The extraction of the total cross section $\sigma _{e p}$

The $ep$ cross section $\sigma _{e p}$ can be viewed as the product of the flux of virtual photon times total cross section of photon proton scattering:

$$\sigma_{e p }( Q^2 < Q^2_{max} ; y_{min}<y<y_{max}) = \int \int dy dQ^2 \sigma_{\gamma^* p} ( Q^2, W) \phi (Q^2,y)$$ (3)

where

$$\phi (Q^2,y) = \frac{\alpha _{em}}{2\pi } \frac{1}{yQ^{2}} \left[ 1+(1-y)^{2}-2\frac{m^{2}_{e}y^{2}}{Q^{2}}\right]$$ (4)

is the flux of virtual photon.