Some nontrivial aspects of Poincaré and CPT invariance of flavor vacuum

Abstract

We study the explicit form of Poincaré and discrete transformations of flavor states in a two-flavor scalar model, which represents the simplest example of the field mixing. Because of the particular form of the flavor vacuum condensate, we find that the aforementioned symmetries are spontaneously broken. The ensuing vacuum stability group is identified with the Euclidean group Eð3Þ. With the help of Fabri-Picasso theorem, we show that flavor vacua with different time labels and in different Lorentz frames are unitarily inequivalent to each other and they constitute a manifold of zero-flavor-charge states. Despite the spontaneous breakdown of Poincaré and CPT symmetries that characterizes such vacua, we provide arguments on the absence of Goldstone Bosons. We also prove that the phenomenologically relevant oscillation formula is invariant under these transformations. In particular we prove that flavor oscillation formula on flavor vacuum has the same form in all Lorentz frames, by means of general arguments, valid at all energy scales.

Neutrino Mixing and Oscillations in Quantum Field Theory: A Comprehensive Introduction

“…This reminds us of a similar scenario in the quantization in the presence of a curved background [56], of unstable particles [54], and of quantum dissipative systems [57]. This fact, which is compatible with the simple observation that flavor states cannot be interpreted in terms of irreducible representations of the Poincaré group [66,114], stimulated studies of possible recovering of Lorentz invariance for mixed fields, e.g., in Reference [115], where nonlinear realizations of the Poincaré group [116,117] have been related to non-standard dispersion relations for the mixed particles. It has been recently shown, in the simpler case of boson mixing, that such Poincaré symmetry breaking (and related CPT breakdown) is actually an SSB, which has to be traced in the mechanism of dynamical mixing generation, and that the QFT flavor oscillation formula is, however, Lorentz invariant [114].…”

Neutrino mixing and oscillations in quantum field theory: a comprehensive introduction

“…We have also seen how the vacuum structure emerges as a condensate and that its Poincaré group properties exhibit a peculiar character, namely at each time t the flavor vacuum state is unitarily inequivalent to the one at a different time t . This reminds us of a similar scenario in the quantization in the presence of a curved background [56], of unstable particles [54], and of quantum dissipative systems [57].This fact, which is compatible with the simple observation that flavor states cannot be interpreted in terms of irreducible representations of the Poincaré group [66,115], stimulated studies of possible recovering of Lorentz invariance for mixed fields, e.g. in ref.…”

“…[116], where nonlinear realizations of the Poincaré group [117,118] have been related to non-standard dispersion relations for the mixed particles. It has been recently shown, in the simpler case of boson mixing, that such Poincaré symmetry breaking (and related CP T breakdown) is actually a SSB, which has to be traced in the mechanism of dynamical mixing generation, and that QFT flavor oscillation formula is however Lorentz invariant [115]. However, observable effects of such violation in the cosmological scenario could be possible.…”

Time–Energy Uncertainty Relation for Neutrino Oscillations: Historical Development, Applications, and Future Prospects

“…As already mentioned, |V k | 2 → 0 in the relativistic limit |k| m j , j = 1, 2, and the oscillation formula reduces to the standard result, as it should be. It has been proven in the simple case of scalar field mixing that the above oscillation formula is the time component of a Lorentz-covariant formula, though the flavor vacuum breaks the Lorentz invariance [83]. Furthermore, connections between implications of the QFT treatment of mixing and extended (Tsallis-like) statistics have been explored in [84].…”