Coherence of neutrino flavor mixing in quantum field theory

Several recent works have examined neutrino flavor mixing by considering the neutrino production/mixing/detection as a single process in the context of quantum field theory (QFT) [1–8]. Such a framework clarifies several conceptual difficulties associated with the familiar quantum mechanical (QM) model of the flavor mixing process (see Ref. [9] for a listing of some of these). One conceptual difficulty associated with the simplified QM picture is that it postulates neutrino flavor eigenstates of indefinite mass, while in QFT external particles (asymptotic states) are generally required to be on-shell. Hence the usual methods of calculating neutrino production rates in QFT would be rates for neutrinos of a particular mass, precluding interference between neutrino states of different mass. In a QFT description of a neutrino mixing experiment, this problem is resolved by considering the neutrinos to be virtual particles. After all, it is the measurable, on-shell external charged leptons associated with the neutrino production and detection processes that operationally define what is meant by “neutrino flavor mixing”; the neutrinos themselves are not directly observed. In the relativistic limit, the same factors that constitute the “oscillation amplitude” in the simplified quantum mechanical picture can be identified in the amplitude for the overall neutrino production/mixing/detection process. While descriptions of neutrino flavor mixing in QFT have provided insight, some shortcomings remain. As noted in Ref. [8], one problem is that the calculations [1–7] are not carried out to normalized event rates. Without normalization, one cannot definitely say that one has identified an “oscillation probability.” In addition, Refs. [1–3,5,6] are restricted to particular neutrino production and detection reactions, while Ref. [4] employs idealized two-state systems as source and detector. Since one would hope to justify the use of the simple QM model in general circumstances, such restrictions should not be required. Another potential pitfall is a failure to distinguish between macroscopic stationarity and microscopic stationarity. Some previous studies invoke microscopic stationarity, either implicitly [3,7,8], or with explicit reference to bound states [2,6] in the source and/or detector. While sources and detectors as a whole can sometimes be considered stationary on a macroscopic basis, the claim that individual particles in the source and/or detector remain unperturbed in coherent states over macroscopic time scales is dubious. A good example is the Sun: While macroscopic variables such as density, pressure, and so on may be stationary, zooming in to atomic scales one sees a roiling thermodynamic bath of particles being created, destroyed, and scattered on rapid time scales. Clearly there is no hope of appealing