agenda.infn.it · Issues of the MSSM) [GeV] 1 t ~ m(200 300 400 500 600 700 800 900 1000) [GeV] 1 0...

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

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+

Djouadi, Phys.Rept. 457 (2008) 1-216

〈Φ〉0 =(

0v/√2

Contents

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

♦ ...

Contents

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)

1-loop

2-loop

FeynHiggs

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)

1-loop

2-loop

FeynHiggs

Issues of the MSSM

) [GeV]1t~m(

200 300 400 500 600 700 800 900 1000

10 χ∼m

0χ∼ W b →1t~

0χ∼ t →1t~

0χ∼ b f f' →1t~

0χ∼ W b →1t~

0χ∼ t →1t~

0χ∼ b f f' →1t~

0χ∼ W b →1t~

0χ∼ t →1t~

0χ∼ b f f' →1t~

0χ∼ c →1t~

-1=8 TeV, 20 fbs

χ∼,1t~

∆) <

0χ∼,

0χ∼ t →1t~

0χ∼ W b →1t~

0χ∼ c →1t~

0χ∼ b f f' →1t~

production, 1t~1t

~ May 2018

ATLAS Preliminary

0χ∼W b

0χ∼c

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

Conclusions

Contents

Conclusions

Field Content

G ≡ SU(3)c × SU(3)L × U(1)X

(uLdLDL

), Q2 =

(cLsLSL

), Q1,2 ∈ (3, 3,−1/3)

(bLtLTL

), Q3 ∈ (3, 3, 2/3)

(lLνll cR

), l ∈ (1, 3, 0), l = e, µ, τ

)∈ (1, 3, 1), η =

)∈ (1, 3, 0), χ =

χ−−

)∈ (1, 3,−1)

Field Content

G ≡ SU(3)c × SU(3)L × U(1)X

(uLdLDL

), Q2 =

(cLsLSL

), Q1,2 ∈ (3, 3,−1/3)

(bLtLTL

), Q3 ∈ (3, 3, 2/3)

(lLνll cR

), l ∈ (1, 3, 0), l = e, µ, τ

)∈ (1, 3, 1), η =

)∈ (1, 3, 0), χ =

χ−−

)∈ (1, 3,−1)

Field Content

G ≡ SU(3)c × SU(3)L × U(1)X

(uLdLDL

), Q2 =

(cLsLSL

), Q1,2 ∈ (3, 3,−1/3)

(bLtLTL

), Q3 ∈ (3, 3, 2/3)

(lLνll cR

), l ∈ (1, 3, 0), l = e, µ, τ

)∈ (1, 3, 1), η =

)∈ (1, 3, 0), χ =

χ−−

)∈ (1, 3,−1)

Field Content

G ≡ SU(3)c × SU(3)L × U(1)X

(uLdLDL

), Q2 =

(cLsLSL

), Q1,2 ∈ (3, 3,−1/3)

(bLtLTL

), Q3 ∈ (3, 3, 2/3)

(lLνll cR

), l ∈ (1, 3, 0), l = e, µ, τ

)∈ (1, 3, 1), η =

)∈ (1, 3, 0), 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)]

Qem3 = Y3 + T3 Qem

3 = Y3 − T3

Y3 =√3T8 + X1 Y—3 = −

√3T8 + X1

Ti = λi/2 , i = 1, . . . 8

T8 = diag[ 12√3

(1, 1,−2)]

Qem3 = Y3 + T3 Qem

3 = Y3 − T3

Y3 =√3T8 + X1 Y—3 = −

√3T8 + X1

Ti = λi/2 , i = 1, . . . 8

T8 = diag[ 12√3

(1, 1,−2)]

SU(3)× SU(3)× U(1): an exotic possibility

(uLdLDL

), Q2 =

(cLsLSL

), Q1,2 ∈ (3, 3,−1/3)

(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 ±±

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 ±±

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 ±±

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 ±±

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 ±±

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 =

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

LYuk.q,triplet =

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 Q3 ρT ∗R)

+ h.c.

vρ � vη,χ⇓

LYuk.q,triplet =

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 Q3 ρT ∗R)

+ h.c.

vρ � vη,χ⇓

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

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

LYuk.l ,sextet = Gσ

ab l ia · l

jbσ∗i ,j

1 σ+1 /√2 σ0/

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±±)

LYuk.l ,sextet = Gσ

ab l ia · l

jbσ∗i ,j

1 σ+1 /√2 σ0/

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

Conclusions

Embedding of the Hypercharge Y : Qem(β)

Qem3 = Y3 + T3 Qem

3 = Y3 − T3

Y3 = βT8 + X1 Y3 = −βT8 + X1

Embedding of the Hypercharge Y : Qem(β)

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 =

D, S 16 −

√3β2

23 − 1

353 − 4

6 +√

3β2 − 1

323 − 4

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

) (1, 3, 0

)+(1, 2,− 1

)+(1, 1,−1

) (Σ+ 1√

2Σ0 1√

Σ0 Σ− 1√2`e

1√2νe 1√

2`e Ee

)Lα=µ,τ

(1, 3,− 2

) (1, 2,− 1

)+(1, 1,−1

)(να, `α, Eα)T

`cα (1, 1, 1)

(1, 1, 1

Qα(3, 3, 1

) (3, 2, 1

)+(3, 1, 2

)(dα,−uα,Uα)T

(3, 1,− 2

) (3, 1,− 2

(3, 1, 1

) (3, 1, 1

φi=1,2(1, 3, 1

) (1, 2, 1

)+(1, 1, 0

i ,H0i , σ

φ3(1, 3,− 2

) (1, 2,− 1

)+(1, 1,−1

3 ,H−3 , σ−3

S(1, 6, 2

) (1, 3, 1

)+(1, 2, 1

)+(1, 1, 0

) (∆++ 1√

2∆+ 1√

S1√2

∆+ ∆0 1√2

H0S σ0

Fonseca, Hirsch, JHEP 1608 (2016) 003

Le(1, 6,− 1

) (1, 3, 0

)+(1, 2,− 1

)+(1, 1,−1

) (Σ+ 1√

2Σ0 1√

Σ0 Σ− 1√2`e

1√2νe 1√

2`e Ee

)Lα=µ,τ

(1, 3,− 2

) (1, 2,− 1

)+(1, 1,−1

)(να, `α, Eα)T

`cα (1, 1, 1)

(1, 1, 1

Qα(3, 3, 1

) (3, 2, 1

)+(3, 1, 2

)(dα,−uα,Uα)T

(3, 1,− 2

) (3, 1,− 2

(3, 1, 1

) (3, 1, 1

φi=1,2(1, 3, 1

) (1, 2, 1

)+(1, 1, 0

i ,H0i , σ

φ3(1, 3,− 2

) (1, 2,− 1

)+(1, 1,−1

3 ,H−3 , σ−3

S(1, 6, 2

) (1, 3, 1

)+(1, 2, 1

)+(1, 1, 0

) (∆++ 1√

2∆+ 1√

S1√2

∆+ ∆0 1√2

H0S σ0

Le(1, 6,− 1

) (1, 3, 0

)+(1, 2,− 1

)+(1, 1,−1

) (Σ+ 1√

2Σ0 1√

Σ0 Σ− 1√2`e

1√2νe 1√

2`e Ee

)Lα=µ,τ

(1, 3,− 2

) (1, 2,− 1

)+(1, 1,−1

)(να, `α, Eα)T

`cα (1, 1, 1)

(1, 1, 1

Qα(3, 3, 1

) (3, 2, 1

)+(3, 1, 2

)(dα,−uα,Uα)T

(3, 1,− 2

) (3, 1,− 2

(3, 1, 1

) (3, 1, 1

φi=1,2(1, 3, 1

) (1, 2, 1

)+(1, 1, 0

i ,H0i , σ

φ3(1, 3,− 2

) (1, 2,− 1

)+(1, 1,−1

3 ,H−3 , σ−3

S(1, 6, 2

) (1, 3, 1

)+(1, 2, 1

)+(1, 1, 0

) (∆++ 1√

2∆+ 1√

S1√2

∆+ ∆0 1√2

H0S σ0

Contents

Conclusions

Y ±± + j j @ the LHC

Y −−

Y ±± + j j @ the LHC

q Y −−

Y −−

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

Y ±± @ the LHC

B−−

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

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

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

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

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

Distributions

Contents

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

� 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

2ξ14v2

ρvσ +1

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

2ξ14v2

ρvη +1

2ξ34vηv2

+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

There are similar expressions for the pseudoscalars

Ai = RPi1Im ρ0 + RP

i2Im η0 + RPi3Imχ0 + RP

i4Im σ0 + RPi5Im σ0

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

(vρIm ρ0 − vηIm η0 + vσIm σ0

), N1 =

√v2ρ + v2

η + v2σ ;

A20 = 1

(−vρIm ρ0 + vχImχ0

), N2 =

√v2ρ + v2

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

(−vηη+ + vχ(χ−)∗ + vσ(σ−2 )∗

), NW =

√v2η + v2

χ + v2σ ;

H+Y = 1

(vρρ+ − vη(η−)∗ + vσσ+

), 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

√12− 9 sec2 θW V (pZ ′

α , pY ++µ , pY−−

where θW is the Weinberg angle.

Relevant Couplings: V 0 − H±± − H∓∓Defining S

(p1µ, p2

µ − p2µ, we have

γα H++i H−−j = −i sin θW

[(g2 + g1

√cot2 θW − 3

i1 R2Cj1 + R2C

i2 R2Cj2

)+ 2g2

i3 R2Cj3 + R2C

i4 R2Cj4

H++iα , p

H−−jα

)= −2ieδij S

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

θW R2Ci2 R2C

j2 − g2 cos 2θW R2Ci3 R2C

+ 2g2 sin2θW R2C

i4 R2Cj4

H++iα , p

H−−jα

)Z ′α H++

i H−−j =i2

sec2 θW√12− 9 sec2 θW

√cot2 θW − 3(cos 2θW − 1) + g2(2 cos 2θW − 1)

i1 R2Cj1

√cot2 θW − 3(cos 2θW − 1) + 2g2(2 cos 2θW − 1)

i2 R2Cj2

+ 2g2(2 cos 2θW − 1)(

R2Ci3 R2C

j3 + 2R2Ci4 R2C

H++iα , p

H−−jα

Vector Bilepton Couplings

The relevant vertices for vector bileptons are

` ` Y ++ ={− i√

2g2γµ PL

i√2g2γ

d T Y−− ={− i√

2g2γµ PL

D u Y−− ={ i√

2g2γµ PL

hi Y ++Y−− = i2g2

(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

agenda.infn.it · Issues of the MSSM) [GeV] 1 t ~ m(200 300 400 500 600 700 800 900 1000) [GeV] 1 0...

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