Instanton propagator and instanton induced processes in scalar model

The propagator in the instanton background in the $(- \lambda \phi^{4})$ scalar model in four dimensions is studied.Leading and sub-leading terms of its asymptotics for large momenta and its on-shell double residue are calculated analytically. These results are applied to the analysis of the initial-state and initial-final-state corrections and the calculation of the next-to-leading (propagator) correction to the exponent of the cross section of instanton induced multiparticle scattering processes.