A diagrammatic treatment of neutrino oscillations

We present a covariant wave-packet approach to neutrino flavor transitions in vacuum. The approach is based on the technique of macroscopic Feynman diagrams describing the lepton number violating processes of production and absorption of virtual massive neutrinos at the macroscopically separated space-time regions ("source" and "detector"). Accordingly, the flavor transitions are a result of interference of the diagrams with neutrinos of different masses in the intermediate states. The statistically averaged probability of the process is representable as a multidimensional integral of the product of the factors which describe the differential flux density of massless neutrinos from the source, differential cross section of the neutrino interaction with the detector and a dimensionless factor responsible for the flavor transition. The conditions are analyzed under which the last factor can be treated as the flavor transition probability in the usual quantum-mechanical sense.Comment: 27 pages,7 figures, iopart class. Includes minor corrections made in proofs. References update

Neutrino oscillations and the effect of the finite lifetime of the neutrino source

We consider a neutrino source at rest and discuss a condition for the existence of neutrino oscillations which derives from the finite lifetime $\tau_S$ of the neutrino source particle. This condition is present if the neutrino source is a free particle such that its wave function is non-stationary. For a Gaussian wave function and with some simplifying assumptions, we study the modification of the usual oscillation probability stemming from $\tau_S$. In the present accelerator experiments the effect of $\tau_S$ can be neglected. We discuss some experimental situations where the source lifetime becomes relevant in the oscillation formula.Comment: 13 pages latex file with 2 figure