Lepton Numbers in the Framework of Neutrino Mixing

Abstract

In this short review we discuss the notion of lepton numbers. The strong evidence in favor of neutrino oscillations obtained recently in the Super-Kamiokande atmospheric neutrino experiment and in solar neutrino experiments imply that the law of conservation of family lepton numbers L e , L µ and L τ is strongly violated. We consider the states of flavor neutrinos ν e , ν µ and ν τ and we discuss the evolution of these states in space and time in the case of non-conservation of family lepton numbers due to the mixing of light neutrinos. We discuss and compare different flavor neutrino discovery experiments. We stress that experiments on the search for ν µ → ν τ and ν e → ν τ oscillations demonstrated that the flavor neutrino ν τ is a new type of neutrino, different from ν e and ν µ . In the case of neutrino mixing, the lepton number (only one) is connected with the nature of massive neutrinos. Such conserved lepton number exist if massive neutrinos are Dirac particles. We review possibilities to check in future experiments whether the conserved lepton number exists.

Coherence and Wave Packets in Neutrino Oscillations

“…(4.20) and (4.21) with ∆m 2 kj = ∆m 2 (∆m 2 is the squared-mass difference and ϑ is the mixing angle; see the reviews in Refs. [12,41,52,13]). An incoherent average of the probability in the plane-wave approximation over a gaussian energy spectrum with width σ E reads…”

Theory of Neutrino Oscillations

“…In the ultrarelativistic approximation the characteristics of the production and detection processes that depend on the neutrino mass can be neglected, leading to a correct approximate description of flavor neutrinos through the states (1) (see also Ref. [6]). …”

“…Therefore, the probability of neutrino oscillations is Lorentz invariant [15,16] and must be derived in a covariant way. In fact, the oscillation probability has been derived without special assumptions about the energies and momenta of the different massive neutrino components both in the plane wave approach [17,15,6] and in the wave packet treatment [7,8,14,9].…”

“…In conclusion, the standard expression for the probability of neutrino oscillations is robust and can be derived starting from realistic assumptions in the plane wave approach [17,15,6], in a quantum mechanical wave packet treatment [7,8,14,9] and in the framework of Quantum Field Theory (see Ref. [13] and references therein).…”

Fock states of flavor neutrinos are unphysical

“…The main reason is that neutrino oscillations is a consequence of neutrino mixing (see Refs. [4][5][6][7][8][9][10][11][12] and the the recent review by B. Kayser in Ref. [13]), which consists in a mismatch between flavor and mass: the lefthanded flavor neutrino fields ν αL , with α = e, µ, τ , are unitary linear combinations of the massive neutrino fields ν kL ,…”