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Register a new userCovariant asymmetric wave packet for a field-theoretical description of neutrino oscillations
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We consider a class of models for the relativistic covariant wave packets which can be used as asymptotically free in and out states in the quantum field theoretical formalisms for description of the neutrino flavor oscillation phenomenon. We demonstrate that the new asymmetric wave packet (AWP) is an appropriate alternative for the more convenient symmetric wave packets, like the so-called relativistic Gaussian packet (RGP) widely used in the QFT-based approaches to neutrino oscillations. We show that RGP is not a particular case of AWP, although many properties of these models are almost identical in the quasistable regime. We discuss some features of AWP distinguishing it from RGP.
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The phenomena of particle mixing and flavor oscillations in elementary particle physics can be addressed by the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and anti-neutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{alpha i}$ (for $alpha = e, mu, tau$ and $i = 1, 2, 3$). When the matter parameter $a equiv 2sqrt{2} G^{}_{rm F} N^{}_e E$ is taken as an independent variable, a complete set of first-order ordinary differential equations for $widetilde{m}^2_i$ and $|V^{}_{alpha i}|^2$ have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the continuous symmetries characterized by one-parameter Lie groups and the discrete symmetry associated with the permutations of three neutrino mass eigenstates. The implications of these symmetries for solving the differential equations and looking for differential invariants are discussed.
Kinematical aspects of pion decay $pi to mu u$ is studied, with neutrino mixing taken into account. An attempt is made to derive the transition probability for such a sequence of processes: a $pi^+$ produced at $(vec{x}_{pi},t_{pi})$ with momentum $vec{p}_{pi}$ decays into a $mu^+$ and a $ u_{mu}$ somewhere in space-time and then the $mu^+$ is detected at $(vec{x}_{mu},t_{mu})$ with momentum $vec{p}_{mu}$ and a $ u_{alpha}$ (a neutrino with flavor $alpha = e$, $mu$, $...$) is detected at $(vec{x}_{ u},t_{ u})$ with momentum $vec{p}_{ u}$. It is shown that (1) if all the particles involved are treated as plane-waves, the energy-momentum conservation would eliminate the neutrino oscillating terms, leaving each mass-eigenstate to contribute separately to the transition probability; (2) if one treats all the particles involved as wave-packets, the neutrino oscillating terms would appear and would be multiplied by two suppression factors, which result from distinction in velocity and in energy between the two interfering neutrino mass-eigenstates. An approximate treatment which takes account of the two complementary features, each of the particles involved propagates along its classical trajectory on the one hand and energies and momenta of the particles involved are conserved during the decay on the other hand, is proposed and similarity and difference between our approach and that of Dolgov et al. are discussed.
The wave-packet treatment of neutrino oscillation developed previously is extended to the case in which momentum distribution functions are taken to be a Gaussian form with both central values and dispersions depending on the mass eigenstates of the neutrinos. It is shown among other things that the velocity of the neutrino wave packets does not in general agree with what one would expect classically and that relativistic neutrinos emitted from pions nevertheless do follow, to a good approximation, the classical trajectory.
The disappearance of reactor $bar{ u}_e$ observed by the Daya Bay experiment is examined in the framework of a model in which the neutrino is described by a wave packet with a relative intrinsic momentum dispersion $sigma_text{rel}$. Three pairs of nuclear reactors and eight antineutrino detectors, each with good energy resolution, distributed among three experimental halls, supply a high-statistics sample of $bar{ u}_e$ acquired at nine different baselines. This provides a unique platform to test the effects which arise from the wave packet treatment of neutrino oscillation. The modified survival probability formula was used to fit Daya Bay data, providing the first experimental limits: $2.38 cdot 10^{-17} < sigma_{rm rel} < 0.23$. Treating the dimensions of the reactor cores and detectors as constraints, the limits are improved: $10^{-14} lesssim sigma_{rm rel} < 0.23$, and an upper limit of $sigma_{rm rel} <0.20$ is obtained. All limits correspond to a 95% C.L. Furthermore, the effect due to the wave packet nature of neutrino oscillation is found to be insignificant for reactor antineutrinos detected by the Daya Bay experiment thus ensuring an unbiased measurement of the oscillation parameters $sin^22theta_{13}$ and $Delta m^2_{32}$ within the plane wave model.
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