PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Γ 1HDM (Σ ± m → l± m Z) ≃ λ2 M Σ
32π (1− M2 Z
2
M )2 (1+2 M2 Z
2
), (3.67)
Σ M Σ
Γ 1HDM (Σ ± m → ν mW ± ) ≃ λ2 M Σ
16π (1− M2 Z
2
M )2 (1+2 M2 Z
2
). (3.68)
Σ M Σ
where λ is the triplet fermion – lepton doublet – Higgs doublet Yukawa coupling in the
one Higgs doublet model, and all mixing terms are neglected. This should be compared
with the corresponding expression given in Eq. (3.62), which on neglecting all mixing and
hence flavor effects reduces to (for m lj = 0)
Γ 2HDM (Σ 0 m → ν mZ) ≃ Y 2 Σ M Σ
64π
Γ 2HDM (Σ 0 m → l∓ m W± ) ≃ Y 2 Σ M Σ
32π
Γ 2HDM (Σ ± m → l ± mZ) ≃ Y 2 Σ M Σ
32π
Γ 2HDM (Σ ± m → ν m W ± ) ≃ Y 2 Σ M Σ
16π
v ′ 2
V 2(1− M2 Z
v ′ 2
V 2(1− M2 W
v ′ 2
V 2(1− M2 Z
M Σ
2 )2 (1+2 M2 Z
M Σ
2
), (3.69)
2
M )2 (1+2 M2 W
2
), (3.70)
Σ M Σ
2
M )2 (1+2 M2 Z
2
),
Σ M Σ
(3.71)
v ′ 2
V 2(1− Z
2
M )2 (1+2 M2 Z
2
).
Σ M Σ
(3.72)
where V 2 = v 2 +v ′2 is the electroweak breaking scale. The scale of the Yukawa coupling
constants and VEVs are fixed by the neutrino mass m ν ∼ λ 2 V 2 /M Σ for the one Higgs
doublet model and m ν ∼ Y 2 Σ v′2 /M Σ . If one replaces λ 2 and Y 2 Σ v′2 /V 2 with m ν M Σ /V 2 in
both set of expressions, one can see that the the decay rates of heavy fermions into gauge
bosons are identical for both models.
The rates for decay into Higgs for the one Higgs doublet model neglecting flavor effects,
is given by (for m lj = 0)
Γ 1HDM (Σ 0 m → ν m H 0 ) ≃ λ2 M Σ
64π (1− M2 H
M Σ
2 )2 , (3.73)
Γ 1HDM (Σ ± m → l ± mH 0 ) ≃ λ2 M Σ
32π (1− M2 H
M Σ
2 )2 . (3.74)
For the two Higgs doublet model, the corresponding decay rates are given by Eq. (3.52),
which on neglecting all flavor effects reduces to (for m lj = 0)
Γ 2HDM (Σ 0 m → ν m h 0 /A 0 ) ≃ Y Σ 2 cos2 αM Σ
(1− M2 h/A
2
64π M )2 , (3.75)
Σ
Γ 2HDM (Σ ± m → l mh ± 0 /A 0 ) ≃ Y Σ 2 cos2 αM Σ
(1− M2 h/A
2
32π M )2 , (3.76)
Σ
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