## Dissertations, Theses, and Masters Projects

Fall 2016

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

Physics

Todd Averett

David Armstrong

Carl Carlson

Wouter Deconinck

Jian-Ping Chen

#### Abstract

The $g_2^p$ collaboration performed the first measurement of the reaction $\vec{p}(\vec{e},e')X$ in the kinematic range 0.02 $<$ Q$^2$ $<$ 0.2 GeV$^2$ in the resonance region. Experiment E08-027 took place in Hall A at the Thomas Jefferson National Accelerator Facility from March-May of 2012. Data was taken with a longitudinally polarized electron beam, using an NH$_3$ target polarized in both parallel and perpendicular configurations. Very preliminary results for $g_1^p$ and $g_2^p$ are shown in this thesis. to extract the spin structure functions, asymmetries are calculated from data taken with a 2.2 GeV electron beam and a 5 T target field, and combined with the Bosted model proton cross section. Preliminary dilution factors and preliminary radiative corrections are included in the asymmetry analysis. Sum rules and $\chi$PT allow us to test the Burkhardtt-Cottingham (BC) sum rule and obtain the spin polarizability quantities $\gamma_0$ and $\delta_{LT}$. The BC sum rule, valid for all values of $Q^2$, says that the integral of $g_2$ over all Bjorken $x$ vanishes. The very preliminary result presented here shows the contribution to the integral from the measured kinematic region. Although the contribution from the resonance region is not consistent with the expected result of zero, an extrapolation to high and low $x$ must be included to test whether the BC sum rule is satisfied. The difficulty in $\chi$PT calculations of $\gamma_0$ and $\delta_{LT}$ is how to include the resonance contributions, particularly the $\Delta$-resonance, which dominates. Recent developments have found better agreement with neutron experimental results, however this is little proton data to compare with the calculations, particularly at low $Q^2$. The very preliminary results shown here do not show agreement with any of the current $\chi$PT predictions. However, as this is only the contribution from the measured kinematic region, it is necessary to include the extrapolation outside the resonance region to draw a stronger conclusion. Further analysis is ongoing, and preliminary results, including a cross section extracted from data instead of a model prediction, are expected within the next year.

#### DOI

http://doi.org/10.21220/S2WC7K