Perturbation Theory for Unstable Fundamental Fields

Unstable particles (Z , W and higgs bosons and top quark) are at the focus of current high energy physics research. However, a satisfactory theoretical formalism that would allow systematic calculations for the processes involving such particles at the high level of precision required, say, for LEP2 where the planned experimental precision warrants theoretical calculations at the twoloop level [1], is still lacking (for recent discussions see [2], [3]). This Letter describes a systematic and rather simple if unconventional modification of the standard Perturbation Theory that appears to relieve the latter of the known difficulties associated with instability of heavy particles. (The physical situations we are concerned with here correspond to decay times much less than the observation time, so the issues of time evolution do not emerge; for a recent discussion see e.g. [4].) Consider the amplitude A Q ( ) of the process q q W l l 1 2 1 2 → → .