Jets and jet multiplicities in high-energy photon-nucleon interactions.

We discuss the theory of jet events in high-energy photon-proton interactions using a model which gives a good description of the data available on total inelastic γp cross sections up to √ s=210 GeV. We show how to calculate the jet cross sections and jet multiplicities and give predictions for these quantities for energies appropriate for experiments at the HERA ep collider and for very high energy cosmic ray observations. PACS number(s): 13.60.Hb, 13.87.Ce, 12.40.Lk 1 The hadronic structure of the photon and its interaction with hadrons are currently subjects of considerable interest.The ZEUS and H1 groups at the ep collider HERA have presented preliminary results [1] on the γp photoproduction cross section at 210 GeV center-of-mass energy which show the rise with energy typical of other hadronic interactions. It was shown by Gandhi and Sarcevic [2] in a simple model that this rise can be used to discriminate between different sets of photon structure functions. The hadronic behavior of the photon at very high energies (∼ 10 GeV photon energy) is also of interest for the theory of air showers triggered by cosmic ray photons [3]. We have developed an improved QCD-based model of the photon interaction with nucleons [4] which gives predictions for the total inelastic γp cross section which agree well with the HERA data. The model has the interesting feature that the information needed to calculate σ inel is largely determined by high energy πN scattering. In this paper, we will use the model to discuss the total jet cross section σ jet and the probabilities for multiple-jet events, and give our predictions for those quantities at HERA energies and the energies relevant for cosmic ray experiments. We begin by sketching our model for inelastic γp scattering. The theory is developed in more detail in [4]. The incoming physical photon state |γ〉phys can be expressed as a superposition of the bare photon and the set of virtual hadronic states |m〉 which can be distinguished in the subsequent interaction, and appear with probabilities Pm. Accordingly, the total inelastic γp cross section is given in a semiclassical picture as σ inel = (1− Phad)σdir + ∑