In this paper searches are presented for the pair production of first and second generation scalar leptoquarks and limits are given on the quark-lepton compositeness scale from proton-antiproton collision data at a center-of-mass energy 1.96 TeV, collected with Run II D0 Detector in 2002-2004. No evidence for a leptoquark signal has been observed. From the upper bounds on the product of cross section times branching ratio beta=Br(LQ to lj), a lower mass limits of M(LQ1) > 241 GeV and M(LQ2) > 247 GeV for the first and second LQ generation are set for beta=1. These results, combined with those obtained by D0 in Run I at a center-of-mass energy of 1.8 TeV, allow to exclude scalar LQ masses up to 256 GeV and 251 GeV (for beta=1) for the first and second generation, respectively. The dilepton mass spectra in pp -> l+l-+X interactions are studied using dielectron (dimuon) data samples, corresponding to an integrated luminosity of 271 pb-1 (406 pb-1). The mass spectra being a probe for new physics are examined for new interactions of quarks and leptons from a common composite structure. No excess of events is found over the expectation from Standard Model processes. The current experimental lower limits on the compositeness scale vary, for different chirality channels, from 3.6 to 9.1 TeV for the (eeqq) and from 4.2 to 9.8 TeV for the (mumuqq) contact interaction.
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