Abstract
The mechanism of the generation of the neutrino mass term at present is unknown. We also do not know if neutrinos with definite masses are Dirac or Majorana particles. However, as we will see later, it was established by all existing experimental data that neutrino mixing takes place. The unitary mixing matrix U is the object of central interest of theory and experiment. Here we will consider the general properties of the matrix U in the Dirac and Majorana cases.
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Notes
- 1.
Under the change \(\theta \to \pi + \theta\), the \(2\times 2\) mixing matrix
$$\left( \begin{array}{cc} \cos\theta & \sin\theta \\ - \sin\theta & \cos\theta \\ \end{array} \right)$$changes sign. Only squares of the mixing matrix enter into observable quantities. Thus, angles θ and \(\pi + \theta\) cannot be distinguished. From (5.64) it is obvious that this argument is applicable to the general \(3\times 3\) matrix.
- 2.
It is obvious that from this relation follows: \(V_{\mu e}=V_{e\mu}=V_{\tau e}=V_{e\tau}, V_{\mu \mu}=V_{\tau\tau}\).
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© 2011 Springer-Verlag Berlin Heidelberg
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Bilenky, S. (2011). Neutrino Mixing Matrix. In: Introduction to the Physics of Massive and Mixed Neutrinos. Lecture Notes in Physics, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14043-3_5
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DOI: https://doi.org/10.1007/978-3-642-14043-3_5
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Online ISBN: 978-3-642-14043-3
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