Prospects to search for a new massless neutral gauge boson, the paraphoton, in e+ e- collisions at center-of-mass energies of 0.5 and 1 TeV are studied. The paraphoton naturally appears in models with abelian kinetic mixing. A possible realistic model independent lowest order effective Lagrangian contains magnetic interactions of the paraphoton with the Standard Model fermion fields. These interactions are proportional to the fermion mass and grow with energy, with however very weak paraphoton couplings to ordinary matter. At the ILC, a potentially interesting process to search for the paraphoton is its radiation off top quarks, so that the event topology to be searched for is a pair of acoplanar top quark jets with missing energy. By combining many discriminating features of signal and background events efficient paraphoton event selection was achieved allowing to set limits for the top-paraphoton coupling. Arguments in favor of the missing energy as the paraphoton with spin 1 are discussed.
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