Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Appendix A
The MNSP matrix and its
parametrization
In the standard model CP-violation is limited to the hadronic sector. Since the
experimental evidence that neutrinos oscillate (meaning they are massive) the
standard model has to be extended and a mixing matrix for leptons introduced.
Since leptons constitutes a family of three particles (of non-degenerate masses),
CP-violation becomes possible in the leptonic sector. In the standard model,
neutrinos are the only elementary fermions with zero charge. This unique status
implies that neutrinos can be of two different types, namely either Dirac or Majorana
particles. Double beta decay experiments can discriminate the nature of
neutrino. Let us first focus on the case where neutrinos are Dirac particles. At
the end of this appendix we will comment on the Majorana case.
A.1 The Dirac neutrino case
If neutrinos are Dirac particles they are the same as the other fermions and
neutrinos with right helicity must exist. The right and left handed spinors are
mixed via a mass matrix, and the Dirac mass term for neutrinos is:
−LD = ν f
iL (mD)ij ν f
jR + h.c. (A.1)
Here the superscript f is used to denote the flavour eigenstate fields. Therefore,
the part of the Lagrangian that describes the lepton masses and charged current
interactions is
−LW+m+D = g √ l
2 f
iL γ µ ν f
iL W − µ + l f
iL(ml)ijl f
jR + νf
iL (mD)ij ν f
jR + h.c. (A.2)
where the li can be e, µ, τ. This expression shows that neutrino oscillations, due
to the presence of the Dirac neutrino mass term, violate individual lepton flavour
number Le, Lµ and Lτ while the total lepton number L = Le + Lµ + Lτ is still
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