Abstract
As is well known, the neutrino was originally postulated by Wolfgang Pauli in order to ‘save’ the conservation of energy in beta decay. As it turned out later after careful examination.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Wolfgang Pauli in 1930 initially chose the name ‘neutron.’ The term ‘neutrino’ was introduced later by Enrico Fermi. In 1956, the electron neutrino was detected experimentally for the first time, and in 1962, the muon neutrino. The tauon was observed in 1975, but the corresponding neutrino only in 2000. There may be still other types of neutrinos. These (as yet hypothetical) sterile neutrinos interact only via gravity and not—like the other neutrinos—through the weak interaction (hence the adjective ‘sterile’). See e.g. D. Castelvecchi, Icy telescope throws cold water on sterile neutrino theory, Nature, https://doi.org/10.1038/nature.2016.20382 (Aug 2016), and literature referenced there.
- 2.
We remind the reader: \(E^{2}=m_{0}^{2}c^{4}+p^{2}c^{2}\).
- 3.
Call the Hamiltonian for free neutrino motion H. We have \(H\left| \nu _{1}\right\rangle =E_{1}\left| \nu _{1}\right\rangle \) and \(H\left| \nu _{2}\right\rangle =E_{2}\left| \nu _{2}\right\rangle \) with \(\Delta E=E_{1}-E_{2}>0\).
- 4.
Here, H denotes a (still) unknown operator and not the well-known operator \(-\frac{\hbar ^{2}}{2m}{\varvec{\nabla }}^{2}+V\). Double meanings of this type are quite common in quantum mechanics. We will learn the reason for this in later chapters.
- 5.
Numerical examples: the electron in this system of units has a rest mass of about 0.5 MeV. The accelerator LHC operates with protons of energies of up to 7 TeV.
- 6.
Of course, this is a key parameter—if it is 10\(^{-6}\) eV instead of 10\(^{-3}\) eV, then the length increases correspondingly by a factor of 1000.
- 7.
A recent review which also contains the values cited in Table 8.1 is given by G.L. Fogli et al., ‘Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP violation searches’, http://arXiv.org/abs/1205.5254v3 (2012).
- 8.
The first three matrices are (except for the phase shift \(\delta \)) the rotation matrices \(D_{x}\left( \theta _{23}\right) D_{y}\left( \theta _{13}\right) D_{z}\left( \theta _{12}\right) \). The first matrix describes e.g. a rotation by the angle \(\theta _{23}\) around the x axis.
- 9.
The values for the mixing angles and the mass differences are from Neutrino Mixing - Particle Data Group, pdg.lbl.gov/2017/listings/rpp2017-list-neutrino-mixing.pdf (30. 5. 2017). The precise determination of these angles is a current topic; see for instance Eugenie S. Reich, ‘Neutrino oscillations measured with record precision’, Nature 08 March 2012, where the measurement of the angle \({\theta }_{13}\) is discussed, or P. Adamson et al. (NOvA Collaboration), Measurement of the Neutrino Mixing Angle \({\theta }_{23}\) in NOvA, Phys. Rev. Lett 118, 151802 (10. 4. 2017).
- 10.
Since measured values are real, we can interpret them as eigenvalues of Hermitian operators.
- 11.
These properties are not mutually exclusive: A unitary operator or a projection operator can also be e.g. Hermitian.
- 12.
Since these operators exhibit only a few species and are fairly well-behaved, one could also speak of a ‘pet zoo’.
- 13.
These are essentially the three components of the orbital angular momentum operator for angular momentum 1; see Chap. 16, Vol. 2.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Pade, J. (2018). Neutrino Oscillations. In: Quantum Mechanics for Pedestrians 1. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-00464-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-00464-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00463-7
Online ISBN: 978-3-030-00464-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)