Measurement of Compton scattering at MAMI for the extraction of the electric and magnetic polarizabilities of the proton

TL;DR

This study precisely measured Compton scattering on protons to extract electric and magnetic polarizabilities with unprecedented accuracy, using advanced experimental setups and multiple theoretical models.

Contribution

It provides the most precise proton polarizability measurements to date by combining high-statistics data with comprehensive theoretical analysis.

Findings

Proton electric polarizability: 10.99 ± 0.16 (stat) ± 0.47 (sys) ± 0.17 (spin) ± 0.34 (model)

Proton magnetic polarizability: 3.14 ± 0.21 (stat) ± 0.24 (sys) ± 0.20 (spin) ± 0.35 (model)

Utilized upgraded photon tagging and nearly 4π detector for high-precision data collection.

Abstract

A precise measurement of the differential cross-sections $d\sigma/d\Omega$ and the linearly polarized photon beam asymmetry $\Sigma_3$ for Compton scattering on the proton below pion threshold has been performed with a tagged photon beam and almost $4\pi$ detector at the Mainz Microtron. The incident photons were produced by the recently upgraded Glasgow-Mainz photon tagging facility and impinged on a cryogenic liquid hydrogen target, with the scattered photons detected in the Crystal Ball/TAPS set-up. Using the highest statistics Compton scattering data ever measured on the proton along with two effective field theories (both covariant baryon and heavy-baryon) and one fixed-$t$ dispersion relation model, constraining the fits with the Baldin sum rule, we have obtained the proton electric and magnetic polarizabilities with unprecedented precision: \begin{align*} &{}\alpha_{E1} = 10.99 \pm 0.16 \pm 0.47 \pm 0.17 \pm 0.34 &{}\beta_{M1} = 3.14 \pm 0.21 \pm 0.24 \pm 0.20 \pm 0.35 \end{align*} in units of $10^{-4}$\,fm$^3$ where the errors are statistical, systematic, spin polarizability dependent and model dependent.