Inclusive Single- and Dijet Rates in Next-to-Leading Order QCD for γ*p and γ*γ Collisions

Abstract

We present one-and two-jet inclusive cross sections for γ * γ scattering and virtual photoproduction in ep collisions. The hard cross sections are calculated in next-to-leading order QCD. Soft and collinear singularities are extracted using the phase-space-slicing method. The initial state singularity of the virtual photon depends logarithmically its' virtuality. This logarithm is large and has to be absorbed into the parton distribution function of the virtual photon. We define for this purpose an MS factorization scheme similar to the real photon case. We numerically study the dependence of the inclusive cross sections on the transverse energies and rapidities of the outgoing jets and on the photon virtuality. The ratio of the resolved to the direct cross section in ep collisions is compared to ZEUS data. under Contract 05 7 HH 92P (0), and by EEC Program Human Capital and Mobility through Network Physics at High Energy Colliders under Contract CHRX-CT93-0357 (DG12 COMA). Recently, data has been presented by the ZEUS [23] and the H1 [24] collaborations for electron-proton collisions involving photons with small, but notvanishing P 2 that allow a test of the virtual photon structure. So far, there has only been one measurement of the virtual photon structure function from the PLUTO collaboration at the PETRA e + e − collider [25]. In [26] we made a comparison of theoretical NLO predictions for γ * p inclusive jet production with data from [23], by extending the methods used in [11,12]. This extension will be described in detail in this work. Some theoretical studies of inclusive γ * p cross sections in LO have been presented in [27,28,29]. We also include the case of γ * γ scattering that will become important at LEP2 [30], which is an extension of the work from [20,21].Since the partonic subprocesses of ep and γ * γ scattering are very similar, we will take over the notation 'SR' and 'DR' from the γγ case to ep scattering to simplify the discussion. In ep scattering, the SR component denotes the contribution, where the virtual photon is directly interacting with the partons from the proton, whereas in the DR component the resolved photon interacts with the partons from the proton.The extension from real to virtual photoproduction is done by taking the Weizsäcker-Williams formula to describe the momentum spread of the virtual photon, but keeping P 2 fixed, not integrating over the region of small P 2 and not assuming P 2 = 0. This is described by the unintegrated Weizsäcker-Williams formula. In the hard process, the matrix elements for finite P 2 have to be taken. The matrix elements and the initial and final state singularities for the SR contribution with P 2 = 0 have been calculated in [31,32] in connection with deepinelastic ep scattering (DIS) at HERA, where P 2 is large. Since we consider P 2 to be finite, the photon initial state singularities encountered in real photoproduction do not occur. Instead, when integrating over the phase-space of the final state particles, a logarithm of the type ln(P 2 /E 2 T...