DIS kinematics

The event kinematics of deep inelastic scattering, DIS, are determined by the negative square of the four-momentum transfer at the lepton vertex, Q² $\equiv$ - q², and the Bjorken scaling variable, x = Q²/2P ^. q, where P is the four-momentum of the proton. In the quark parton model (QPM), the interacting quark from the proton carries the four-momentum xP. The variable y, the fractional energy transfer to the proton in its rest frame, is related to x and Q² by y $\simeq$ Q²/xs, where $\sqrt{s}$ is the positron-proton centre of mass energy. Because the H1 and ZEUS detectors are almost hermetic the kinematic variables x and Q² can be reconstructed in a variety of ways using combinations of positron and hadronic system energies and angles [1].

Neutral current (NC) DIS occurs when an uncharged boson ( $\gamma$, Z⁰) is exchanged between the lepton and proton. In QPM there is a 1+1 parton configuration, fig. 1a, which consists of a single struck quark and the proton remnant, denoted by ``+1''. At HERA energies there are significant higher-order quantum chromodynamic (QCD) corrections: to leading order in the strong coupling constant, $\alpha_{\rm s}^{}$, these are QCD-Compton scattering (QCDC), where a gluon is radiated by the scattered quark and boson-gluon-fusion (BGF), where the virtual boson and a gluon fuse to form a quark-antiquark pair. Both processes have 2+1 partons in the final state, as shown in fig. 1. There also exists calculations for the higher, next-to-leading (NLO) processes.

HERA provides a unique opportunity to study the scale behaviour of Quantum Chrmodynamics in a single experiment with a cleaner background environment than that obtainable at hadron colliders. The data presented here were taken in 1994 and onwards at the ep collider HERA using the H1 and ZEUS detectors. During this period HERA operated with positrons of energy E_e = 27.5 GeV and protons with energy 820 GeV. A detailed descriptions of the H1 and ZEUS detectors can be found in refs. [2] and [3] respectively.