Quantum Field Theory of Neutrino Oscillations

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.