arXiv2009
JLab has been at the forefront of a program to measure the nucleon spin-dependent structure functions over a wide kinematic range, and data of unprecedented quality has been extracted in all three experimental halls. Moments of these quantities have proven to be powerful tools to test QCD sum rules and provide benchmark tests of Lattice QCD and Chiral Perturbation Theory. Precision measurements of $g_{1,2}^n$ and $g_1^p$ have been performed as part of the highly successful `extended GDH program', but data on the $g_2^p$ structure function remain scarce. We discuss here JLab experiment E08-027, which will measure quantity $g_2^p$ in the resonance region at low $Q^2$. These data will be used to test the Burkhardt-Cottingham sum rule and to extract the higher moments $δ_{LT}^p(Q^2)$ and $\overline{d}_2^p(Q^2)$. Data in the $Q^2$ range $0.02<Q^2<0.4$ GeV$^2$ will provide unambiguous benchmark tests of $χ$PT calculations on the lower end, while probing the transition region at the high $Q^2$ end where parton-like behaviour begins to emerge. This data will also have a significant impact on our theoretical understanding of the hyperfine structure of the proton, and reduce the systematic uncertainty of previous experiments which extracted the $g_1^p$ structure from purely longitudinal measurements.