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<p>Experiments at Jefferson Lab have been conducted to extract the nucleon spin-dependent
structure functions over a wide kinematic range. Higher moments of these quantities
provide tests of QCD sum rules and predictions of chiral perturbation theory ($\chi$PT).
While precise measurements of $g_{1}^n$, $g_{2}^n$, and $g_1^p$ have been extensively
performed, the data of $g_2^p$ remain scarce. Discrepancies were found between existing
data related to $g_2$ and theoretical predictions. Results on the proton at large
$Q^2$ show a significant deviation from the Burkhardt-Cottingham sum rule, while results
for the neutron generally follow this sum rule. The next-to-leading order $\chi$PT
calculations exhibit discrepancy with data on the longitudinal-transverse polarizability
$\delta_{LT}^n$. Further measurements of the proton spin structure function $g_2^p$
are desired to understand these discrepancies.</p><p>Experiment E08-027 (g2p) was
conducted at Jefferson Lab in experimental Hall A in 2012. Inclusive measurements
were performed with polarized electron beam and a polarized ammonia target to obtain
the proton spin-dependent structure function $g_2^p$ at low Q$^2$ region (0.02$<$Q$^2$$<$0.2
GeV$^2$) for the first time. The results can be used to test the Burkhardt-Cottingham
sum rule, and also allow us to extract the longitudinal-transverse spin polarizability
of the proton, which will provide a benchmark test of $\chi$PT calculations. This
thesis will present and discuss the very preliminary results of the transverse asymmetry
and the spin-dependent structure functions $g_1^p$ and $g_2^p$ from the data analysis
of the g2p experiment .</p>
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