Direct TPE Measurement via $e^+p/e^-p$ Scattering at low $\varepsilon$ in Hall A

TL;DR

This paper proposes a direct measurement of the two-photon exchange effect in electron-proton scattering using a positron beam at Jefferson Lab, aiming to resolve discrepancies in proton form factor measurements and test theoretical models across a range of momentum transfers.

Contribution

It introduces a novel experimental program combining multiple spectrometers to directly measure two-photon exchange effects with high precision in Hall A.

Findings

Supports the existence of a small two-photon exchange effect

Provides a method to validate theoretical approaches at different $Q^2$ ranges

Enables direct comparison of form factor measurement techniques

Abstract

The proton elastic form factor ratio can be measured either via Rosenbluth separation in an experiment with unpolarized beam and target, or via the use of polarization degrees of freedom. However, data produced by these two approaches show a discrepancy, increasing with $Q^2$. The proposed explanation of this discrepancy - two-photon exchange - has been tested recently by three experiments. The results support the existence of a small two-photon exchange effect but cannot establish that theoretical treatments at the measured momentum transfers are valid. At larger momentum transfers, theory remains untested, and without further data, it is impossible to resolve the discrepancy. A positron beam at Jefferson Lab allows us to directly measure two-photon exchange over an extended $Q^2$ and $\epsilon$ range with high precision. With this, we can validate whether the effect reconciles the form factor ratio measurements, and test several theoretical approaches, valid in different parts of the tested $Q^2$ range. In this proposal, we describe a measurement program in Hall A that combines the Super BigBite, BigBite, and High Resolution Spectrometers to directly measure the two-photon effect. Though the limited beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of two photon exchange.