614
K. Earl et al.
Ni
l
β
Φ
Nk
lα
Φ
Ni
lβ
Φ
Nk
lα
Φ
+
+
Ni
lα
Φ
Ni
lβ
Φ
Nk
l
α
Φ
Ni
l
β
Φ
Nk
l
α
Φ
+
+
Ni
l
α
Φ
Fig. 1 Diagrams responsible for the decay of the heavy neutrino N into SM particles (top row)
and the mirror particles (bottom row), contributing to the calculation of the CP violating parameters
iα and
iα
The middle diagrams of Fig. 1 involving the same type of particles in the loop as
in the final states are relevant only in the flavored case. They give rise respectively
to the first terms in the square brackets of Eqs. (11) and (12) which vanish only if
one sums over α.
Summing over α, one can verify that Eq. (10) holds with
i =
i =
1
8π
1
(y † y) ii + (y
† y ) ii
k
√
x k
1 − x k
Im[(y
y
) ik (y
† y) ik ].
(13)
This parameter measures the total amount of CP violation induced by the decay of
the heavy neutrino N i . Compared to the standard leptogenesis result [2, 3], there is
no triangle or vertex diagram contribution and the CP violation comes only from the
interference between the tree-level and the one-loop self-energy diagrams [1].
2 Flavor Enhancement
Here we will discuss a novel enhancement effect that can be achieved in this
model [4]. Assuming that |y | | |y|, from Eqs. (11) and (12), we have the following
parametric dependence:
iα ∼ a(y
4 /y
) + b(y
2 ),
(14)
iα ∼ a(y
) + b(y
2 ),
(15)
where a(x) represents the “purely flavor terms” i.e. the first terms in the square
brackets of Eqs. (11) and (12) while b(x) represents the second terms in the square
brackets of Eqs. (11) and (12). Notice that the purely flavored term in the
parameter is enhanced by a factor of ∼ y /y 2 ∼ P −1 with P the branching ratio
K. Earl et al.
Ni
l
β
Φ
Nk
lα
Φ
Ni
lβ
Φ
Nk
lα
Φ
+
+
Ni
lα
Φ
Ni
lβ
Φ
Nk
l
α
Φ
Ni
l
β
Φ
Nk
l
α
Φ
+
+
Ni
l
α
Φ
Fig. 1 Diagrams responsible for the decay of the heavy neutrino N into SM particles (top row)
and the mirror particles (bottom row), contributing to the calculation of the CP violating parameters
iα and
iα
The middle diagrams of Fig. 1 involving the same type of particles in the loop as
in the final states are relevant only in the flavored case. They give rise respectively
to the first terms in the square brackets of Eqs. (11) and (12) which vanish only if
one sums over α.
Summing over α, one can verify that Eq. (10) holds with
i =
i =
1
8π
1
(y † y) ii + (y
† y ) ii
k
√
x k
1 − x k
Im[(y
y
) ik (y
† y) ik ].
(13)
This parameter measures the total amount of CP violation induced by the decay of
the heavy neutrino N i . Compared to the standard leptogenesis result [2, 3], there is
no triangle or vertex diagram contribution and the CP violation comes only from the
interference between the tree-level and the one-loop self-energy diagrams [1].
2 Flavor Enhancement
Here we will discuss a novel enhancement effect that can be achieved in this
model [4]. Assuming that |y | | |y|, from Eqs. (11) and (12), we have the following
parametric dependence:
iα ∼ a(y
4 /y
) + b(y
2 ),
(14)
iα ∼ a(y
) + b(y
2 ),
(15)
where a(x) represents the “purely flavor terms” i.e. the first terms in the square
brackets of Eqs. (11) and (12) while b(x) represents the second terms in the square
brackets of Eqs. (11) and (12). Notice that the purely flavored term in the
parameter is enhanced by a factor of ∼ y /y 2 ∼ P −1 with P the branching ratio