On flavor violation for massive and mixed neutrinos

Abstract

We discuss flavor charges and states for interacting mixed neutrinos in QFT. We show that the Pontecorvo states are not eigenstates of the flavor charges. This implies that their use in describing the flavor neutrinos produces a violation of lepton charge conservation in the production/detection vertices. The flavor states defined as eigenstates of the flavor charges give the correct representation of mixed neutrinos in charged current weak interaction processes.In this report we analyze the definition of the flavor charges in the canonical formalism for interacting (Dirac) neutrinos with mixing. On this basis, we study the flavor states for mixed neutrinos in the QFT formalism [1]- [7] and in the Pontecorvo formalism [8]- [11]. We show that Pontecorvo mixed states are not eigenstates of the neutrino flavor charges and we estimate how much the leptonic charge is violated on these states.A realistic description of flavor neutrinos starts by taking into account the (charged current) weak interaction processes in which they are created, together with their charged lepton counterparts. In the Standard Model, flavor is strictly conserved in the production and detection vertices of such interactions. The flavor violations are due only to loop corrections and are thus expected to be extremely small [12]. Therefore, we define the flavor neutrino states as eigenstates of flavor charges. This is obtained in a QFT treatment where the flavor charges are defined in the usual way from the symmetry properties of the neutrino Lagrangian.Here we consider the decay process W + → e + + ν e and we study the case where the neutrino mixing is present. We consider for simplicity the case of two generations. After spontaneous symmetry breaking, the relevant terms of the Lagrangian density for charged current weak inter-includes the neutrino non-diagonal mass matrix M ν and the mass matrix of charged leptons M l :L int is the interaction Lagrangian given by [13]

Some nontrivial aspects of Poincaré and CPT invariance of flavor vacuum

“…This complementarity between E and Q A fluctuations on M might also be viewed as a direct manifestation of flavor-energy uncertainty relations [36]. 11 As in the case of time-translation, we can now show that different states in the flavor vacuum manifold are physically equivalent. In other words, flavor oscillations can be equivalently described in every Lorentz frame.…”

“…Indeed, it has been suggested in [54], that, in gauge theories with Lorentz SSB, in the sense of a vector gauge boson acquiring a vacuum expectation value, the massless U(1) photon plays the role of such a Goldstone boson. In the current, nongauge, context, although the flavor currents (89) acquire nonzero vacuum expectation values (90) in terms of the 11 In fact, for any label time τ there exists Q σ ðτÞ such that Q σ ðτÞj0ðτ; ξÞi A;B ¼ 0 [cf. Eq.…”

“…These two spaces are unitarily inequivalent to each other, and the flavor vacuum is structurally similar to a BCS condensate. Such a proposal, if realized in nature, will have important phenomenological consequences, which have been examined over the years since its development [8], and pertain to both, particle physics, specifically particle oscillations, in particular neutrinos [9][10][11], and cosmology [12], where it was argued that the flavor vacuum condensate structure can contribute to the dark energy of the Universe. It is worthy of stressing that, as argued in [13], there are significant differences between the respective neutrino oscillation formulas in the flavor and mass eigenstate formalisms that can lead to observable effects in a nonrelativistic energy regime.…”

Dark matter and dark energy via nonperturbative (flavor) vacua

“…However, in the field-theoretical framework the decomposition of the fields (3) into ladder operators associated with flavour particle states is highly non-trivial [3]. It has been shown, indeed, that states defined as the relativistic equivalent of (1), for which |ν 1,2 belongs to the massm 1,2 irreducible representation of the Poincaré group, are not eigenstates of the flavour charge operators [11,14], which for the theory (4) read [11] Among all flavour states defined in the BV approach, the one called flavour vacuum and defined by…”

“…In short: flavour states can be built by means of specific creation/annihilation operators for flavour particles; it can be shown that the only state that is annihilated by all annihilation operators is the flavour vacuum defined via(11).…”