Off mass shell effects in associated production of the top quark pair and Higgs boson at a linear collider

We discuss effects related to the fact that the final state particles of a reaction e+ e- -> t \bar{t} H are actually produced and they decay off mass shell. For the intermediate mass Higgs boson, which decays preferably into a b\bar{b}-quark pair, the reaction will be observed through reactions with 8 fermions in the final state. Such reactions, already in the lowest order of the standard model, receive contributions typically from a few dozen thousands of the Feynman diagrams, the vast majority of which constitute background to the signal of associated production of the top quark pair and Higgs boson. In order to illustrate pure off mass shell effects we neglect the background contributions and compare the `signal' cross section with the cross section in the narrow width approximation for e+ e- -> b u \bar{d} \bar{b} mu- \bar{nu}_mu b \bar{b}, which is one of possible detection channels of the associated production of the top quark pair and Higgs boson at a linear collider.Comment: 11 pages, 4 figures, version published in Acta Physica Polonica