On the Kinematic Reconstruction of Deep Inelastic Scattering at HERA: the $Σ$ Method

We review and compare the reconstruction methods of the inclusive deep inelastic scattering variables used at HERA. We introduce a new prescription, the $\Sigma$ method, which allows to measure the structure function of the proton $F_2(x,Q^2)$ in a large kinematic domain, and in particular in the low x-low$Q^2$ region, with small systematic errors and small radiative corrections. A detailed comparison between the $\Sigma$ method and the other methods is shown. Extensions of the $\Sigma$ method are presented. The effect of QED radiation on the kinematic reconstruction and on the structure function measurement is discussed.