The Proton Spin Structure Function $g_2$ and Generalized Polarizabilities in the Strong QCD Regime

TL;DR

This paper reports the first measurements of the proton's generalized spin polarizabilities in the low Q^2 regime, providing critical data to test and refine Chiral Perturbation Theory predictions in strong QCD interactions.

Contribution

The study presents the first data for the transverse-longitudinal spin polarizability δ_{LT} and extends measurements of ar{d_2} to very low Q^2, offering new insights into nucleon structure and QCD.

Findings

Measured δ_{LT} and ar{d_2} at low Q^2 for the first time.

Results challenge existing χPT calculations, highlighting discrepancies.

Data improve understanding of nucleon spin structure in strong QCD regime.

Abstract

The strong interaction is not well understood at low energy, or for interactions with low momentum transfer $Q^2$, but one of the clearest insights we have comes from Chiral Perturbation Theory ($\chi$PT). This effective treatment gives testable predictions for the nucleonic generalized polarizabilities -- fundamental quantities describing the nucleon's response to an external field. We have measured the proton's generalized spin polarizabilities in the region where $\chi$PT is expected to be valid. Our results include the first ever data for the transverse-longitudinal spin polarizability $\delta_{LT}$, and also extend the coverage of the polarizability $\bar{d_2}$ to very low $Q^2$ for the first time. These results were extracted from moments of the structure function $g_2$, a quantity which characterizes the internal spin structure of the proton. Our experiment ran at Jefferson Lab using a polarized electron beam and a polarized solid ammonia (NH$_3$) target. The $\delta_{LT}$ polarizability has remained a challenging quantity for $\chi$PT to reproduce, despite its reduced sensitivity to higher resonance contributions; recent competing calculations still disagree with each other and also diverge from the measured neutron data at very low $Q^2$. Our proton results provide discriminating power between existing calculations, and will help provide a better understanding of this strong QCD regime.