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Beyond-Standard-Model: the 331 case and itssignatures at the LHC
Antonio Costantini
Laboratori Nazionali di Frascati
13 September 2018
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Elementary Particles
Brout-Englert-Higgs Mechanism - 1964
Elementary Particles
Brout-Englert-Higgs Mechanism - 1964
Brout-Englert-Higgs Mechanism in a Nutshell
V (Φ) = µ2Φ†Φ + λ(Φ†Φ)2 Φ =(φ+
φ
)
Djouadi, Phys.Rept. 457 (2008) 1-216
〈Φ〉0 =(
0v/√2
)
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Some Issues of the SM
♦ evidence of dark matter from e.g. the rotation curve ofgalaxies
♦ evidence of (very tiny) mass of neutrinos from neutrinooscillation
♦ lack of explanation of the hierarchy v � MPlanck
♦ lack of explanation of nQf = nLf = 3
♦ ...
Some Issues of the SM
♦ evidence of dark matter from e.g. the rotation curve ofgalaxies
♦ evidence of (very tiny) mass of neutrinos from neutrinooscillation
♦ lack of explanation of the hierarchy v � MPlanck
♦ lack of explanation of nQf = nLf = 3
♦ ...
Some Issues of the SM
♦ evidence of dark matter from e.g. the rotation curve ofgalaxies
♦ evidence of (very tiny) mass of neutrinos from neutrinooscillation
♦ lack of explanation of the hierarchy v � MPlanck
♦ lack of explanation of nQf = nLf = 3
♦ ...
Some Issues of the SM
♦ evidence of dark matter from e.g. the rotation curve ofgalaxies
♦ evidence of (very tiny) mass of neutrinos from neutrinooscillation
♦ lack of explanation of the hierarchy v � MPlanck
♦ lack of explanation of nQf = nLf = 3
♦ ...
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Supersymmetry!
WMSSM = yuUHuQ − yd DHd Q − yeE Hd L + µHuHd
Higgs in the MSSM
♦ At tree-levelmH ≤ mZ
♦ In tension withdiscovered Higgsmex
H ∼ 125 GeV
♦ Need of largequantumcorrection∆mH ∼ 30 GeV
♦ Large splitting∆t12 -4 -3 -2 -1 0 1 2 3 4
Xt (TeV)
80
90
100
110
120
130
140
Mh (
GeV
)
1-loop
2-loop
FeynHiggs
Djouadi, Phys.Rept. 459 (2008) 1-241
Higgs in the MSSM
♦ At tree-levelmH ≤ mZ
♦ In tension withdiscovered Higgsmex
H ∼ 125 GeV
♦ Need of largequantumcorrection∆mH ∼ 30 GeV
♦ Large splitting∆t12 -4 -3 -2 -1 0 1 2 3 4
Xt (TeV)
80
90
100
110
120
130
140
Mh (
GeV
)
1-loop
2-loop
FeynHiggs
Djouadi, Phys.Rept. 459 (2008) 1-241
Issues of the MSSM
) [GeV]1t~m(
200 300 400 500 600 700 800 900 1000
) [G
eV]
10 χ∼m
(
0
100
200
300
400
500
600
700
800
1
0χ∼ W b →1t~
/ 1
0χ∼ t →1t~
1
0χ∼ b f f' →1t~
/ 1
0χ∼ W b →1t~
/ 1
0χ∼ t →1t~
1
0χ∼ b f f' →1t~
/ 1
0χ∼ W b →1t~
/ 1
0χ∼ t →1t~
1
0χ∼ b f f' →1t~
/ 1
0χ∼ c →1t~
1
0χ∼ c →1t~
-1=8 TeV, 20 fbs
t
) < m
10
χ∼,1t~
m(
∆W
+ m
b
) < m
10
χ∼,1t~
m(
∆) <
01
0χ∼,
1t~ m
(∆
1
0χ∼ t →1t~
/ 1
0χ∼ W b →1t~
/ 1
0χ∼ c →1t~
/ 1
0χ∼ b f f' →1t~
production, 1t~1t
~ May 2018
ATLAS Preliminary
1
0χ∼W b
1
0χ∼c
1
0χ∼b f f'
Observed limits Expected limits All limits at 95% CL
-1=13 TeV, 36.1 fbs
0L [1709.04183]1L [1711.11520]2L [1708.03247]Monojet [1711.03301]
c0L [1805.01649]
Run 1 [1506.08616]
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Field Content
G ≡ SU(3)c × SU(3)L × U(1)X
Q1 =
(uLdLDL
), Q2 =
(cLsLSL
), Q1,2 ∈ (3, 3,−1/3)
Q3 =
(bLtLTL
), Q3 ∈ (3, 3, 2/3)
l =
(lLνll cR
), l ∈ (1, 3, 0), l = e, µ, τ
ρ =
(ρ++
ρ+
ρ0
)∈ (1, 3, 1), η =
(η+
η0
η−
)∈ (1, 3, 0), χ =
(χ0
χ−
χ−−
)∈ (1, 3,−1)
Field Content
G ≡ SU(3)c × SU(3)L × U(1)X
Q1 =
(uLdLDL
), Q2 =
(cLsLSL
), Q1,2 ∈ (3, 3,−1/3)
Q3 =
(bLtLTL
), Q3 ∈ (3, 3, 2/3)
l =
(lLνll cR
), l ∈ (1, 3, 0), l = e, µ, τ
ρ =
(ρ++
ρ+
ρ0
)∈ (1, 3, 1), η =
(η+
η0
η−
)∈ (1, 3, 0), χ =
(χ0
χ−
χ−−
)∈ (1, 3,−1)
Field Content
G ≡ SU(3)c × SU(3)L × U(1)X
Q1 =
(uLdLDL
), Q2 =
(cLsLSL
), Q1,2 ∈ (3, 3,−1/3)
Q3 =
(bLtLTL
), Q3 ∈ (3, 3, 2/3)
l =
(lLνll cR
), l ∈ (1, 3, 0), l = e, µ, τ
ρ =
(ρ++
ρ+
ρ0
)∈ (1, 3, 1), η =
(η+
η0
η−
)∈ (1, 3, 0), χ =
(χ0
χ−
χ−−
)∈ (1, 3,−1)
Field Content
G ≡ SU(3)c × SU(3)L × U(1)X
Q1 =
(uLdLDL
), Q2 =
(cLsLSL
), Q1,2 ∈ (3, 3,−1/3)
Q3 =
(bLtLTL
), Q3 ∈ (3, 3, 2/3)
l =
(lLνll cR
), l ∈ (1, 3, 0), l = e, µ, τ
ρ =
(ρ++
ρ+
ρ0
)∈ (1, 3, 1), η =
(η+
η0
η−
)∈ (1, 3, 0), χ =
(χ0
χ−
χ−−
)∈ (1, 3,−1)
Embedding of the Hypercharge Y
Electromagnetic charge in the 331 model is given by
Qem3 = Y3 + T3 Qem
3 = Y3 − T3
Y3 =√3T8 + X1 Y—3 = −
√3T8 + X1
Ti = λi/2 , i = 1, . . . 8
λi Gell-Mann matrices
T8 = diag[ 12√3
(1, 1,−2)]
Embedding of the Hypercharge Y
Electromagnetic charge in the 331 model is given by
Qem3 = Y3 + T3 Qem
3 = Y3 − T3
Y3 =√3T8 + X1 Y—3 = −
√3T8 + X1
Ti = λi/2 , i = 1, . . . 8
λi Gell-Mann matrices
T8 = diag[ 12√3
(1, 1,−2)]
Embedding of the Hypercharge Y
Electromagnetic charge in the 331 model is given by
Qem3 = Y3 + T3 Qem
3 = Y3 − T3
Y3 =√3T8 + X1 Y—3 = −
√3T8 + X1
Ti = λi/2 , i = 1, . . . 8
λi Gell-Mann matrices
T8 = diag[ 12√3
(1, 1,−2)]
SU(3)× SU(3)× U(1): an exotic possibility
Q1 =
(uLdLDL
), Q2 =
(cLsLSL
), Q1,2 ∈ (3, 3,−1/3)
Q3 =
(bLtLTL
), Q3 ∈ (3, 3, 2/3)
QemD = Qem
S = −4/3
QemT = 5/3
Exotic Quarks!
From SU(3)L × U(1)X to U(1)em
SU(3)L × U(1)X
‖〈ρ〉⇓
SU(2)L × U(1)Y
‖〈η〉 , 〈χ〉⇓
U(1)em
W1, · · · ,W8 , BX
‖〈ρ〉⇓
W1,W2,W3,BY ,Y ±,Y ±±,Z ′
‖〈η〉 , 〈χ〉⇓
γ,Z ,Z ′,W±,Y ±,Y ±±
From SU(3)L × U(1)X to U(1)em
SU(3)L × U(1)X
‖〈ρ〉⇓
SU(2)L × U(1)Y
‖〈η〉 , 〈χ〉⇓
U(1)em
W1, · · · ,W8 , BX
‖〈ρ〉⇓
W1,W2,W3,BY ,Y ±,Y ±±,Z ′
‖〈η〉 , 〈χ〉⇓
γ,Z ,Z ′,W±,Y ±,Y ±±
From SU(3)L × U(1)X to U(1)em
SU(3)L × U(1)X
‖〈ρ〉⇓
SU(2)L × U(1)Y
‖〈η〉 , 〈χ〉⇓
U(1)em
W1, · · · ,W8 , BX
‖〈ρ〉⇓
W1,W2,W3,BY ,Y ±,Y ±±,Z ′
‖〈η〉 , 〈χ〉⇓
γ,Z ,Z ′,W±,Y ±,Y ±±
From SU(3)L × U(1)X to U(1)em
SU(3)L × U(1)X
‖〈ρ〉⇓
SU(2)L × U(1)Y
‖〈η〉 , 〈χ〉⇓
U(1)em
W1, · · · ,W8 , BX
‖〈ρ〉⇓
W1,W2,W3,BY ,Y ±,Y ±±,Z ′
‖〈η〉 , 〈χ〉⇓
γ,Z ,Z ′,W±,Y ±,Y ±±
From SU(3)L × U(1)X to U(1)em
SU(3)L × U(1)X
‖〈ρ〉⇓
SU(2)L × U(1)Y
‖〈η〉 , 〈χ〉⇓
U(1)em
W1, · · · ,W8 , BX
‖〈ρ〉⇓
W1,W2,W3,BY ,Y ±,Y ±±,Z ′
‖〈η〉 , 〈χ〉⇓
γ,Z ,Z ′,W±,Y ±,Y ±±
From SU(3)L × U(1)X to U(1)em
SU(3)L × U(1)X
‖〈ρ〉⇓
SU(2)L × U(1)Y
‖〈η〉 , 〈χ〉⇓
U(1)em
W1, · · · ,W8 , BX
‖〈ρ〉⇓
W1,W2,W3,BY ,Y ±,Y ±±,Z ′
‖〈η〉 , 〈χ〉⇓
γ,Z ,Z ′,W±,Y ±,Y ±±
Yukawa Interactions: Quark Sector
LYuk.q,triplet =
(y1
d Q1η∗dR + y2
d Q2η∗sR + y3
d Q3χ b∗R+ y1
u Q1χ∗u∗R + y2
u Q2χ∗c∗R + y3
u Q3η t∗R+ y1
E Q1 ρ∗D∗R + y2
E Q2 ρ∗S∗R + y3
E Q3 ρT ∗R)
+ h.c.
vρ � vη,χ⇓
mD,S,T = O(TeV ) if y iE ∼ 1
Yukawa Interactions: Quark Sector
LYuk.q,triplet =
(y1
d Q1η∗dR + y2
d Q2η∗sR + y3
d Q3χ b∗R+ y1
u Q1χ∗u∗R + y2
u Q2χ∗c∗R + y3
u Q3η t∗R+ y1
E Q1 ρ∗D∗R + y2
E Q2 ρ∗S∗R + y3
E Q3 ρT ∗R)
+ h.c.
vρ � vη,χ⇓
mD,S,T = O(TeV ) if y iE ∼ 1
Yukawa Interactions: Quark Sector
LYuk.q,triplet =
(y1
d Q1η∗dR + y2
d Q2η∗sR + y3
d Q3χ b∗R+ y1
u Q1χ∗u∗R + y2
u Q2χ∗c∗R + y3
u Q3η t∗R+ y1
E Q1 ρ∗D∗R + y2
E Q2 ρ∗S∗R + y3
E Q3 ρT ∗R)
+ h.c.
vρ � vη,χ⇓
mD,S,T = O(TeV ) if y iE ∼ 1
Yukawa Interactions: Lepton Sector
LYukl , triplet = Gη
ab(l iaαε
αβ l jbβ)η∗kεijk + h.c.
= Gηab l i
a · ljb η∗kεijk + h.c.
a and b are flavour indicesα and β are Weyl indices (l i
a · ljb ≡ l i
aαεαβ l j
bβ)i , j , k = 1, 2, 3, are SU(3)L indices
l ia · l
jb η∗kεijk is antisymmetric
⇓Gη
ab has to be antisymmetric
Yukawa Interactions: Lepton Sector
LYukl , triplet = Gη
ab(l iaαε
αβ l jbβ)η∗kεijk + h.c.
= Gηab l i
a · ljb η∗kεijk + h.c.
a and b are flavour indicesα and β are Weyl indices (l i
a · ljb ≡ l i
aαεαβ l j
bβ)i , j , k = 1, 2, 3, are SU(3)L indices
l ia · l
jb η∗kεijk is antisymmetric
⇓Gη
ab has to be antisymmetric
Yukawa Interactions: Lepton Sector
LYuk.l ,sextet = Gσ
ab l ia · l
jbσ∗i ,j
with
σ =
σ++
1 σ+1 /√2 σ0/
√2
σ+1 /√2 σ0
1 σ−2 /√2
σ0/√2 σ−2 /
√2 σ−−2
∈ (1, 6, 0)
Gσab is symmetric
H±± → l±l± allowed (η 6⊃ η±±)
Yukawa Interactions: Lepton Sector
LYuk.l ,sextet = Gσ
ab l ia · l
jbσ∗i ,j
with
σ =
σ++
1 σ+1 /√2 σ0/
√2
σ+1 /√2 σ0
1 σ−2 /√2
σ0/√2 σ−2 /
√2 σ−−2
∈ (1, 6, 0)
Gσab is symmetric
H±± → l±l± allowed (η 6⊃ η±±)
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Embedding of the Hypercharge Y : Qem(β)
Electromagnetic charge in the 331 model is given by
Qem3 = Y3 + T3 Qem
3 = Y3 − T3
Y3 = βT8 + X1 Y3 = −βT8 + X1
Embedding of the Hypercharge Y : Qem(β)
Electromagnetic charge in the 331 model is given by
Qem3 = Y3 + T3 Qem
3 = Y3 − T3
Y3 = βT8 + X1 Y3 = −βT8 + X1
Field Content for Generic β
particles Q(β) β = − 1√3 β = 1√
3 β = −√3 β =
√3
D, S 16 −
√3β2
23 − 1
353 − 4
3T 1
6 +√
3β2 − 1
323 − 4
353
E − 12 +
√3β2 −1 0 −2 1
V − 12 +
√3β2 −1 0 −2 1
Y 12 +
√3β2 0 1 −1 2
HV − 12 +
√3β2 −1 0 −2 1
HY12 +
√3β2 0 1 −1 2
HW 1 1 1 1 1
Cao, Liu, Xie, Yan, Zhang, Phys.Rev. D93 (2016) no.7, 075030
β Parameter: Possible Values in the 331
The β parameter is constrained from the Z ′ mass expression. Hasto satisfy
1− (1 + β2)s2W > 0
⇓
|β| <√3
β = n√3 , n = 1, 2, 3 gives fractional electric charge for various
particle. n = 2 imply ±5/6 and ±7/6 for the electric charge ofheavy fermions and ±1/2 and ±3/2 for heavy leptons.
Buras, De Fazio, Girrbach, JHEP 1402 (2014) 112
β Parameter: Possible Values in the 331
The β parameter is constrained from the Z ′ mass expression. Hasto satisfy
1− (1 + β2)s2W > 0
⇓
|β| <√3
β = n√3 , n = 1, 2, 3 gives fractional electric charge for various
particle. n = 2 imply ±5/6 and ±7/6 for the electric charge ofheavy fermions and ±1/2 and ±3/2 for heavy leptons.
Buras, De Fazio, Girrbach, JHEP 1402 (2014) 112
331 Model: A Flipped Version
Name 331 rep. SM group decomposition Components
Le(1, 6,− 1
3
) (1, 3, 0
)+(1, 2,− 1
2
)+(1, 1,−1
) (Σ+ 1√
2Σ0 1√
2νe
1√2
Σ0 Σ− 1√2`e
1√2νe 1√
2`e Ee
)Lα=µ,τ
(1, 3,− 2
3
) (1, 2,− 1
2
)+(1, 1,−1
)(να, `α, Eα)T
`cα (1, 1, 1)
(1, 1, 1
)`cα
Qα(3, 3, 1
3
) (3, 2, 1
6
)+(3, 1, 2
3
)(dα,−uα,Uα)T
ucα
(3, 1,− 2
3
) (3, 1,− 2
3
)ucα
dcα
(3, 1, 1
3
) (3, 1, 1
3
)dcα
φi=1,2(1, 3, 1
3
) (1, 2, 1
2
)+(1, 1, 0
) (H+
i ,H0i , σ
0i
)T
φ3(1, 3,− 2
3
) (1, 2,− 1
2
)+(1, 1,−1
) (H0
3 ,H−3 , σ−3
)T
S(1, 6, 2
3
) (1, 3, 1
)+(1, 2, 1
2
)+(1, 1, 0
) (∆++ 1√
2∆+ 1√
2H+
S1√2
∆+ ∆0 1√2
H0S
1√2
H+S
1√2
H0S σ0
S
)
Fonseca, Hirsch, JHEP 1608 (2016) 003
331 Model: A Flipped Version
Name 331 rep. SM group decomposition Components
Le(1, 6,− 1
3
) (1, 3, 0
)+(1, 2,− 1
2
)+(1, 1,−1
) (Σ+ 1√
2Σ0 1√
2νe
1√2
Σ0 Σ− 1√2`e
1√2νe 1√
2`e Ee
)Lα=µ,τ
(1, 3,− 2
3
) (1, 2,− 1
2
)+(1, 1,−1
)(να, `α, Eα)T
`cα (1, 1, 1)
(1, 1, 1
)`cα
Qα(3, 3, 1
3
) (3, 2, 1
6
)+(3, 1, 2
3
)(dα,−uα,Uα)T
ucα
(3, 1,− 2
3
) (3, 1,− 2
3
)ucα
dcα
(3, 1, 1
3
) (3, 1, 1
3
)dcα
φi=1,2(1, 3, 1
3
) (1, 2, 1
2
)+(1, 1, 0
) (H+
i ,H0i , σ
0i
)T
φ3(1, 3,− 2
3
) (1, 2,− 1
2
)+(1, 1,−1
) (H0
3 ,H−3 , σ−3
)T
S(1, 6, 2
3
) (1, 3, 1
)+(1, 2, 1
2
)+(1, 1, 0
) (∆++ 1√
2∆+ 1√
2H+
S1√2
∆+ ∆0 1√2
H0S
1√2
H+S
1√2
H0S σ0
S
)
Fonseca, Hirsch, JHEP 1608 (2016) 003
331 Model: A Flipped Version
Name 331 rep. SM group decomposition Components
Le(1, 6,− 1
3
) (1, 3, 0
)+(1, 2,− 1
2
)+(1, 1,−1
) (Σ+ 1√
2Σ0 1√
2νe
1√2
Σ0 Σ− 1√2`e
1√2νe 1√
2`e Ee
)Lα=µ,τ
(1, 3,− 2
3
) (1, 2,− 1
2
)+(1, 1,−1
)(να, `α, Eα)T
`cα (1, 1, 1)
(1, 1, 1
)`cα
Qα(3, 3, 1
3
) (3, 2, 1
6
)+(3, 1, 2
3
)(dα,−uα,Uα)T
ucα
(3, 1,− 2
3
) (3, 1,− 2
3
)ucα
dcα
(3, 1, 1
3
) (3, 1, 1
3
)dcα
φi=1,2(1, 3, 1
3
) (1, 2, 1
2
)+(1, 1, 0
) (H+
i ,H0i , σ
0i
)T
φ3(1, 3,− 2
3
) (1, 2,− 1
2
)+(1, 1,−1
) (H0
3 ,H−3 , σ−3
)T
S(1, 6, 2
3
) (1, 3, 1
)+(1, 2, 1
2
)+(1, 1, 0
) (∆++ 1√
2∆+ 1√
2H+
S1√2
∆+ ∆0 1√2
H0S
1√2
H+S
1√2
H0S σ0
S
)
Fonseca, Hirsch, JHEP 1608 (2016) 003
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
Y ±± + j j @ the LHC
p
p j
j
Y −−
Y ++
Y ±± + j j @ the LHC
q
Q
Y ++
q Y −−
g
Q
g
g
Y ++
q Y −−
Q
g
g
Q
q
q
V 0
q g
q
g
Y ++
Y −−
q
g
q
g
q
Q
Y ++
Y −−
q
g
g
qg
Q
Q
Y ++
Y −−
q
arXiv:1707.01381 [hep-ph]
Benchmark point
Benchmark Point
mh1 = 125.1 GeV mh2 = 3172 GeV mh3 = 3610 GeVma1 = 3595 GeVmh±1
= 1857 GeV mh±2= 3590 GeV
mh±±1= 3734 GeV
mY±± = 873.3 GeV mY± = 875.7 GeVmZ ′ = 3229 GeVmD = 1650 GeV mS = 1660 GeV mT = 1700 GeV
∣∣∣∣gh1ZZ
gSMhZZ
∣∣∣∣ = 1.0± 0.1∣∣∣∣gh1WW
gSMhWW
∣∣∣∣ = 1.0± 0.1
mY±± consistent with bound frommuonium-antimuonium conversion
mZ ′ < 2mQ ⇒ Z ′ → QQ blocked
Benchmark point
Benchmark Point
mh1 = 125.1 GeV mh2 = 3172 GeV mh3 = 3610 GeVma1 = 3595 GeVmh±1
= 1857 GeV mh±2= 3590 GeV
mh±±1= 3734 GeV
mY±± = 873.3 GeV mY± = 875.7 GeVmZ ′ = 3229 GeVmD = 1650 GeV mS = 1660 GeV mT = 1700 GeV
∣∣∣∣gh1ZZ
gSMhZZ
∣∣∣∣ = 1.0± 0.1∣∣∣∣gh1WW
gSMhWW
∣∣∣∣ = 1.0± 0.1
mY±± consistent with bound frommuonium-antimuonium conversion
mZ ′ < 2mQ ⇒ Z ′ → QQ blocked
Signal and Background Cross Section
SIGNAL
pp → Y ++Y−−jj → (`+`+)(`−`−)jj ` = e, µ√
s = 13 TeV and NNPDFLO1 parton distributions (MadGraphdefault)
σ(pp → YYjj → 4`jj) ' 3.7 fb
BACKGROUNDS
pp → ZZ jj → (`+`−)(`+`−)jjpp → ttZ → (j`+ν`)(j`−ν`)(`+`−)
σ(pp → ZZ jj → 4`jj) ' 6.4 fb , σ(pp → ttZ jj → 4` 2ν jj) ' 8.6 fb
Signal and Background Cross Section
SIGNAL
pp → Y ++Y−−jj → (`+`+)(`−`−)jj ` = e, µ√
s = 13 TeV and NNPDFLO1 parton distributions (MadGraphdefault)
σ(pp → YYjj → 4`jj) ' 3.7 fb
BACKGROUNDS
pp → ZZ jj → (`+`−)(`+`−)jjpp → ttZ → (j`+ν`)(j`−ν`)(`+`−)
σ(pp → ZZ jj → 4`jj) ' 6.4 fb , σ(pp → ttZ jj → 4` 2ν jj) ' 8.6 fb
Bileptons Distributions
arXiv:1707.01381 [hep-ph]
Y ±± @ the LHC
q
B−−
q
hi
B++
q
B−−
q
V 0
B++
q
B−−
Q
q
B++
arXiv:1806.04536 [hep-ph]
Signal & Backgrounds at 13 TeV
Benchmark Point
mY±± ' mH±± ∼ 870 GeV
Br(Y±± → l±l±) = Br(H±± → l±l±) = 13
SIGNAL
pp → Y ++Y−−(H++H−−)→ (l+l+)(l−l−) l = e, µ
σ(pp → YY → 4l) ' 4.3 fb σ(pp → HH → 4l) ' 0.3 fb
BACKGROUNDS
pp → ZZ → (l+l−)(l+l−)
σ(pp → ZZ → 4l) ' 6.1 fb
arXiv:1806.04536 [hep-ph]
Number of Events (13 TeV and L=300 fb−1)
Defining the significance s to discriminate a signal S from abackground B as
σS = S√B + σ2
B
,
σB systematic error on B (σB ' 0.1B)
N(YY ) ' 1302, N(HH) ' 120, N(ZZ ) ' 1836
⇓
σYY ' 6.9, σBSMHH = 0.6, σBYY
HH = 0.9
arXiv:1806.04536 [hep-ph]
Number of Events (13 TeV and L=300 fb−1)
Defining the significance s to discriminate a signal S from abackground B as
σS = S√B + σ2
B
,
σB systematic error on B (σB ' 0.1B)
N(YY ) ' 1302, N(HH) ' 120, N(ZZ ) ' 1836
⇓
σYY ' 6.9, σBSMHH = 0.6, σBYY
HH = 0.9
arXiv:1806.04536 [hep-ph]
Distributions
arXiv:1806.04536 [hep-ph]
Contents
The Standard Model of Elementary ParticlesBasicsIssuesA Popular Solution
331 ModelMinimal Formulation331 Model for Generic βSame-Sign Leptons Phenomenology
Conclusions
♦ SM issues: dark matter, neutrino masses ... → needs to beimproved
♦ supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
♦ models with larger gauge symmetry have rich phenomenology
♦ 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
♦ minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
♦ models with larger gauge group appear in GUT theories
� SM issues: dark matter, neutrino masses ... → needs to beimproved
♦ supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
♦ models with larger gauge symmetry have rich phenomenology
♦ 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
♦ minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
♦ models with larger gauge group appear in GUT theories
� SM issues: dark matter, neutrino masses ... → needs to beimproved
� supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
♦ models with larger gauge symmetry have rich phenomenology
♦ 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
♦ minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
♦ models with larger gauge group appear in GUT theories
� SM issues: dark matter, neutrino masses ... → needs to beimproved
� supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
� models with larger gauge symmetry have rich phenomenology
♦ 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
♦ minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
♦ models with larger gauge group appear in GUT theories
� SM issues: dark matter, neutrino masses ... → needs to beimproved
� supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
� models with larger gauge symmetry have rich phenomenology
� 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
♦ minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
♦ models with larger gauge group appear in GUT theories
� SM issues: dark matter, neutrino masses ... → needs to beimproved
� supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
� models with larger gauge symmetry have rich phenomenology
� 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
� minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
♦ models with larger gauge group appear in GUT theories
� SM issues: dark matter, neutrino masses ... → needs to beimproved
� supersymmetry provides possible answer to DM, hierarchyproblem ... but (the minimal version!) is in tension withexperimental data
� models with larger gauge symmetry have rich phenomenology
� 331 model(s) explain the observed number of fermion families(nQf = nLf = 3κ)
� minimal version of 331 has the almost unique feature ofdoubly-charged gauge boson
� models with larger gauge group appear in GUT theories
Thanks
Back-up
Slides
EWSB Details: the Potential
The (lepton-number conserving) potential of the model is given by
V = m1 ρ†ρ+ m2 η
†η + m3 χ†χ+ λ1(ρ†ρ)2 + λ2(η†η)2 + λ3(χ†χ)2
+ λ12ρ†ρ η†η + λ13ρ
†ρχ†χ+ λ23η†η χ†χ
+ ζ12ρ†η η†ρ+ ζ13ρ
†χχ†ρ+ ζ23η†χχ†η
+ m4 Tr(σ†σ) + λ4(Tr(σ†σ))2 + λ14ρ†ρTr(σ†σ) + λ24η
†ηTr(σ†σ)+ λ34χ
†χTr(σ†σ)+ λ44Tr(σ†σ σ†σ) + ζ14ρ
†σ σ†ρ+ ζ24η†σ σ†η + ζ34χ
†σ σ†χ
+ (√2fρηχεijkρi ηj χk +
√2fρσχρT σ† χ+ ξ14ε
ijk ρ∗lσliρjηk
+ ξ24εijkεlmn ηiηlσjmσkn + ξ34ε
ijk χ∗lσliχjηk) + h.c.
EWSB Details: Minimization ConditionsIn the broken Higgs phase, the minimization conditions
∂V∂vφ
= 0, 〈φ0〉 = vφ, φ = ρ, η, χ, σ
will define the tree-level vacuum. We remind that we areconsidering massless neutrinos choosing the neutral field σ0
1 to beinert. The explicit expressions of the minimization conditions arethen given by
m1vρ + λ1v3ρ +
12λ12vρv2
η − fρηχvηvχ +12λ13vρv2
χ −1√
2ξ14vρvηvσ + fρσχvχvσ
+12λ14vρv2
σ +14ζ14vρv2
σ = 0
m2vη +12λ12v2
ρvη + λ2v3η − fρηχvρvχ +
12λ23vηv2
χ −1
2√
2ξ14v2
ρvσ +1
2√
2v2χvσ
+12λ24vηv2
σ − ξ24vηv2σ = 0
m3vχ + λ3v3χ +
12λ13v2
ρvχ − fρηχvρvη +12λ23v2
ηvχ +1√
2ξ34vηvχvσ + fρσχvρvσ
+12λ34vχv2
σ +14ζ34vχv2
σ = 0
m4vσ +12λ14v2
ρvσ + λ44v3σ +
12λ4v3
σ + fρσχvρvχ −1
2√
2ξ14v2
ρvη +1
2√
2ξ34vηv2
χ
+12λ14v2
ρvσ +14ζ14v2
ρvσ +12λ24v2
ηvσ − ξ24v2ηvσ +
12λ34v2
χvσ +14ζ34v2
χvσ = 0
EWSB Details: Neutral Scalars
For the CP-even Higgs bosons we have
Hi = RSi1Re ρ0 + RS
i2Re η0 + RSi3Reχ0 + RS
i4Reσ0 + RSi5Reσ0
1,
There are similar expressions for the pseudoscalars
Ai = RPi1Im ρ0 + RP
i2Im η0 + RPi3Imχ0 + RP
i4Im σ0 + RPi5Im σ0
1.
Here, however, we have two Goldstone bosons responsible for thegeneration of the masses of the neutral gauge bosons Z and Z ′given by
A10 = 1
N1
(vρIm ρ0 − vηIm η0 + vσIm σ0
), N1 =
√v2ρ + v2
η + v2σ ;
A20 = 1
N2
(−vρIm ρ0 + vχImχ0
), N2 =
√v2ρ + v2
χ.
EWSB Details: Charged ScalarsFor the charged Higgs bosons the interaction eigenstates are
H+i = RC
i1ρ+ + RC
i2(η−)∗ + RCi3η
+ + RCi4(χ−)∗ + RC
i5σ+1 + RC
i6(σ−2 )∗
Here we have two Goldstones because in the 331 model there arethe W± and the Y± gauge bosons,
H+W = 1
NW
(−vηη+ + vχ(χ−)∗ + vσ(σ−2 )∗
), NW =
√v2η + v2
χ + v2σ ;
H+Y = 1
NY
(vρρ+ − vη(η−)∗ + vσσ+
1
), NY =
√v2ρ + v2
η + v2σ .
For the doubly-charged Higgs states we have
H++i = R2C
i1 ρ++ + R2C
i2 (χ−−)∗ + R2Ci3 σ
++1 + R2C
i4 (σ−−2 )∗.
The structure of the corresponding Goldstone boson is
H++0 = 1
N(−vρρ++ + vχ(χ−−)∗ −
√2vσσ++
1 +√2vσ(σ−−2 )∗
).
Relevant Couplings: V 0 − Y ±± − Y ∓∓
V 0(p1)Y ++(p2)Y−−(p3) vertex is given in terms of the momentaby
V (p1µ, p2
ν , p3ρ) = gµν(p2
ρ − p1ρ) + gνρ(p3
µ − p2µ) + gµρ(p1
ν − p3ν).
Characterizing the vector boson V as photon, Z or Z ′, we obtain:
γα Y ++µ Y−−ν = −2ig2 sin θW V (pγα, pY ++
µ , pY−−ν )
Zα Y ++µ Y−−ν = i
2g2(1− 2 cos 2θW ) sin θW V (pZα , pY ++
µ , pY−−ν )
Z ′α Y ++µ Y−−ν = − i
2g2
√12− 9 sec2 θW V (pZ ′
α , pY ++µ , pY−−
ν ),
where θW is the Weinberg angle.
Relevant Couplings: V 0 − H±± − H∓∓Defining S
(p1µ, p2
µ
)= p1
µ − p2µ, we have
γα H++i H−−j = −i sin θW
[(g2 + g1
√cot2 θW − 3
)(R2C
i1 R2Cj1 + R2C
i2 R2Cj2
)+ 2g2
(R2C
i3 R2Cj3 + R2C
i4 R2Cj4
)]S
(p
H++iα , p
H−−jα
)= −2ieδij S
(p
H++iα , p
H−−jα
)Zα H++
i H−−j =i2
sec θW{
cos 2θW
(g2 + g1
√cot2 θW − 3
)− g1
√cot2 θW − 3)R2C
i1 R2Cj1
− 2[(
g2 + g1
√cot2 θW − 3
)sin2
θW R2Ci2 R2C
j2 − g2 cos 2θW R2Ci3 R2C
j3
+ 2g2 sin2θW R2C
i4 R2Cj4
]}S
(p
H++iα , p
H−−jα
)Z ′α H++
i H−−j =i2
sec2 θW√12− 9 sec2 θW
{[3g1
√cot2 θW − 3(cos 2θW − 1) + g2(2 cos 2θW − 1)
]R2C
i1 R2Cj1
+[
3g1
√cot2 θW − 3(cos 2θW − 1) + 2g2(2 cos 2θW − 1)
]R2C
i2 R2Cj2
+ 2g2(2 cos 2θW − 1)(
R2Ci3 R2C
j3 + 2R2Ci4 R2C
j4
)}S
(p
H++iα , p
H−−jα
).
Vector Bilepton Couplings
The relevant vertices for vector bileptons are
` ` Y ++ ={− i√
2g2γµ PL
i√2g2γ
µ PR
d T Y−− ={− i√
2g2γµ PL
0 PR
D u Y−− ={ i√
2g2γµ PL
0 PR
hi Y ++Y−− = i2g2
2
(vρRS
i1 + vχRSi3
)
Bileptones: Simulation Details
♦ kT algorithm with R = 1 for jets cluster
♦ pT ,j > 30 GeV, pT ,` > 20 GeV
♦ |ηj | < 4.5, |η`| < 2.5
♦ ∆Rjj > 0.4,∆R`` > 0.1,∆Rj` > 0.4
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