Comparison to the theory

In order to see if this number is meaningful, we compare it, for example, with the value given by the ALLM97 parametrisation [7], that includes the new low $x$ and low $Q^2$ HERA data. The theoretical value is

$$\sigma_{e p}^{ALLM}(Q^2<0.3; y> 0.6) = 0.989 \;\; \mu b.$$ (13)

The result is in agreement with the extracted cross section. It is important to stress that even if this analysis can, in principle, improve the knowledge of the $\sigma _{e p}$ one has to notice that the experimental result has to be taken with some care. For example, it depends critically on the shape of the background assumed and a more refined study should be performed.

Table: In the table are reported the deviations on the unfolded number of events due to the different systematic studies. In addition is shown the result obtained in the nominal analisys and the corrected one.

$h_l$	$\mu_l \cdot 10^{-3}$	$\delta \mu_l\cdot 10^{-3}$	$u_l\cdot 10^{-3}$
1 positron energy scale	$\left\{ \begin{array}{c} +1\sigma \;\;\;232.1 \\ -1 \sigma \;\;\;229.4 \end{array} \right .$	-0.76	1.3
2 hadron energy scale	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 235.4 \\ -1 \sigma \;\;\; 226.5 \end{array} \right .$	-0.28	4.7
3 X position	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 231.3 \\ -1 \sigma \;\;\; 231.4 \end{array} \right .$	-0.12	0.05
4 Y position	$\left\{ \begin{array}{c} +1 \sigma \;\;\;231.1 \\ -1 \sigma \;\;\; 231.3 \end{array} \right .$	-0.30	0.1
5 $F_L$	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 231.5 \\ -1 \sigma \;\;\;231.5 \end{array} \right .$	0.0	0.0
6 vertex position	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 231.7 \\ -1 \sigma \;\;\;231.3 \end{array} \right .$	-0.01	0.2
7 Php efficiencies	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 217.2 \\ -1 \sigma \;\;\;248.9 \end{array} \right .$	1.59	15.9
8 Beam gas	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 230.1 \\ -1 \sigma \;\;\; 233.0 \end{array} \right .$	0.10	1.5
9 $E-P_z$ cut	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 228.6 \\ -1 \sigma \;\;\; 235.7 \end{array} \right .$	0.62	3.5
10 $y_{JB}$	$\left\{ \begin{array}{c} +1 \sigma \;\;\; 230.6 \\ -1 \sigma \;\;\; 231.2 \end{array} \right .$	-0.60	0.3
		0.24	17.0
Nominal analisys: $\mu_0 \pm u_0$		(231.5 $\pm$ 2.0) $\cdot 10^3$
Final result: $\mu_f \pm u_f$		(232 $\pm$ 17) $\cdot 10^3$