Inclusive Jet Production in γp and γγ Processes: Direct and Resolved Photon Cross Sections in Next-To-Leading Order QCD

Abstract

The production of jets in low Q 2 ep scattering (photoproduction) and in low Q 2 e + e − scattering (γγ scattering) allows for testing perturbative QCD and for measuring the proton and photon structure functions. This requires exact theoretical predictions for one-and two-jet cross sections. We describe the theoretical formalism, giving sufficient details, for calculating the direct and resolved processes in γp and γγ reactions in next-to-leading order QCD. We present the complete analytical results for the Born terms, the virtual, and the real corrections. To separate singular and regular regions of phase space we use the phase space slicing method with an invariant mass cut-off. In this way, all soft and collinear singularities are either canceled or absorbed into the structure functions. Using a flexible Monte Carlo program, we evaluate the cross sections numerically and perform various tests and comparisons with other calculations. We consider the scale dependence of our results and compare them to data from the experiments H1 and ZEUS at HERA and OPAL at LEP.

Di-Jet production in photon-photon collisions at

“…the requirement that both electrons remain undetected. 3 The OPAL detector A detailed description of the OPAL detector can be found in Ref. [15], and therefore only a brief account of the main features relevant to the present analysis will be given here.…”

“…x + = X jets=1;2 (E + p z ) X hadrons (E + p z ) and x = X jets=1;2 (E p z ) X hadrons (E p z ) ; (3) where p z is the momentum component along the z axis of the detector and E is the energy of the jets or hadrons. These variables give some separation between direct and resolved di-jet events [1].…”

“…The data points are compared in Figure 3b to a NLO perturbative QCD calculation [3]. The contribution of the di erent processes to all double-resolved events depends on the parametrisation of the parton distribution functions.…”

“…Depending on the type of photon-photon interaction di erent matrix elements for the QCD scattering process contribute. These matrix elements have been calculated in leading order (LO) [2] and next-to-leading order (NLO) [3]. The matrix element of the scattering between two bare photons is the one for the process !qq.…”

“…The dependence of the jet shapes on QCD parton radiation calculated in the Leading-Log Approximation (LLA), and the di erences between the jet shapes of direct and resolved processes, have recently been measured at HERA [7]. 1 Positrons are also referred to as electrons 3 The measurement of inclusive jet cross-sections in and p interactions can constrain the gluonic content of the photon [8,9]. This is done by comparing the jet cross-sections to the LO QCD models PYTHIA and PHOJET, using di erent parametrisations of the parton distribution functions of the photon, and to NLO QCD calculations [10,11].…”