Connecting spatial moments and momentum densities

TL;DR

This paper introduces a new method to determine spatial moments from momentum space densities, enhancing the analysis of experimental data such as proton form factors, with potential implications for resolving the proton radius puzzle.

Contribution

A novel technique for extracting spatial moments directly from momentum space densities, applicable to various moments including negative and fractional orders.

Findings

Method successfully applied to proton electric form factor

Enables calculation of a wide range of moments from momentum data

Provides a new tool for analyzing experimental density measurements

Abstract

The precision of experimental data and analysis techniques is a key feature of any discovery attempt. A striking example is the proton radius puzzle where the accuracy of the spectroscopy of muonic atoms challenges traditional electron scattering measurements. The present work proposes a novel method for the determination of spatial moments from densities expressed in the momentum space. This method provides a direct access to even, odd, and more generally any real, negative and positive moment with order larger than $-3$. As an illustration, the application of this method to the electric form factor of the proton is discussed in detail.