This paper is dedicated to the memory of Professor Guido Altarelli who sadly passed away as it went to press. The results which it presents are founded on the principles and the formalism which he developed in his pioneering theoretical work on Quantum Chromodynamics in deep-inelastic lepton-nucleon scattering nearly four decades ago rent e ± p scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb −1 and span six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and Bjorken x. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. In addition to the experimental uncertainties, model and parameterisation uncertainties were assessed for these parton distribution functions. Variants of HERAPDF2.0 with an alternative gluon parameterisation, HERAPDF2.0AG, and using fixedflavour-number schemes, HERAPDF2.0FF, are presented. The analysis was extended by including HERA data on charm and jet production, resulting in the variant HERAPDF2.0Jets. The inclusion of jet-production cross sections made a simultaneous determination of these parton distributions and the strong coupling constant possible, resulting in α s (M 2 Z ) = 0.1183 ± 0.0009(exp) ± 0.0005(model/parameterisation) ± 0.0012(hadronisation) and results on electroweak unification and scaling violations are also presented. H1 and ZEUS

A combination is presented of the inclusive deep inelastic cross sections measured by the H1 and ZEUS Collaborations in neutral and charged current unpolarised e ± p scattering at HERA during the period 1994-2000. The data span six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and in Bjorken x. The combination method used takes the correlations of systematic uncertainties into account, resulting in an improved accuracy. The combined data are the sole input in a NLO QCD analysis which determines a new set of parton distributions, HERAPDF1.0, with small experimental uncertainties. This set includes an estimate of the model and parametrisation uncertainties of the fit result.

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep → eXY , where Y is a proton or a low mass proton excitation carrying a fraction 1−x I P > 0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t| < 1 GeV 2 . Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5 ≤ Q 2 ≤ 1600 GeV 2 , triple differentially in x I P , Q 2 and β = x/x I P , where x is the Bjorken scaling variable. At low x I P , the data are consistent with a factorisable x I P dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α IP (0) = 1.118 ± 0.008 (exp.) +0.029 −0.010 (model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q 2 and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q 2 range studied. Total and differential cross sections are also measured for the diffractive charged current process e + p →ν e XY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q 2 at fixed x I P and x or on x at fixed Q 2 and β.

A measurement of charm and beauty dijet photoproduction cross sections at the ep collider HERA is presented. Events are selected with two or more jets of transverse momentum p jet 1(2) t > 11(8) GeV in the central range of pseudo-rapidity −0.9 < η jet 1(2) < 1.3. The fractions of events containing charm and beauty quarks are determined using a method based on the impact parameter, in the transverse plane, of tracks to the primary vertex, as measured by the H1 central vertex detector. Differential dijet cross sections for charm and beauty, and their relative contributions to the flavour inclusive dijet photoproduction cross section, are measured as a function of the transverse momentum of the leading jet, the average pseudo-rapidity of the two jets and the observable x obs γ . Taking into account the theoretical uncertainties, the charm cross sections are consistent with a QCD calculation in next-to-leading order, while the predicted cross sections for beauty production are somewhat lower than the measurement.

We consider the implications of the recent determination of the universal infrared background for the propagation of photons up to 20 TeV from the active galaxy Markarian 501 as observed by HEGRA. At 20 TeV the mean free path for photon-photon collisions on the infrared background would be much shorter than the distance to Markarian 501, implying absorption factors of the order of exp(−10), or greater, and consequently an excessive power output for this active galaxy. Possible solutions of this problem are discussed.