PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

theory. The fields which get integrated out can be either a gauge singlet neutrino field
N R , or the SU(2) triplet field ∆ with hypercharge Y = +2, or an SU(2) triplet field Σ R
with hypercharge Y = 0. Accordingly, the seesaw is characterized as type-I, type-II and
type-IIIseesaw respectively. InFig. 2.3we present theFeynmandiagramofthefourpoint
function LLHH. For the type-I seesaw, the coupling κ ij is Y T ν i
Y νj
M
while for type-III and
type-II seesaw the coupling κ ij is Y Σ T Y Σj i and Y ∆µ ∆
respectively, where Y
M M∆
2 ν , Y Σ and Y ∆ are
the Yukawa couplings and µ ∆ is the coupling between Higgs triplet ∆ and the standard
model Higgs doublet H. Below, we discuss in detail the different seesaw mechanisms.
Type-I Seesaw
The standard model is extended by adding the gauge singlet right handed neutrino N R .
The Majorana neutrino in this case is N = N R +NR C . The right handed neutrino being a
gauge singlet, interacts only with the standard model lepton doublet L and the Higgs H
via the Yukawa interaction,
−L Y = Y ν ¯NR ˜H† L+ 1 2 M ¯N R N C R
+h.c, (2.14)
where ˜H = iσ 2 H ∗ and M is the lepton number violating mass term of the right handed
neutrino N R . After the Higgs H takes vacuum expectation value v, the following neutrino
mass matrix will be generated from Eq. (2.14),
L m = 1 2
( ) (
ν
C
0 vYν
T
L
N R
vY ν M
)(
νL
N C R
)
+h.c. (2.15)
Assuming M ≫ vY ν , the diagonalization of the mass matrix gives two eigenvalues M and
m ν ∼ m T D M−1 m D , where we have defined m D = vY ν . One can identify the eigenvalue M
as the mass matrix of the heavy right handed neutrino and the later one m ν is the mass
matrix of the standard model neutrinos.
Type-II Seesaw
Standard model neutrino masses can be generated by adding the SU(2) triplet Higgs
to the standard model field contents [24]. The Higgs triplet ∆ has U(1) Y hypercharge
Y = +2 and has the following Yukawa interaction,
−L Y = Y ∆ L T Ciσ 2 ∆L+h.c (2.16)
where the Higgs triplet ∆ is,
(
∆
∆ =
+ / √ 2 ∆ ++
∆ 0 −∆ + / √ 2
)
. (2.17)
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