to zero momentum transfer (Q2=0) which is prone to model-dependent assumptions. We show that the data at finite momentum transfer can be used to establish a rigorous lower bound on the proton charge radius, while bypassing the model-dependent assumptions that go into the fitting and extrapolation of the ep data. The near-future precise ep experiments at very low Q2, such as PRad, are expected to set a stringent lower bound on the proton radius.

Highlights

The proton charge radius is traditionally accessed in elastic electron-proton scattering at small momentum transfers [1,2]
Let us recall that a spin-1/2 particle, such as the proton, has two electromagnetic form factors
An extraction of the proton charge radius from ep scattering requires an extrapolation to zero momentum transfer, which nowadays is entangled in the analysis of ep data

Summary

Introduction

The proton charge radius is traditionally accessed in elastic electron-proton (ep) scattering at small momentum transfers (low Q ) [1,2]. A “weak link” of the proton-radius extractions from ep experiments is the extrapolation to zero momentum transfer. Similar extrapolation problems should exist in the extractions based on lattice QCD, since the lowest momentum transfer therein is severely limited by the finite volume. We show that the form-factor data at finite Q 2 provide a lower bound on the proton charge radius.

Basic ingredients of the radius extraction

Positivity bounds

Direct determination

Overall normalization factor

Conclusion