Future Lepton Collider signatures of the minimal U(1)x ... · Future Lepton Collider signatures of...

FutureLeptonCollidersignaturesoftheminimalU(1)xextendedStandardModel

NobuchikaOkadaUniversityofAlabama

[email protected],FL,Dec.15,2018

IncollaborationwithArindamDas(OsakaU.,Japan)SatomiOkada(U.ofAlabama)DigeshRaut(U.ofDelaware)

Paperinpreparation

ProblemsoftheStandardModel

AlthoughtheStandardModel(SM)isthebesttheorysofar,NewPhysicsbeyondSMisstronglysuggestedbybothexperimental&theoreticalpointsofview

Whatismissing?

1.Neutrinomassesandflavormixings2.Darkmattercandidate3.andmore

NewPhysicsmustsupplementthemissingpieces

MinimalgaugedB-LextensionoftheStandardModel

Ø  B-ListheuniqueanomalyfreeglobalsymmetryintheSM

Ø  GaugingtheglobalB-Lsymmetrymaybenatural

Ø  Anomalyfreerequirementà3right-handedneutrinos

Ø  Seesawmechanismisautomaticallyimplemented

AsimplegaugeextensionoftheSMforneutrinomasses

Intermsofhighenergycolliderphysics,wefocusonthegaugedU(1)extendedmodel@TeV

MinimalGaugedB-LExtensionoftheSM

Themodelisbasedon

ParticleContents

Newfermions:

Newscalar:

Mohapatra&Marshak;Wetterich;others

2

SU(3)c SU(2)L U(1)Y U(1)B−L

qiL 3 2 +1/6 +1/3uiR 3 1 +2/3 +1/3

diR 3 1 −1/3 +1/3ℓiL 1 2 −1/2 −1N i 1 1 0 −1eiR 1 1 −1 −1H 1 2 −1/2 0Φ 1 1 0 +2

TABLE I: Particle content. In addition to the SM particlecontents, the right-handed neutrino N i (i = 1, 2, 3 denotesthe generation index) and a complex scalar Φ are introduced.

SU(3)c × SU(2)L × U(1)Y × U(1)B−L and the particlecontent is listed in Table 1 [33]. The SM singlet scalar (Φ)breaks the U(1)B−L gauge symmetry down to Z2 (B−L)

by its vacuum expectation value (vev), and at the sametime generates the right-handed neutrino masses. TheLagrangian terms relevant for the seesaw mechanism aregiven by

L ⊃ −Y ijD N iH†ℓjL −

1

2Y iNΦN icN i + h.c., (1)

where the first term yields the Dirac neutrino mass afterelectroweak symmetry breaking, while the right-handedneutrino Majorana mass term is generated by the secondterm associated with the B − L gauge symmetry break-ing. Without loss of generality, we use the basis whichdiagonalizes the second term and makes Y i

N real and pos-itive.Consider the following tree level action in the Jordan

frame:

StreeJ =

!

d4x√−g

"

−#

m2P

2+ ξHH†H + ξΦ†Φ

$

R

+(DµH)†gµν(DνH)− λH

#

H†H −v2

2

$2

+(DµΦ)†gµν(DνΦ)− λ

#

Φ†Φ−v2B−L

2

$2

−λ′(Φ†Φ)(H†H)%

, (2)

where v and vB−L are the vevs of the Higgs fields H andΦ respectively. To simplify the discussion, we assumethat λ′ is sufficiently small so it can be ignored, and alsoξH ≪ ξ.The relevant one-loop renormalization group improved

effective action can be written as [41]

SJ =

!

d4x√−g

"

−#

m2P + ξG(t)2φ2

2

$

R

+1

2G(t)2(∂φ)2 −

1

4λ(t)G(t)4φ4

&

, (3)

where t = ln(φ/µ) and G(t) = exp(−' t0 dt′γ(t′)/(1 +

γ(t′))), with

γ(t) =1

(4π)2

(

1

2

)

i

(Y iN (t))2 − 12 g2B−L(t)

*

(4)

being the anomalous dimension of the inflaton field.gB−L denotes the U(1)B−L gauge coupling and µ therenormalization scale. In the presence of the nonmini-mal gravitational coupling, the one loop renormalizationgroup equations (RGEs) of λ, gB−L, ξ and Y i

N are givenby [32, 33]

(4π)2dλ

dt= (2 + 18 s2)λ2 − 48λ g2B−L + 96g4B−L

+2λ)

i

(Y iN )2 −

)

i

(Y iN )4, (5)

(4π)2dgB−L

dt=

#

32 + 4 s

3

$

g3B−L, (6)

(4π)2dξ

dt= (ξ + 1/6)

+

(1 + s2)λ− 2γ,

, (7)

(4π)2dY i

N

dt= (Y i

N )3 − 6g2B−LYiN +

1

2Y iN

)

j

(Y jN )2,

(8)

where the s factor is defined as

s(φ) ≡

-

1 + ξφ2

m2

P

.

1 + (6ξ + 1) ξφ2

m2

P

. (9)

In the Einstein frame with a canonical gravity sector,the kinetic energy of φ can be made canonical with re-spect to a new field σ = σ(φ) [7],

#

dσ

dφ

$2

=G(t)2Ω(t) + 3m2

P (∂φΩ(t))2/2

Ω(t)2, (10)

where,

Ω(t) = 1 + ξG(t)2φ2/m2P . (11)

The action in the Einstein frame is then given by

SE =

!

d4x√−gE

"

−1

2m2

PRE +1

2(∂Eσ)

2 − VE(σ)

&

,

(12)with

VE(φ) =14λ(t)G(t)4 φ4

-

1 + ξ φ2

m2

P

.2 . (13)

In our numerical work, we employ above potential withthe RGEs given in Eqs. (5-8). However, for a qualitativediscussion it is reasonable to use the following leading-logapproximation of the above potential:

VE(φ) ≃

-

λ0

4 +96 g2

B−L

16 π2 ln/

φµ

0.

φ4

-

1 + ξ φ2

m2

P

.2 , (14)

R

i=1,2,3

MoregeneralU(1)extendedSM

ParticleContents

Appelquist,Dobrescu&Hopper,PRD68(1998)035012

i=1,2,3

SU(3)C SU(2)L U(1)Y U(1)XqiL 3 2 1/6 (1/6)xH + 1/3uiR 3 1 2/3 (2/3)xH + 1/3

diR 3 1 −1/3 (−1/3)xH + 1/3ℓiL 1 2 −1/2 (−1/2)xH − 1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH − 1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2

Table 1: The particle content of the minimal U(1)X extended SM with Z2-parity. Inaddition to the SM particle content (i = 1, 2, 3), the three RHNs (N j

R (j = 1, 2) andNR) and the U(1)X Higgs field (Φ) are introduced. The unification into SU(5)×U(1)X isachieved only for xH = −4/5, and xH is quantized in our model.

SU(3)C×SU(2)L×U(1)Y×U(1)X

A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (1)

The KK modes of Ay are eaten by KK modes of the SM gauge bosons and become their

longitudinal degrees of freedom like the ordinary Higgs mechanism.

The 5D Lagrangian relevant to our DM physics is given by

LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (2)

c = ! = 1 (3)

E = mc2 E = !ω (4)

1

Ø U(1)xcharge:Ø  B-Llimit:


diR 3 1 −1/3 (−1/3)xH + 1/3ℓiL 1 2 −1/2 (−1/2)xH − 1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH − 1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (1)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (2)

c = ! = 1 (3)

E = mc2 E = !ω (4)

1

SU(3)C SU(2)L U(1)Y U(1)XqiL 3 2 1/6 (1/6)xH +1/3uiR 3 1 2/3 (2/3)xH +1/3

diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)

MN i =Y kN√2vX (3)

A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (5)

1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

Z

h

−mZ gX xH

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)

1

0

U(1)xsymmetrybreakingvia

U(1)xgaugeboson(Z’boson)massHeavyMajorananeutrinomass

MassscaleiscontrolledbyU(1)xSym.Br.scaleU(1)xsymbreakingalsogeneratesRHNmass

NewYukawatermsinLagrangian

1 Introduction

The dark matter relic abundance is measured at the 68% limit as [?]

ΩDMh2 = 0.1198± 0.0015. (1)

xΦ = 1 (2)

U(1)X = U(1)Y ⊕ U(1)B−L (3)

xH → 0 (4)

xH → ∞ (5)

Z ′ (6)

αX =g2X4π

(7)

mZ′ (8)

xH (9)

mDM (10)

mZ′ = 4 TeV (11)

xH = 0 (12)

αX = 0.027 (13)

αX = 10−4.5, 10−4, 10−3.5, 10−3, 10−2.5, 10−2, 10−1.75 (14)

LY ukawa ⊃ −!

i,j

Y ijD ℓ

iLHN j

R − 1

2

!

k

Y kNΦN

k CR Nk

R + h.c., (15)

U(1)Y

U(1)B−L

U(1)X In this section, we evaluate the relic abundance of the dark matter NR and identify

an allowed parameter region that satisfies the upper bound on the dark matter relic density of

ΩDMh2 ≤ 0.1213. The dark matter relic abundance is evaluated by integrating the Boltzmann

equation given by

dY

dx= − s⟨σv⟩

xH(mDM)

"Y 2 − Y 2

EQ

#, (16)

where temperature of the universe is normalized by the mass of the right-handed neutrino

x = mDM/T , H(mDM) is the Hubble parameter at T = mDM , Y is the yield (the ratio of

1

SeesawmechanismafterEWsym.breaking


diR 3 1 −1/3 (−1/3)xH + 1/3ℓiL 1 2 −1/2 (−1/2)xH − 1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH − 1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

⟨Φ⟩ = vX√2

(1)

A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (2)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (3)

c = ! = 1 (4)

1


diR 3 1 −1/3 (−1/3)xH + 1/3ℓiL 1 2 −1/2 (−1/2)xH − 1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH − 1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (5)

1


diR 3 1 −1/3 (−1/3)xH + 1/3ℓiL 1 2 −1/2 (−1/2)xH − 1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH − 1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (5)

1

Modelproperties&Phenomenology

Newparticles:Z’bosonHeavyMajorananeutrinosU(1)xHiggsboson

Phenomenology

•  Z’bosonproduction&decay•  Z’bosonmediatedprocesses•  Heavyneutrinoproduction•  U(1)xHiggsbosonphenomenology•  more

WefocusonZ’boson&heavyneutrinophenomenology.

Z’bosonphenomenology

Properties:electricallyneutralheavyvectorbosoncouplingswithSMparticles


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

Z ′

Z

h

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

Z ′

Z

h

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

Z ′

Z

h

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

Z ′

Z

h

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

Z

h

−mZ gX xH

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)

1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

Z

h

−mZ gX xH

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)

1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

Z

h

−mZ gX xH

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1

-4 -2 0 2 4

-1.0

-0.5

0.0

0.5

1.0

xH

CL/CR

Left/right-handedleptoncouplings

Z’bosonbranchingratios(1generation)

-3 -2 -1 0 1 2

0.00

0.05

0.10

0.15

xH

BranchingRatios

ee

uu

dd

NN

Zh


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

Z

h

−mZ gX xH

mZ′ ≫ mf , mh

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1

CurrentStatusI:LEPconstraints

-20 -10 0 10 20Λ− Λ+ [TeV]

A1

A0

V0

RL

LR

AA

VV

RR

LL

e+e-+µ+µ−+τ+τ−e+e-

µ+µ−

τ+τ−

LEP: e+e− → l+l−

-20 -10 0 10 20Λ− Λ+ [TeV]

A1

A0

V0

RL

LR

AA

VV

RR

LL

qq_uu_dd−

LEP: e+e− → hadrons

Figure 3.9: The 95% confidence limits on Λ±, for constructive (+) and destructive interference(−) with the SM, for the contact interaction models discussed in the text. Results are shownfor e+e− → e+e−, e+e− → µ+µ−, and e+e− → τ+τ− as well as for e+e− → uu, e+e− → ddand e+e− → qq. For e+e− → ℓ+ℓ−, universality in the contact interactions between leptons isassumed.

60

TheLEPElectroweakWorkingGroup,arXiv:1302.3415

Constraintson4-Fermioperators

e+

e-


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = YfxH +QB−L

xH → 0

f

f

⟨Φ⟩ = vX√2

(1)

mZ′ = 2 gX vX (2)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (4)



1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf ,mh

2× vX ≥ 6.9TeV

CℓL =

gℓL!(gℓL)

2 + (gℓR)2

(1)

CℓR =

gℓR!(gℓL)

2 + (gℓR)2

(2)

±Λ2 (3)

1

CℓL =

gℓL√(gℓL)

2 + (gℓR)2

(1)

CℓR =

gℓR√(gℓL)

2 + (gℓR)2

(2)

±Λ2 (3)QeQf

(2vX)2(4)

xH = 0 (5)

xH = −1.2 (6)

xH = −2 (7)

gX = gZ (8)

mZ′ = 7TeV (9)

mN = 40GeV (10)

mN = 200GeV (11)∣∣∣σ

σSM− 1

∣∣∣ (12)

Z ′ (13)

⟨Φ⟩ = vX√2

(14)

mZ′ = 2 gX vX (15)


A(0)y =

1√2

⎛

⎝0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (17)



2

inU(1)xmodel

InterpretationoftheLEPconstraintsintoU(1)xZ’boson

-3 -2 -1 0 1 20

2

4

6

8

10

12

14

xH

mZ'g X

[TeV

]=2v

X[TeV

]

U(1)xsymmetrybreakingVEVcanbeaslowas1TeV

B-Llimit


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

Z

h

−mZ gX xH

mZ′ ≫ mf , mh

2× vX ≥ 6.9TeV

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1

Das,Oda,NO&Takahashi,PRD93(2016)115038

CurrentStatusII:LHCRun2constraints

1 2 3 4 5

5×10-5

1×10-4

5×10-4

0.001

0.005

0.010

MZ'SSM [TeV]

B[pb]

ATLASwith36.1/fb

LHCconstraintsarealreadyverysevere(forsequentialZ’boson)

Searchforanarrowresonancewithdileptonfinalstates

*CMScollaborationhassimilarresults

2.0 2.5 3.0 3.5 4.0 4.5 5.00.01

0.05

0.10

0.50

1

mZ'[TeV]

g XInterpretationoftheATLAS2017constraintintoU(1)xZ’boson

xH = 0 (4)

xH = −0.8 (5)

(6)

⟨Φ⟩ = vX√2

(7)

mZ′ = 2 gX vX (8)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (10)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (11)

c = ! = 1 (12)

E = mc2 E = !ω (13)

2

xH = 0 (4)

xH = −0.8 (5)

(6)

⟨Φ⟩ = vX√2

(7)

mZ′ = 2 gX vX (8)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (10)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (11)

c = ! = 1 (12)

E = mc2 E = !ω (13)

2

CurrentLHCconstraintsonU(1)xZ’bosonareevenstrongerthansequentialZ’boson

NO,S.Okada&D.Raut,PLB780(2018)422

B-Lmodel:

Ø  LHCconstraintsarealreadyverysevereforU(1)xZ’boson.Ø  IfwetakeZ’bosonmassaroundafewTeV,gaugecouplingis

verysmall<0.1.

CurrentstatusoftheminimalU(1)xmodel

FutureHigh-LuminosityLHCprospects(ATLASTDR2018)Z’à e+e−

u Highmassdi-electronresonancesearch

u InterpretationinsequentialSMZ’model

u Statisticslimitedu Mainexperimentalconcerniselectronmomentumresolution

5

ATLAS-TDR-027http://cdsweb.cern.ch/record/2285582/files/ATLAS-TDR-027.pdf

HL-LHCwillconstrainthemodelmoreseverely(ifnoZ’bosonevidence)

Goal:SSMZ’mass>6.5TeV

``CanFutureLeptonColliderdosomethingmoreafterLHC?’’

Inthistalk,IwilldiscussFutureLeptonCollidersignaturesoftheU(1)model

Youmayask

FutureLeptonColliderProjects

InternationalLinearCollider(ILC)

Ø  Electron-positioncolliderØ  JapanisthemostlikelyhostØ  1stRunwith250GeVcolliderenergy

CompactLinearCollider(CLIC)Ø  AlternativetoILCinEuropeØ  Highercolliderenergyupto3TeV

ILCprojectinJapan

Ø JapanisthemostlikelyhostØ Japanesegovernmentplanstomakeadecisionsoon(February/March,2019?)

Ø Cost:$5billionàILCenergywith250GeV

WhatcanwedowithILC250GeV?

Ø  HiggsFactoryØ  Precisemeasurementsof

HiggsbosonpropertiesàNewphysicseffectsrelatedtotheSMHiggssector

``CanFutureLeptonColliderdosomethingmoreafterHL-LHC?’’

``CanwedosomethingaboutU(1)xmodelwithILC250GeVafterHL-LHC?’’

PositiveAnswers?

HowcanweavoidLHCconstraints?

2.0 2.5 3.0 3.5 4.0 4.5 5.00

10

20

30

40

mZ'[TeX]

v X[TeV

]

InterpretationoftheATLAS2017constraintsintoU(1)xZ’boson

U(1)xHiggsVEVversusZ’bosonmass

B-Llimit

Evenfor5TeVZ’mass,theLHCboundismoreseverethanLEP.However,thelowerboundonU(1)xHiggsVEVisdramaticallyreducingasZ’bosonmassisincreasing.

xH = 0 (4)

xH = −0.8 (5)

(6)

⟨Φ⟩ = vX√2

(7)

mZ′ = 2 gX vX (8)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (10)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (11)

c = ! = 1 (12)

E = mc2 E = !ω (13)

2

ProspectiveHL-LHCboundsfromATLASTDR2018

B-Llimit

ForZ’mass=7.5TeV,theupperboundongxcanbeaslargeastheSMZboson

Upperboundonthegaugecoupling

3 4 5 6 70.01

0.05

0.10

0.50

1

mZ'[TeV]

g X

ProspectiveHL-LHCboundsfromATLASTDR2018

B-Llimit

ForZ’mass=7.5TeV,thelowerboundonVEVcanbeaslowas6.5TeV.

LowerboundontheU(1)HiggsVEV

3 4 5 6 75

10

50

100

mZ'[TeV]

v X[TeV

]

FutureLeptonColliderstudyontheU(1)xmodel

Weset


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




mZ′ = 7.5TeV gX = gZ (1)

QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf ,mh

2× vX ≥ 6.9TeV

1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




mZ′ = 7.5TeV gX = gZ (1)

QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf ,mh

2× vX ≥ 6.9TeV

1

ThisisbeyondtheHL-LHCsearchreachwith3000/fb

(1)


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → f f

h

−mZ gX xH

mZ′ ≫ mf , mh

2× vX ≥ 6.9TeV

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

h

−mZ gX xH

mZ′ ≫ mf , mh

2× vX ≥ 6.9TeV

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1

xH = 0 (4)

xH = −0.8 (5)

gX = 0.5 (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2

Deviationscanbeaslargeas10%forxH=0at1TeVILC

500 1000 1500 2000 2500 30000.01

0.10

1

10

100

s [GeV]

deviations

[%]

xH = 0 (4)

xH = −1.2 (5)

gX = gz (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2

xH = 0 (4)

xH = −1.2 (5)

gX = gz (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2

xH = 0 (4)

xH = −1.2 (5)

gX = gZ (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2

(Photon,Z&Z’bosonsmediatedprocess)


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




mZ′ = 7.5TeV gX = gZ (1)

QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf ,mh

2× vX ≥ 6.9TeV

1

(2)


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

h

−mZ gX xH

mZ′ ≫ mf , mh

2× vX ≥ 6.9TeV

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1

500 1000 1500 2000 2500 3000

0.5

1

5

10

50

100

s [GeV]

deviation[%]

xH = 0 (4)

xH = −1.2 (5)

gX = gz (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2

xH = 0 (4)

xH = −1.2 (5)

xH = −2 (6)

gX = gZ (7)∣

∣

∣

σ

σSM− 1

∣

∣

∣(8)

⟨Φ⟩ = vX√2

(9)

mZ′ = 2 gX vX (10)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (12)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (13)

c = ! = 1 (14)

E = mc2 E = !ω (15)

2

Deviationcanbeaslargeas5%forxH=-1.2at1TeVILC

NotethatZ’contributionisvanishingfortheB-Llimit

(ZbosonassociatedHiggsproductionviaZandZ’)

xH = 0 (4)

xH = −1.2 (5)

gX = gZ (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




mZ′ = 7.5TeV gX = gZ (1)

QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf ,mh

2× vX ≥ 6.9TeV

1

(3)HeavyMajoranaNeutrinopairproduction

500 1000 1500 2000 2500 30000.001

0.010

0.100

1

10

s [GeV]

(e+e-

NN)[fb]


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf , mh

2× vX ≥ 6.9TeV

CℓL =

gℓL!

(gℓL)2 + (gℓR)

2(1)

CℓR =

gℓR!

(gℓL)2 + (gℓR)

2(2)

(3)

1

xH = 0 (4)

xH = −1.2 (5)

xH = −2 (6)

gX = gZ (7)

mZ′ = 7TeV (8)∣

∣

∣

σ

σSM− 1

∣

∣

∣(9)

⟨Φ⟩ = vX√2

(10)

mZ′ = 2 gX vX (11)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (13)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (14)

c = ! = 1 (15)

E = mc2 E = !ω (16)

2

xH = 0 (4)

xH = −1.2 (5)

xH = −2 (6)

gX = gZ (7)

mZ′ = 7TeV (8)

mN = 40GeV (9)

mN = 200GeV (10)∣

∣

∣

σ

σSM− 1

∣

∣

∣(11)

⟨Φ⟩ = vX√2

(12)

mZ′ = 2 gX vX (13)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (15)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (16)

c = ! = 1 (17)

2

xH = 0 (4)

xH = −1.2 (5)

xH = −2 (6)

gX = gZ (7)

mZ′ = 7TeV (8)

mN = 40GeV (9)

mN = 200GeV (10)∣

∣

∣

σ

σSM− 1

∣

∣

∣(11)

⟨Φ⟩ = vX√2

(12)

mZ′ = 2 gX vX (13)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (15)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (16)

c = ! = 1 (17)

2

Crosssectionfor40GeVmassissizableevenatILC250GeVILC!

xH = 0 (4)

xH = −1.2 (5)

gX = gZ (6)∣

∣

∣

σ

σSM− 1

∣

∣

∣(7)

⟨Φ⟩ = vX√2

(8)

mZ′ = 2 gX vX (9)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (11)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (12)

c = ! = 1 (13)

E = mc2 E = !ω (14)

2


diR 3 1 −1/3 (−1/3)xH +1/3ℓiL 1 2 −1/2 (−1/2)xH −1N i

R 1 1 0 −1eiR 1 1 −1 (−1)xH −1H 1 2 −1/2 (−1/2)xH

Φ 1 1 0 +2




mZ′ = 7.5TeV gX = gZ (1)

QX = Yf xH +QB−L

xH → 0

f

f

Z ′

e+e− → µ+µ−

e+e− → Z h

e+e− → Z ′∗ → N N

h

−mZ gX xH

mZ′ ≫ mf ,mh

2× vX ≥ 6.9TeV

1

SignaturesofheavyMajorananeutrino

Ø  ``Smoking-gun’’signatureoftheMajorananature:samesigndileptonfinalstates

Figure 6: Representative Feynman diagrams for the Higgs portal Majorana neutrino pairproduction and subsequent decay modes.

respectively.Let us now consider the production cross section for the RHNs at the LHC from the and

h productions and their decays. Using Eqs. (4.1), (4.2) and (4.10), the cross section formulasare given by

(pp ! ! NN) = sin2 h(m) BR( ! NN),

(pp ! h ! NN) = cos2 h(mh) BR(h ! NN), (4.11)

respectively, and they are controlled by four parameters, Y , , m and mN . Throughoutthis section, we fix mN = 20 GeV, for simplicity. The representative diagrams of the RHNproductions including their decays are shown in Fig. 6. We will discuss the decay of RHNsinto the SM final states in details in Sec. 5. In the remainder of the analysis in this section,we fix the lifetime of RHNs to yield the best reach of XX in Fig. 1 for both the futureHL-LHC and MATHUSLA displaced vertex searches, namely, min(HL LHC) = 20.7 andmin(MATH) = 0.3 fb, which corresponds to c = 3.1 and 58.4 m, respectively. Here, weidentify X with the RHN while S is either h or .

We first consider the case where h and masses are almost degenerate, mh ' m = 126

GeV. In this case, the total cross section XX is given by the sum of the productions from and h.10 The best search reach of the displaced vertex signatures at the HL-LHC or theMATHUSLA are expressed as

min = (pp ! ! NN) + (pp ! h ! NN)

'sin

2 BR( ! NN) + cos2 BR(h ! NN)

h(mh), (4.12)

where we have used the approximation h(m) ' h(mh). Hence, the best search reach isexpressed as a function of Y and for the fixed values of mN = 20 GeV, mh = 125 GeV andm = 126 GeV. In Fig. 7, our results are shown in (Y, sin )-plane. This plots show (i) thebest reaches of displaced vertex searches at the HL-LHC (dashed curve) and the MATHUSLA

10 Although and h are almost degenerate, we do not consider the interference between the processes,pp ! ! NN and pp ! h ! NN , since their decay width is much smaller (a few MeV) than their massdifferences. Hence, in evaluation the total cross section, we simply add the individual production cross sectionin Eq. (4.11).

10

xH = 0 (4)

xH = −1.2 (5)

xH = −2 (6)

gX = gZ (7)

mZ′ = 7TeV (8)

mN = 40GeV (9)

mN = 200GeV (10)∣

∣

∣

σ

σSM− 1

∣

∣

∣(11)

Z ′ (12)

⟨Φ⟩ = vX√2

(13)

mZ′ = 2 gX vX (14)


A(0)y =

1√2

⎛

⎝

0 0 H+

0 0 H0

H− H0∗ 0

⎞

⎠ . (16)




LDM = −1

2Tr

[

FMNFMN

]

−(cL2Tr [WµνW

µν ] +cY4

Tr [BµνBµν ]

)

(δ(y) + δ(y − πR)) (17)

c = ! = 1 (18)

2

Samesigndilepton+jets

Ø  Displacedvertexsignature

Ncanbelonglivedwhenlightestneutrinoisverylight

Figure 20: In the left panel, the red and the green shaded region correspond to the constraint oneffective netrino mass (hmi) for the NH and IH, respectively. The horizontal shaded regionsfrom the top to bottom, correspond to the current EXO-200 experiment and the future reach ofEXO-200 phase-II, and nEXO experiments, respectively [77]. In the right panel, the solid linedepicts the total decay length of RHN plotted against the mass of the corresponding lightestlight-neutrino mass. The dashed (solid) line correspond to fixed RHN mass of 20 (40) GeV. Inboth the panels, vertical solid lines correspond to the three benchmark points for the lightestneutrino masses for the NH and the IH, namely, mlightest = 0.1, 0.01, and 0.001 eV.

7 ConclusionsIt is quite possible that new particles in new physics beyond the SM are completely singletunder the SM gauge group. This is, at least, consistent with the null results on the searchfor new physics at the LHC. If this is the case, we may expect that such particles very weaklycouple with the SM particles and thus have a long lifetime. Such particles, once produced at thehigh energy colliders, provide us with the displaced vertex signature, which is very clean withnegligible SM background. In the context of the minimal gauged BL extended SM, we haveconsidered the prospect of searching for the heavy neutrinos of the type-I seesaw mechanismat the future high energy colliders. For the production process of the heavy neutrinos, we haveinvestigated the production of Higgs bosons and their subsequent decays into a pari of heavyneutrinos. With the parameters reproducing the neutrino oscillation data, we have shown thatthe heavy neutrinos are long-lived and their displaced vertex signatures can be observed at thenext generation displaced vertex search experiments, such as the HL-LHC, the MATHUSLA,the LHeC, and the FCC-eh. We have found that the lifetime of the heavy neutrinos is controlledby the lightest light neutrino mass, which leads to a correlation between the displaced vertexsearch and the search limit of the future neutrinoless double beta-decay experiments.

Note added: While completing this manuscript, we noticed a paper by F. Deppisch, W.Liu and M. Mitra [78] which also considers the displaced vertex signature of the heavy neutrinos.

26

Jana,NO&Raut,PRD98(2018)035023xH = 0

(4)

xH = −1.2

(5)

xH = −2

(6)

gX = g

Z

(7)

mZ ′ = 7TeV

(8)

mN = 40GeV

(9)

mN = 200GeV

(10)

∣

∣

∣

σσSM − 1

∣

∣

∣

(11)

⟨Φ⟩ = vX√2

(12)

mZ ′ = 2 g

X vX

(13)

MN i = Y k

N√2 v

X

(14)

A (0)y = 1√2

⎛

⎝0

0H +

00

H 0

H −

H 0∗

0

⎞

⎠

.

(15)

The KK modes of Ay are eaten by KK modes of the SM

gauge bosons and become their

longitudinal degrees of freedomlike the ordinary Higgs mechanism.

The 5D Lagrangian relevant to our DMphysics is given by

LDM

=− 12 Tr [

FMN F M

N ]

− (

cL2 Tr [W

µνW µν] + cY

4 Tr [BµνB µν

])

(δ(y) + δ(y − πR))(16)

c =! = 1

(17)

2

Summary

Ø WehaveconsideredtheminimalU(1)xextendedSMØ WehavediscussedZ’bosonsignatureswithavarietyoffinal

stets,suchasleptonpair,ZhandheavyneutrinopairatFutureLeptonCollider

Ø  AlthoughthecurrentLHCconstraints(HL-LHCprospects)are

verysevere,wecanavoidtheLHCconstraintsbytakingZ’bosonmass>7TeV.

Ø NeverthelessZ’bosonisveryheavyandoutofLHCsearch

reach,FutureLeptonCollidercanexploretheU(1)xmodel.

Ø MajorananeutrinosearchseemspromisingevenatILC250GeVwithagoralintegratedluminosityof3000/fb

15

!ank y"for y"r a$ention!

15

!ank y"for y"r a$ention!

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