Photoproduction

At very low ${Q^2}$, deep inelastic scattering turns into quasi-real photon proton scattering. The lepton proton cross section is given in terms of a photon proton cross section by the Weizsäcker-Williams formula [11] for the photon flux $F(y,{Q^2})$:

$$\frac{d^2 \sigma_{ep}(s)}{d y d {Q^2}} = \sigma^{\gamma p}_{tot}(ys) \cdot (1 + \delta_{RC}) \cdot F(y,{Q^2})$$

$$= \sigma^{\gamma p}_{tot}(ys) \cdot (1 + \delta_{RC}) \cdot \frac{\... ...}} ( \frac{1+(1-y)^2}{y} - \frac{2(1-y)}{y} \cdot \frac{(m_e y)^2}{{Q^2}(1-y)})$$ (17)

The factor $(1 + \delta_{RC})$ takes into account QED radiative corrections to the e-p Born cross section. $\delta_{RC}$ is small ($< 5\%$) over most of the phase space. The photon proton cross section has been measured over a wide range of center-of-mass energy and is in the range of $100\,{\mu {\mbox{\rm b}}}$ to $200\,{\mu {\mbox{\rm b}}}$ as shown in figure 2.5. This translates into a positron proton cross section with $W\,>\,10\,{\mbox{\rm GeV}}$ and for ${Q^2}$ from the kinematical limit to about $1\,{{\mbox{\rm GeV}}}^2$ of $40\,{\mu {\mbox{\rm b}}}$.

Figure: The figure shows the total photoproduction cross section $\sigma^{\gamma p}_{\mbox{\em tot}}$ in dependence of the center-of-mass energy of the $\gamma p$ system. Shown are the values measured by ZEUS and H1, and low energy measurements of many other experiments. The figure has been taken from [12].