PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Σ − -> e
m 1 m
h 0
Σ − -> e
m 2 m
h 0
Σ − -> µ
m 1 m
/τ m
h 0
Σ − m 2
-> µ m
/ τ m
h 0 Σ − m 3
-> µ m
/ τ m
h 0
10 0
10 0
10 -2
10 -2
10 -2
Γ(GeV)
10 -4
10 -4
10 -4
10 -6
10 -6
10 -6
10 -8
200 400 600 800 1000 1200
M Σ1
(GeV)
10 0 400 600 800 1000 1200
10 -8
400 600 800 1000 1200
M Σ2
(GeV)
10 -8
M Σ3
(GeV)
Figure 3.5: Variation of Γ(Σ − m i
→ l − m j
h 0 ) with M Σi
factors are given in terms of the 3×3 block matrices S ab and T ab , where a,b = 1,2. We
have seen in the earlier sections that S 12 , T 12 and T 21 are heavily suppressed – the first
one by O(m D /M) and T 12 and T 21 by O((m l m D )/M 2 ). The vertex factors also depend
on the Higgs mixing angle α. In Appendix A, we have shown how the neutrino mass
constrains the neutral Higgs mixing such that sinα ∼ 10 −6 and cosα ∼ 1. Therefore, for
the Σ ± m i
→ l ± mh 0 decay the dominating vertex factor is
C h0 ,R
l ± Σ ± ≃ 1 √
2
S † 11 Y † Σ T 22cosα. (3.55)
We have seen in Eq. (3.46) that S 11 ≃ 1 if we neglect terms of the order of O(m 2 D /M2 ).
Therefore,
⎛ √ ⎞
a 4 2a11 0
C h0 ,R 1
l ± Σ
≃ ⎝a ± 11 √2 1
(a 6 +a 8 ) √2 (a 8 −a 6 ) ⎠. (3.56)
1
a 11 √2 1
(a 6 +a 8 ) √2 (a 6 −a 8 )
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