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Register a new userHow do Neutrinos Propagate ? - Wave-Packet Treatment of Neutrino Oscillation
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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.
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Flavor oscillation of traveling neutrinos is treated by solving the one-dimensional Dirac equation for massive fermions. The solutions are given in terms of squeezed coherent state as mutual eigenfunctions of parity operator and the corresponding Hamiltonian, both represented in bosonic creation and annihilation operators. It was shown that a mono-energetic state is non-normalizable, and a normalizable Gaussian wave packet, when of pure parity, cannot propagate. A physical state for a traveling neutrino beam would be represented as a normalizable Gaussian wave packet of equally-weighted mixing of two parities, which has the largest energy-dependent velocity. Based on this wave-packet representation, flavor oscillation of traveling neutrinos can be treated in a strict sense. These results allow the accurate interpretation of experimental data for neutrino oscillation, which is critical in judging whether neutrino oscillation violates CP symmetry.
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.
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.
We examine the potential of the future medium-baseline reactor neutrino oscillation (MBRO) experiments in studying neutrino wave-packet impact. In our study, we treat neutrinos as wave packets and use the corresponding neutrino flavor transition probabilities. The delocalization, separation and spreading of the wave packets lead to decoherence and dispersion effects, which modify the plane-wave neutrino oscillation pattern, by amounts that depend on the energy uncertainties in the initial neutrino wave packets. We find that MBRO experiments could be sensitive to the wave-packet impact, since the baseline is long enough and also the capability of observing small corrections to the neutrino oscillations due to excellent detector energy resolution. Besides studying the constraints on the decoherence parameter, we also examine the potential wave-packet impacts on the precision of measuring $theta_{12}$ and other oscillation parameters in the future medium-baseline reactor neutrino oscillation experiments. Moreover, we also probe the potential benefits of an additional detector for studying such exotic neutrino physics.
The main goal of the IceCube Deep Core Array is to search for neutrinos of astrophysical origins. Atmospheric neutrinos are commonly considered as a background for these searches. We show that the very high statistics atmospheric neutrino data can be used to obtain precise measurements of the main oscillation parameters.
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