The systematic errors of the data come from several sources, listed in Table \ref{table:norm} for the normalizations and Table \ref{table:syst} for the kinematics dependent uncertainties.

First, a relatively small source of the systematics comes from the bin size. To calculate the kinematic coefficients to obtain the spin asymmetries \(A_1\) and \(A_2\) from the measured asymmetries \(A_\parallel\) and \(A_{80}\) we use an average value of the scattered electron energy \(E^{\prime}\) and angle \(\theta_e\). This creates a systematic uncertainty which can be estimated by calculating the asymmetry at the edges of the bins and taking the standard deviation from the mean value.

The next source of systematic errors is associated with the target polarization. To estimate the effect we gathered several thermal equilibrium measurements. The average error associated with target polarization uncertainty is estimated to be about 5%.

needs better discussion of the \(P_{target}\) systematics. James?

The biggest contributions to the systematic errors comes from the internal radiative corrections and from the \(e^+\) - \(e^-\) pairs backgground.

Figure \ref{fig:npion} shows that at small energies the pion contribution rises faster than the electron contribution. To estimate the systematic uncertainty associated with pion contamination we varied the amount of the NH\(_3\) material in Monte Carlo simulation by about 5% which is equal to the uncertainty in packing fraction and amount of the material in which pair conversion can occure by 10% and then calculated effect of this change to the dilution factor associated with pair symmetric background.

Figure \ref{fig:system_pair} shows ratio between the asymmetry calculated with 5% increase of the NH\(_3\) in target and 10% increase of the material in which pair conversion can occure to the initial asymmetry. The systematic uncertainty from this effect is rather small but it is energy dependent. The main uncertainty associated with pair-symmetric background comes from the model estimation of the number of produced pairs. From the data we obtained that the number of pions we reconstruct are smaller by the factor of two from what we should obtain from Monte-Carlo. This can come either from inefficiency of the two cluster trigger or due to the fact that the model we are using is incomplete. Taking into acoount this effect we estimated the relative error and parametrized as function of energy \(\delta\sigma=0.15/e^{E^{\prime}}\cdot A\).

The systematic uncertainty associated with internal radiative corrections we obtained using the results for the asymmetry obtained from different models and taking the standard deviation from the mean Figure \ref{fig:data_iter}.

The uncertainty in packing fraction contributes to the systematic uncertainty not only through the pair-symmetric background but also through the dilution factor directly. Although due to the difference in cross-section between hydrogen and heavier nuclei the 5% effect in packing fraction transfers to about 2% in Asymmetry. It is important to note that with increase of the packing fraction the dilution factor from pair-symmetric baground is smaller but at the same time the dilution factor from simple nuclon counting is larger. So these two effects are partially canceling each other.