Forward Jet Production in Deep Inelastic Scattering at HERA

The hadronic final state in deep inelastic scattering offers a rich field of research for QCD phenomena. This includes studies of hard parton emissions which result in well defined jets, perturbative effects responsible for multiple gluon emissions and the non-perturbative hadronisation process.

HERA has extended the available region in the Bjorken scaling variable, x_Bj, down to values of x_Bj ~ 10^-4, for values of the four momentum transfer squared, Q², larger than a few GeV², where perturbative calculations in QCD are expected to be valid. At these low x_Bj values, a parton in the proton can induce a QCD cascade, consisting of several subsequent parton emissions, before eventually an interaction with the virtual photon takes place (see figure). The large phase space available at low x_Bj makes the production of forward jets a particularly interesting process for the study of parton dynamics, since jets emitted close to the proton direction lie well away in rapidity from the photon end of the evolution ladder.

In the measurement various constraints are applied, which suppress contributions to the parton evolution described by the conventional equations (DGLAP) and enhance the sensitivity to other parton dynamics. In inclusive forward jet production this is expected to be the case when the transverse momentum squared of the jet and the photon virtuality are of similar order. For the so called BFKL dynamics the fractional momentum carried by the partons are ordered through the parton ladder.

The inclusive forward jet cross-section as a function of x_Bj is shown to the right. The data is compared to various QCD based models. The conventional DGLAP calculations (RG-DIR), in which the partons in the parton ladder are ordered in virtuality, are not sufficient to describe the data. Models which break this ordering in virtuality (CDM and RG-DIR+RES) come significantly closer to the data.

The results are also presented as triple differential cross-sections versus x_Bj, in bins of Q² and the squared transverse momentum of the forward jet. More exclusive final states, like those containing a di-jet system in addition to the forward jet (`2+forward jet'), provide a further handle to control the parton dynamics, and the cross sections have been measured for different rapidity separations between the three jets. The measurements are compared to LO and NLO di-jet calculations (DISENT) and three-jet calculations (NLOJET++), as well as different phenomenological QCD based models (CASCADE, ARIADNE with CDM, RAPGAP and RAPGAP-resolved).

The results demonstrate that an accurate description of the radiation pattern at small x_Bj requires the introduction of terms beyond those included in the DGLAP direct approximation. Higher order parton emissions contribute noticeably to the cross-section. Further it is observed that calculations which include breaking of the transverse momentum ordering, such as CDM and the resolved photon model, provide a better description of the data. The inclusive forward jet measurements are equally well described by CDM and the DGLAP resolved model, and are obviously not sensitive to differences between the models. However, in the more exclusive measurement of `2+forward jet' events a clear differentiation of the models is obtained since, in contrast to CDM, the DGLAP resolved model fails to describe the data.