# New Insight in the $Q^2$-Dependence of Proton Generalized Polarizabilities

## TL;DR

This study investigates the $Q^2$-dependence of proton generalized polarizabilities through virtual Compton scattering at new momentum transfer values, revealing a rapid fall-off of electric polarizability and mapping magnetic polarizability in the low-$Q^2$ region.

## Contribution

It provides new experimental data on proton generalized polarizabilities at unexplored $Q^2$ values, enhancing understanding of proton structure.

## Key findings

- $ ext{Alpha}_{E1}(Q^2)$ decreases rapidly with $Q^2$
- First precise mapping of $eta_{M1}(Q^2)$ at low $Q^2$
- Results differ from previous measurements at $Q^2=0.33$ GeV$^2$

## Abstract

Virtual Compton scattering on the proton has been investigated at three yet unexplored values of the four-momentum transfer $Q^2$: 0.10, 0.20 and 0.45 GeV$^2$, at the Mainz Microtron. Fits performed using either the low-energy theorem or dispersion relations allowed the extraction of the structure functions $P_{LL} -P_{TT} / \epsilon$ and $P_{LT}$, as well as the electric and magnetic generalized polarizabilities $\alpha_{E1}(Q^2)$ and $\beta_{M1}(Q^2)$. These new results show a smooth and rapid fall-off of $\alpha_{E1}(Q^2)$, in contrast to previous measurements at $Q^2$ = 0.33 GeV$^2$, and provide for the first time a precise mapping of $\beta_{M1}(Q^2)$ in the low-$Q^2$ region.