Quantum Field Theory of Neutrino Oscillations
D. Naumov, V. A. Naumov
Abstract
The theory of neutrino oscillations in the framework of the quantum field perturbative theory with relativistic wave packets as asymptotically free in- and out-states is expounded. A covariant wave packet formalism is developed. This formalism is used to calculate the probability of the interaction of wave packets scattered off each other with a nonzero impact parameter. A geometric suppression of the probability of interaction of wave packets for noncollinear collisions is calculated. Feynman rules for the scattering of wave packets are formulated, and a diagram of a sufficiently general form with macroscopically spaced vertices (a “source” and a “detector”) is calculated. Charged leptons ( $$\ell _{\alpha }^{ \pm }$$ in the source and $$\ell _{\beta }^{ \mp }$$ in the detector) are produced in the space-time regions around these vertices. A neutrino is regarded as a virtual particle (propagator) connecting the macrodiagram vertices. An appropriate method of macroscopic averaging is developed and used to derive a formula for the number of events corresponding to the macroscopic Feynman diagram. The standard quantum-mechanical probability of flavor transitions is generalized by considering the longitudinal dispersion of an effective neutrino wave packet and finite time intervals of activity of the “source” and the “detector”. A number of novel and potentially observable effects in neutrino oscillations is predicted.