A New Low $Q^2$ Measurement of the Proton's $g_1$ Spin Structure Function from Longitudinal & Transverse Polarized Data

The proton's spin structure has proven to be far more complicated than was originally believed, and has been the subject of a number of experimental investigations. %Early measurements of the proton's spin structure function $g_1$ showed that the proton does not solely derive its spin from the spins of its quarks, starting the `proton spin crisis'. Of particular interest are the spin structure functions $g_1$ and $g_2$, which can be used to generate moments to directly compare experimental results to Chiral Perturbation Theory and other theories of Quantum Chromodynamics (QCD). The proton's $g_1$ structure function has been the subject of two other recent low momentum transfer experiments, but there are currently no published low momentum transfer measurements which collected data on the proton structure functions using both a longitudinally-polarized and a transversely-polarized target at the same kinematics. In this paper, we present the longitudinally polarized results of the Jefferson Lab E08-027 experiment, along with linked moments which combine this new result with the previously published transversely-polarized data from the same experiment. These results provide a proton $g_1$ extraction measured with very high precision across the resonance region, and provide new information on the value of $g_1$ dependent sum rules and moments.