PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

the sinα term. However, decay to h 0 is driven by the vertex factor
C h0 ,R
νΣ
= 1 0 2 U† 11 Y † Σ U∗ 22cosα. (3.59)
For the decay Σ 0 m i
→ ν mj A 0 we find from Table 3.14 that the dominant vertex factor is
C A0 ,R
νΣ
= − i 0 2 U† 11 Y † Σ U∗ 22cosβ. (3.60)
Since cosβ ≃ cosα, the decay rate and flavor structure for this channel will be similar to
what we found for the Σ 0 m i
→ ν mj h 0 channel. The main difference comes in the difference
between the masses of the h 0 and A 0 Higgs.
For the Σ 0 m i
→ ν mj H 0 decay, one can see from Table 3.14 that the vertex factors for
both P L as well as P R vertices, are suppressed by sinα. Therefore, this decay rate can be
neglected.
Σ ± m → ν mH ±
From Table 3.15 the vertex factor for this decay will be
C H± ,L
νΣ ∓ ≃ U T 11 Y T Σ S 22cosβ. (3.61)
As we have seen in section 3.3, the structure of S 22 is very similar to that of U 22 . Hence,
a comparison of the vertex factor for this process with the one from Σ 0 m i
→ ν mj h 0 and
Σ 0 m i
→ ν mj A 0 shows that all three will have decay rates of comparable magnitude, modulo
the difference in the masses of the scalars h 0 , A 0 and H ± .
3.5.2 Decay to Light Leptons and Vector Bosons
The exotic heavy leptons have gauge interactions. Therefore, it is expected that they will
also decay into final state particles with vector bosons, W ± and Z. The decay width Γ
for Σ ± m i
→ l ± m j
/ν mj V and Σ 0 m i
→ l ± m j
/ν mj V in the m lj = 0 limit is given by
where C V,L
l ± Σ
Γ = M Σ i
32π
[1− M V 2 ] 2 [2+ M Σ 2
M Σ
2
M V
2
](
|(C V,L
l ± Σ ) ji |2 +|(C V,R
l ± Σ ) ji |2 ), (3.62)
and CV,R
l ± Σ are the relevant vertex factors given in Appendix B.2, and M V is the
mass of the vector boson involved. The dominant vertex factor relevant for Σ ± m → l± m Z
and Σ 0 m → l± m W∓ in terms of Y Σ , M, v ′ and the mixing matrices are given respectively by
C Z,L
l ± Σ ± ≃ v′
2
g
c w
U l † Y † Σ M−1 U L h, and C W∓ ,L
l ± Σ 0 ≃ − v′
2 gU l † Y † Σ M−1 U Σ . (3.63)
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