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Feb 15 – 18, 2018
Canada/Eastern timezone

Neutrino oscillation (student talk)

Feb 17, 2018, 7:45 PM


Mrs Fatemeh Najafi (Udem)


Neutrino Oscillations In Quantum Mechanics


Neutrino oscillation is one of the most exciting subjects in elementary particle
physics today. It was rst conrmed in 1998 by the Super-Kamiokande
group from their studies of atmospheric neutrinos. Experimental studies of
neutrino oscillation have been rapidly progressing since then, and a number
of oscillation results have been observed in atmospheric, solar, accelerator,
and reactor neutrinos. The implication of the existence of neutrino oscillation
is that neutrinos have nite masses and mixings, which are not accounted for
in the framework of the standard model of elementary particles. Therefore,
the standard model now must be extended to include the new information.
Because the neutrino masses are extremely small, it is considered to be unnatural
to be included in the standard model similar to the way quark and
charged lepton masses are. Therefore, the neutrino oscillation is believed to
provide an important new concept that will be a big step toward the unied
understanding of elementary particle physics. In this document, we present
studies for neutrino oscillation.

  1. Neutrino oscillation
    Neutrino oscillation is a simple quantum mechanical phenomenon in which
    neutrino changes avour as it propagates. In 1957, Pontecorvo gave the
    concept of neutrino oscillation based on a two-level quantum system. This
    hypothesis was nally conrmed by the Super-Kamiokande experiment which
    presented signicant new data on the decit of muon neutrinos produced
    in the Earth's atmosphere . Neutrino oscillation can only happen if the
    neutrinos are massive particle.
  2. When the neutrino mass is measured
    We consider the neutrino oscillation in pion decay into a neutrino and
    muon. Assume
    that by measuring energies and momenta of the pion and muon involved in
    this decay with high precision in each event and we can determine the energy E and momentum p of the emitted neutrino. If the momentum and energy
    of pion and lepton are observable, the neutrino mass is measurable. But now
    we have a problem, measuring the muon momentum with extreme precision
    would destroy the coherence and oscillation of the components of the entangled
    state corresponding to dierent neutrino mass eigenstates. This result
    is in accordance with Heisenberg's Uncertainty Principle.
  3. Coherence in neutrino oscillation

Since it is not possible to know which mass eigenstate was produced, neutrino
avour eigenstates , and are coherent super positions of mass
eigenstates . The coherence length is such a distance
between the neutrino source and detector at which mass eigenstates i and j are separated
by an interval comparable to the size of the wave packet when they arrive
at the detector is so large that they cannot be observed coherently. Plane
wave treatment cannot describe the coherence of massive neutrinos at a given
time and point, in the simple plane wave approach there is no indication of a
coherence length for neutrino oscillations.Coherence between mass eigenstate waves will occur if the momentum dierence
between the dierent mass eigenstates with the same energy, is much smaller than momentum uncertainty. Since neutrino oscilla
tion are a result of interference of amplitude corresponding to dierent mass
eigenstates, absence of their coherence means that no oscillation will will occur.

This means that for existence oscillation the momentum should not be
determined too precisely. The presence of the momentum or energy spread in
the neutrino beam is one of the oscillation existence condition.
The wave packet is a coherent
superposition of dierent waves whose momenta are distributed around the
most probable value, with a certain width or dispersion. Therefore, a wave
packet is localized in space-time as well as in energy-momentum space. A
wave packet treatment of neutrino oscillations is necessary in order to derive
the oscillation probability in a consistent quantum framework, which must
take into account the localization of the production and detection processes
and the associated momentum uncertainties.

Primary author

Mrs Fatemeh Najafi (Udem)

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