The cross section of the diffractive process e^+p -> e^+Xp is measured at a centre-of-mass energy of 318 GeV, where the system X contains at least two jets and the leading final state proton p is detected in the H1 Very Forward Proton Spectrometer. The measurement is performed in photoproduction with photon virtualities Q^2 <2 GeV^2 and in deep-inelastic scattering with 4 GeV^2<Q^2<80 GeV^2. The results are compared to next-to-leading order QCD calculations based on diffractive parton distribution functions as extracted from measurements of inclusive cross sections in diffractive deep-inelastic scattering.
Deep inelastic scattering (DIS) events, selected from 1993 data taken by the H1 experiment at HERA, are studied in the Breit frame of reference. The fragmentation function of the quark is compared with those of \ee data. It is shown that certain aspects of the quarks emerging from within the proton in \ep interactions are essentially the same as those of quarks pair-created from the vacuum in \ee annihilation. The measured area, peak position and widthof the fragmentation function show that the kinematic evolution variable, equivalent to the \ee squared centre of mass energy, is in the Breit frame the invariant square of the four-momentum transfer. We comment on the extent to which we have evidence for coherence effects in parton showers.
Inclusive jet, dijet and trijet differential cross sections are measured in neutral current deep-inelastic scattering for exchanged boson virtualities 150 < Q^2 < 15000 GeV^2 using the H1 detector at HERA. The data were taken in the years 2003 to 2007 and correspond to an integrated luminosity of 351 pb^{-1}. Double differential Jet cross sections are obtained using a regularised unfolding procedure. They are presented as a function of Q^2 and the transverse momentum of the jet, P_T^jet, and as a function of Q^2 and the proton's longitudinal momentum fraction, Xi, carried by the parton participating in the hard interaction. In addition normalised double differential jet cross sections are measured as the ratio of the jet cross sections to the inclusive neutral current cross sections in the respective Q^2 bins of the jet measurements. Compared to earlier work, the measurements benefit from an improved reconstruction and calibration of the hadronic final state. The cross sections are compared to perturbative QCD calculations in next-to-leading order and are used to determine the running coupling and the value of the strong coupling constant as alpha_s(M_Z) = 0.1165 (8)_exp (38)_{pdf,theo}.
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