Real oscillations of virtual neutrinos

Abstract

We study the conditions for neutrino oscillations in a field-theoretical approach by taking into account that only the neutrino production and detection processes, which are localized in space around the coordinates ${\stackrel{\ensuremath{\rightarrow}}{x}}_{P}$ and ${\stackrel{\ensuremath{\rightarrow}}{x}}_{D}$, respectively, can be manipulated. In this sense the neutrinos whose oscillations are investigated appear as virtual lines connecting production with detection in the total Feynman graph and all neutrino fields or states to be found in the discussion are mass eigenfields or eigenstates. We perform a thorough examination of the integral over the spatial components of the inner neutrino momentum and show that in the asymptotic limit $L=|{\stackrel{\ensuremath{\rightarrow}}{x}}_{D}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{x}}_{P}|\ensuremath{\rightarrow}\ensuremath{\infty}$ the virtual neutrinos become "real" and under certain conditions the usual picture of neutrino oscillations emerges without ambiguities.