PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Figure 2.2: Feynman diagram of neutrinoless double beta decay
double-beta decay process is,
(A,Z) → (A,Z +2)+2e − , (2.7)
which violates lepton number by two units. The decay rate for this process is,
Γ 0ν ββ ∝ |M| 2 |m ee | 2 , (2.8)
where M is the amplitude and m ee which is the ee entry of the neutrino mass matrix
m ee = ∑ i
U 2 eim i
= cos 2 θ 13 (m 1 e 2iα 1
cos 2 θ 12 +m 2 e 2iα 2
sin 2 θ 12 )+m 3 sin 2 θ 13 . (2.9)
Hence this process depends on the Majorana CP violating phases α 1,2 .
2.2 Neutrino Mass
As we have seen in the previous section, the oscillation experiments indeed support a
non-zero neutrino mass which can be either Dirac or Majorana. The Dirac and Majorana
mass terms of a standard model neutrino will respectively be the following,
L Dirac = N R m ν ν L +h.c,
L Majorana = ν C L m ν ν L +h.c. (2.10)
To generate Diracmass termone will require another spinor field N R . Like the mass terms
of all other standard model fermions, this Dirac or Majorana mass term of the standard
model neutrino should also be generated from a gauge invariant Yukawa Lagrangian.
The Dirac mass term of the standard model neutrino conserves lepton number while the
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