Flavor-energy uncertainty relations for neutrino oscillations in quantum field theory

Abstract

In the context of quantum field theory, we derive flavor-energy uncertainty relations for neutrino oscillations. By identifying the non-conserved flavor charges with the "clock observables", we arrive at the Mandelstam-Tamm version of time-energy uncertainty relations. In the ultra-relativistic limit these relations yield the well known condition for neutrino oscillations. Ensuing non-relativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of Fock spaces for flavor and massive neutrinos, are also discussed.Introduction. -Neutrino mixing and oscillations represent one of the most pressing challenges of modern theoretical and experimental particle physics. They were first introduced by Pontecorvo [1] in a close analogy with the phenomenon of Kaon oscillations [2], and subsequently confirmed in a number of experimental settings [3]. While the quantum mechanical (QM) description [4][5][6] is quite successful in tackling high-energy features of neutrino oscillations, the corresponding quantum field theoretical (QFT) description (which could tackle also the lowenergy behavior) is still controversial [6][7][8][9].

Some nontrivial aspects of Poincaré and CPT invariance of flavor vacuum

“…It was recently pointed out [36] that flavor neutrino states share a common feature with unstable particles, in the sense that only their energy (mass) distribution has a physical meaning and the width of this distribution is related to the inverse of the oscillation length which can be again deduced from time-energy uncertainty relation [36,37]. Furthermore, the latter result was recently generalized, in a quantum mechanical context, to stationary curved spacetimes [38].…”

Dynamical generation of field mixing via flavor vacuum condensate

“…Our key finding is that the vacuum state, responsible for dynamical mixing generation, yields the same condensate structure of the flavor vacuum as known from the study of neutrino oscillations, cf., e.g., Refs. [7,8,11,22]. In particular, we have shown that in order to dynamically generate mixing, within our class of models, the classical residual symmetry U (1) V × U (1) m V that responsible for the mixing must be anomalous (only U (1) V symmetry survives quantization), on the account of the flavor vacuum condensate.…”

Flavor neutrino states for pedestrians

“…We finally point out that recently [35], the use of flavor states led to the interpretation of flavor neutrinos as unstable particles, which periodically decay into different neutrino species. This view is also compatible with the formal statement, based on the study of Schwinger-Dyson equations, according to which flavor neutrinos can be formally thought as single-particle bound states, i.e.…”

“…The Lagrangian L is invariant under the global U (1) transformations ν → e iα ν and l → e iα l leading to the conservation of the total flavor charge Q tot l corresponding to the total leptonnumber conservation [15,35]. This can be written in terms of the flavor charges for neutrinos and charged leptons [27]…”