New Method for Measuring the Ratio $\mu_p G_E/G_M$ Based on the Polarization Transfer from the Initial Proton to the Final Electron in the $e \vec p \to \vec e p$ Process

TL;DR

This paper introduces a novel polarization transfer method to measure the proton form factors ratio, leveraging polarization transfer from the initial proton to the final electron in elastic scattering, with potential for high sensitivity.

Contribution

A new approach based on polarization transfer in elastic scattering to determine the Sachs form factors ratio with enhanced sensitivity.

Findings

Difference in electron polarization can reach 70% depending on form factor scaling.

Numerical analysis shows dependence of electron polarization on momentum transfer and scattering angles.

Method applicable to existing experimental setups for improved form factor measurements.

Abstract

In this letter, we propose a new method for measuring the Sachs form factors ratio ($R =\mu_p G_E/G_M$) based on the transfer of polarization from the initial proton to the final electron in the elastic $e \vec p \to \vec e p$ process, in the case when the axes of quantization of spins of the target proton at rest and of the scattered electron are parallel, i.e., when an electron is scattered in the direction of the spin quantization axis of the proton target. To do this, in the kinematics of the SANE collaboration experiment (2020) on measuring double spin asymmetry in the $\vec e\vec p \to e p$ process, using Kelly (2004) and Qattan (2015) parametrizations, a numerical analysis was carried out of the dependence of the longitudinal polarization degree of the scattered electron on the square of the momentum transferred to the proton, as well as on the scattering angles of the electron and proton. It is established that the difference in the longitudinal polarization degree of the final electron in the case of conservation and violation of scaling of the Sachs form factors can reach 70%. This fact can be used to set up polarization experiments of a new type to measure the ratio $R$.