Mirror Dirac Leptogenesis
615
for singlet decay to the SM sector. 1 Hence if N i decays mostly to the mirror sector,
the flavored CP parameters in the mirror sector can be enhanced accordingly. In
this case, even if the flavored CP parameters in the SM are not enhanced, due to
conservation of (B − L) − (B − L ) charge, the enhanced production of mirror
(B − L ) asymmetry will be fed back to the SM sector, resulting in an overall
enhancement of asymmetry production. This is an appealing feature of the model.
As a concrete example, we study N 1 leptogenesis by choosing the following
parameters:
(P 1e , P 1μ , P 1τ ) = 10
−3 (1/3, 1/3, 1/3),
(16)
(P
1e , P
1μ , P
1τ ) = 0.999(8 × 10
−3 , 2 × 10
−3 , 0.99),
(17)
(( 1e , , 1μ , , 1τ ) = −(1/3, 1/3, 1/3))
max
1 ,
(18)
((
1e , ,
1μ , ,
1τ ) = (1000, 990, −1991))
max
1 ,
(19)
where the total CP parameter is 1 =
1 = − max
1 . By setting M 1 = 8 × 10 8 GeV,
f = 500 GeV, m 3 + m 1 = 0.1. The final baryon asymmetry Y B obtained from
solving the BEs as a function of K 1
K 1 ≡
Γ N 1
H (T = M 1 )
(20)
is plotted in Fig. 2. The solid red and purple dashed lines refer respectively to the
case with zero and thermal initial N 1 abundances while the dotted horizontal line is
the observed baryon asymmetry Y B = 8.7 × 10 −11 .
3 Notes and Comments
Regarding the flavor effects, we have the following comments:
• In both cases of thermal and zero initial abundance we have that flavor effects
are impotent in the weak washout regime. In this case the washout terms are
negligible during decays of N 1 , allowing one to sum over the source term and
the final asymmetry will be proportional to the total CP parameter 1 which is
too small in the three-flavor regime. For the parameters specified in the previous
section, as shown in Fig. 2, a sufficient baryon asymmetry can be generated for
K 1 15 and K 1 55 respectively for thermal and zero initial N 1 abundance.
1 For N 1 leptogenesis, the flavored terms will have an additional M 1 /M k>1 suppression while for
N 2 leptogenesis, there can be an enhancement of M 2 /M 1 . Here will assume M 1 /M k>1 is of a
factor of a few and focus on N 1 leptogenesis.
615
for singlet decay to the SM sector. 1 Hence if N i decays mostly to the mirror sector,
the flavored CP parameters in the mirror sector can be enhanced accordingly. In
this case, even if the flavored CP parameters in the SM are not enhanced, due to
conservation of (B − L) − (B − L ) charge, the enhanced production of mirror
(B − L ) asymmetry will be fed back to the SM sector, resulting in an overall
enhancement of asymmetry production. This is an appealing feature of the model.
As a concrete example, we study N 1 leptogenesis by choosing the following
parameters:
(P 1e , P 1μ , P 1τ ) = 10
−3 (1/3, 1/3, 1/3),
(16)
(P
1e , P
1μ , P
1τ ) = 0.999(8 × 10
−3 , 2 × 10
−3 , 0.99),
(17)
(( 1e , , 1μ , , 1τ ) = −(1/3, 1/3, 1/3))
max
1 ,
(18)
((
1e , ,
1μ , ,
1τ ) = (1000, 990, −1991))
max
1 ,
(19)
where the total CP parameter is 1 =
1 = − max
1 . By setting M 1 = 8 × 10 8 GeV,
f = 500 GeV, m 3 + m 1 = 0.1. The final baryon asymmetry Y B obtained from
solving the BEs as a function of K 1
K 1 ≡
Γ N 1
H (T = M 1 )
(20)
is plotted in Fig. 2. The solid red and purple dashed lines refer respectively to the
case with zero and thermal initial N 1 abundances while the dotted horizontal line is
the observed baryon asymmetry Y B = 8.7 × 10 −11 .
3 Notes and Comments
Regarding the flavor effects, we have the following comments:
• In both cases of thermal and zero initial abundance we have that flavor effects
are impotent in the weak washout regime. In this case the washout terms are
negligible during decays of N 1 , allowing one to sum over the source term and
the final asymmetry will be proportional to the total CP parameter 1 which is
too small in the three-flavor regime. For the parameters specified in the previous
section, as shown in Fig. 2, a sufficient baryon asymmetry can be generated for
K 1 15 and K 1 55 respectively for thermal and zero initial N 1 abundance.
1 For N 1 leptogenesis, the flavored terms will have an additional M 1 /M k>1 suppression while for
N 2 leptogenesis, there can be an enhancement of M 2 /M 1 . Here will assume M 1 /M k>1 is of a
factor of a few and focus on N 1 leptogenesis.