Etude et impact du bruit de fond corrélé pour la mesure de l'angle ...

36 2. Neutrino physics
triplet with isospin 1.
Once a right-handed neutrino is introduced to obtain a Dirac mass term, a
Majorana mass term could also be obtained in case the right-handed neutrino
is Majorana particle. The most general mass term can thus be written
as mix of Dirac and Majorana term:
L D+M = L D + L MR + L ML
which could be written as:
L D+M = 1 2
= m D ⌫ L ⌫ R m MR ⌫ c R⌫ R m ML ⌫ c L⌫ L + h.c (2.24)
✓ ◆✓ ◆
⌫ c mL m
L ⌫ D ⌫L
R + h.c. (2.25)
m D m R ⌫ R
tel-00821629, version 1 - 11 May 2013
The term m L is the left-handed neutrino Majorana mass, m R is the righthanded
neutrino Majorana mass and m D is the Dirac mass. The mass
matrix can be diagonalised in term of the mass eigenstate:
⌫ L = cos ✓⌫ 1 +sin✓⌫ 2 (2.26)
⌫ c R = sin ✓⌫ 1 + cos ✓⌫ 2 (2.27)
with eigenstate m 1,2 :
m 1,2 = 1 ✓
q
◆
m L + m R ± (m L mR)
2
2 + m 2 D
and tan 2✓ =
m R
2m D
mL
(2.28)
Since the left handed Majorana mass term requires an Higgs triplet, in
the minimal SM extension, m L is usually set to zero. The right-handed
Majorana neutrino is an electroweak singlet acquiring a mass independently
from the Yukawa coupling.
In the limit where m L = 0 and m R m D :
tan ✓ ' 2m D
m R
' 0;m 1 ' m2 D
m R
and m 2 ' m R (2.29)
with one light left-handed neutrino and one heavy right-handed neutrino:
⌫ 1 ' (⌫ L ⌫L c ) (2.30)
⌫ 2 ' (⌫ R + ⌫R c ) (2.31)
This is the so called see-saw mechanism, which involves two Majorana particles:
a very heavy right-handed neutrino and the observed light left-handed
neutrino. The smallness of the observed neutrino mass could then be explained
in terms of a Dirac mass of the order of the electroweak energy scale,
without the unnatural Yukawa coupling constant, and a much bigger Majorana
mass term. The term m R is generally related to the grand unification