The Proton Structure Function F₂

The proton structure function F₂ is related to the double differential cross section for inclusive ep scattering including photon and Z⁰ exchange via the following formula:

with . is the longitudinal structure function, is the parity violating term, and is the radiative correction. For comparison with other experiments we measure F₂ containing only contributions from virtual photon exchange. Therefore we have to absorb the contributions from the Z⁰ exchange in a correction factor . This correction is 6% for the highest Q² bin shown in this analysis and lower for all the other bins. Also the corrections due to the longitudinal structure function and the radiative corrections are small (lower than 15% and 5% respectively), and can be absorbed in correction factors , from QCD prescriptions, and , from the HERACLES Monte Carlo. This results in the following equation for F₂:

To derive F₂ from the observed double differential cross section, an unfolding method is used.

  
Figure 4: Proton structure function F₂ as a function of x. The inner error bars show the statistical error only, while the outer bars show the statistical and the systematic error added in quadrature. Q² is given in GeV².

The results for the DA method are shown in figure 4. Our most important systematic check is the comparison of the values of F₂ for the DA and the electron method. These two methods use overlapping data samples, but the reconstruction of the kinematic variables is largely independent. Within the statistical errors there is very good agreement between the two methods.