Field-theoretical approach to coherence in neutrino oscillations

We study the conditions for the existence of neutrino oscillations in the field-theoretical approach which combines neutrino production and detection processes in a single Feynman graph. The ''oscillating neutrino" is represented by an inner line of this graph where, due to the macroscopic distance L between source and detector, the neutrino propagators for neutrinos with definite mass are replaced by the projection operators into the neutrino states on mass shell. We use as a concrete model reaction the neutrino source and detector as given in the LSND experiment and we carefully take into account the finite lifetime of the stopped muons which provide the <(upsilon)over bar>(mu), beam. We show that the field-theoretical approach provides a solid method to locate all possible conditions and allows one to separate unambiguously their different origins. Some of these conditions are independent of L whereas others state that coherence is lost when L exceeds a certain "coherence length." Also it turns out that, at least in the concrete situation considered here, the concept of neutrino wave packets is not supported by the field-theoretical approach for realistic experimental conditions, i.e., the neutrino energy spread is incoherent in origin.