Michel parameter in 3-3-1 model with three lepton singlets
We show that the mass matrix of electrically neutral gauge bosons in the
recently proposed model based on SU(3)C ⊗ SU(3)L ⊗ U(1)X group with three lepton
singlets [1] has two exact eigenvalues: a zero corresponding the photon mass and the
second one equaling the mass of the imaginary component A5µ. Hence the neutral nonHermitian gauge boson Xµ0 (defined as 2X A iA µ µ µ o = − 4 5 ' ) is properly determined. With
extra vacuum expectation value of the Higgs field n2, there are mixings among the
Standard Model W boson and the extra charged gauge boson Y carrying lepton number 2
(bilepton) as well as among neutral gauge bosons Z, Z' and X0. These mixings lead to
very rich phenomenology of the model. The leading order of the Michel parameter (ρ) has
quite special form requiring an equality of the vacuum expectation values in the second
step of spontaneous symmetry breaking, namely, k1 = k2.
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Tóm tắt nội dung tài liệu: Michel parameter in 3-3-1 model with three lepton singlets
a
~ ~
( ) ( )
−
y a a a
a y a a a a y
λ
( )
−
62 ƯỜ ĐẠ Ọ Ủ ĐÔ Ộ
λ
( )
a
~ ~
y a a a
− ∓
a a a a y
≡ ~
a a a
a ay
a y a a a
a y
, , ,
1 2
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27
3
1 4 1
2
3 −
3
a
4
2( ) (2 − ) ( ) (
a y a a
,
( )
,
a a a a a
a a y a
3 − 3 2
a a
( )
a a a
Ạ Í Ọ −−− Ố 63
a a a a
a a a a a a
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a a a y
−
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a a a a a a a y y a
4
( )(18 ) (18 18 ) − ∆′
= + 18 + + 18 + 4 + 18 + + ∆′
∆ = + + 18 + + 2 9 + 2 − 108 9 + 2 + + +
+ 18 + 1 + + −
108 + + + +
∆ = + 18 + + 18 + + 2 9 + 2 − −54 +
+ 54 + 18 + + 2 18 + 9 + 2 −
54 9 + 2 + − 56 +
y a y a
64 ƯỜ ĐẠ Ọ Ủ ĐÔ Ộ
54 + + 3 − −
− 54 + ∗
= +
18 + + 2 18 + 9 + 2 −
∗ − 56
−54 9 + 2 +
a a a a a
E a a a a
a E a a a y
−
a y y a a y a a a a
+ + + 18 + + + −
−27 + +
+ ∗
= 27 + ∗
18 + + 2 18 + 9 + 2 −
∗ −
8
−54 9 + 2 +
−28
≅
a a y a a y
a y a a a a
a a a
y a a a
y a a a E
y a a y E y a
E a y E
y a ~ ~
y a a a y a a
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Ạ Í Ọ −−− Ố 65
a a a a a a a
a y a a y a
A a a a a
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a
≅ − 1
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a
18 +
= = ∗
2 9 + 2
1 + − +
18 + + 2 18 + 9 + 2 −
∗ − + O
−54 9 + 2 +
+
−
a a a
E a a a
a y a a a a
E a a a a a a y
1 + = 1
66 ƯỜ ĐẠ Ọ Ủ ĐÔ Ộ
a a
y
=
a a
a a y
a y a a a
a a a
a a a a a a y a a
y a
a a a a
a a a a a y a
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a a a a a
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a a
y a a a a
a a a a a
a
a y a a a
a a a a a a
a a a y a
a a y a a
a a a y y a
Acknowledgment: a y a a a a
a y A E a
a a a y
A a a a a y
Ạ Í Ọ −−− Ố 67
a a y
a a y a y
y
a a y
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a a y y
y
A a y A a
y A y
y A a
a a a a a a a y
a
a a y a
a y a y
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a a
a y a a a a y E
A E a a a a y y
a a a a a a a y a
a a y a
a
a a
a
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a
a a y A a
a a A a a
a y A A a
a E y
A a a a a E A a a
a E
a a y a a
a a y a a a a a y
a y
68 ƯỜ ĐẠ Ọ Ủ ĐÔ Ộ
⊗ ⊗
ơ ơ
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