Tests of “Other” Seesaws

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Tests of “Other” SeesawsThree Neutrinos and Beyond, Rencontres du Vietnam 2019

Richard Ruiz

Center for Cosmology, Particle Physics, and Phenomenology (CP3)Universite Catholique de Louvain

8 August 2019

R. Ruiz - CP3, Universite Catholique de Louvain “Other Seesaws” - Vietnam 2019 1 / 35

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Acknowledgements, Apologies, and Disclaimersfinite time constraints =⇒ many omissions

Topic is on models beyond “Minimum Type I Seesaw Model”Focus largely on tests at now-operating colliders, e.g., LHC

▶ Lots of expt’l synergy; see talks by Deppisch, de Gouvea, Kayser, etc

source material:1 Review on Nu Mass Models at Colliders,

Y. Cai, T. Han, T. Li, RR, [1711.02180]

2 European Strategy Update 2019 Chapter on Nu Mass Models,T. Han, T. Li, X. Marcano, S. Pascoli, RR, C. Weiland [1812.07831]

3 Other community documents and some new results

humble reminder: RH neutrinos are not the only explanation for tiny νmasses nor are they necessary (e.g., Type II Seesaw)

Lack of guidance from data and theory =⇒ broad approach needed(careful about putting all eggs in one basket!)


https://arxiv.org/abs/1711.02180


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motivation for new physics from ν physics


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Nu Masses and New ParticlesNonzero neutrino masses =⇒ new degrees of freedom exist [Ma’98]:

mν 6= 0 + left− handed (LH) Weak currents

LH Majorana Mass : mLν νLν

cL Dirac Mass : mD

ν νLνR

mLν = y〈∆〉 or new dynamics m

Dν = y〈ΦSM〉

(renormalizability)

(gauge invariance)

mν = 0 + renormalizability + gauge inv. =⇒ new particles!

New particles might be charged under new or old gauge symmetriesTypically manifests as processes that do not conserve lepton number(LNV) and/or lepton flavor (LFV) quantum numbers


https://arxiv.org/abs/hep-ph/9805219

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cL Dirac Mass : mD

ν νLνR


Dν = y〈ΦSM〉

(renormalizability)

(gauge invariance)


New particles might be charged under new or old gauge symmetries

Typically manifests as processes that do not conserve lepton number(LNV) and/or lepton flavor (LFV) quantum numbers



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cL Dirac Mass : mD

ν νLνR


Dν = y〈ΦSM〉

(renormalizability)

(gauge invariance)


New particles might be charged under new or old gauge symmetriesTypically manifests as processes that do not conserve lepton number(LNV) and/or lepton flavor (LFV) quantum numbers



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Theory Developments:

Clarity on Lepton Number Violation at Colliders


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Whether or not Ni decouple from collider experiments is now clear:Theorem: In SM + arbitrary number of sterile fermions,mν = 0 =⇒ lepton number (L) conservation Pascoli, et al, [1712.07611]

See also, Pilaftsis [hep-ph/9901206], Kersten and Smirnov [0705.3221 ], + others

In pure Type I scenarios, L-violating processes decouple in two ways:1 High-scale seesaw: µM ≫ ⟨ΦSM⟩ =⇒ mν ∼ mD

(mDµM

), mN ∼ µM

2 Low-scale seesaw: µM ≪ ⟨ΦSM⟩ =⇒ mν ∼ µM

(mDmR

)2, mN ∼ mR

Known also in literature as Inverse Seesaw, Linear Seesaw, Protective Symmetries, etc.

Corollary: Low-scale Type I + if ν approx. massless on expt scale,m2

ν/Q2 ≈ 0 =⇒ approximate L conservation Pascoli, RR, et al, [1812.08750]

=⇒ In Type I models, EW/TeV-scale Dirac-like Ni do not decouple

Collider observation of Ni+ L-violation =⇒ more new particles!Notable since examples of Type II Seesaw mimicking Type I collidersignature known RR, [1703.04669]







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(mDµM

), mN ∼ µM


(mDmR

)2, mN ∼ mR












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(mDµM

), mN ∼ µM


(mDmR

)2, mN ∼ mR












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Tests of High-Scale Type I Seesaw:1

heavy Majorana neutrinos

1Explicitly not topic of this talk :) See talks by F Deppisch, SK Kang, D TrocinoR. Ruiz - CP3, Universite Catholique de Louvain “Other Seesaws” - Vietnam 2019 7 / 35

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Tests of Low-Scale Type I Seesaw:2

heavy Dirac neutrinos (N)

2Also known as Linear Seesaw, Inverse Seesaw, Protective Symmetries, etc.R. Ruiz - CP3, Universite Catholique de Louvain “Other Seesaws” - Vietnam 2019 8 / 35

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Heavy Dirac Neutrinos (N) at Hadron Colliders

... can be produced via mixing through a number of mechanisms

γ W+∗

ℓ+/νℓ

N

(a) (b)

(c)

W+∗/Z∗

gZ∗ h∗

q q′

q

q′

Major recent effort to modernize collider predictions / tools3

Clarity needed on (i) mN ,√

s dependence and (ii) conflicting claims=⇒ more physical/robust collider definitions + public Monte Carlo tools4

3DY@NLO [*1509.06375]; GF [1408.0983, *1602.06957] @NNNLL [*1706.02298]; VBF [1308.2209, *1411.7305,

*1602.06957]; DY,VBF Automation@NLO [*1602.06957]. For details, see review: [*1711.02180]; (*) = U.Pitt. and/or Durham4Event generation up to NLO+PS with HeavyN libraries + MG5aMC@NLO, [feynrules.irmp.ucl.ac.be/wiki/HeavyN]











http://feynrules.irmp.ucl.ac.be/wiki/HeavyN

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Across√

s, wild interplay of PDF and matrix elements Pascoli, RR, et al [1812.08750]

200 400 600 800 1000

[fb

]

2

lNV

) /

NX

→

pp

(σ

1

10

210

310

410

VBF (NLO)

CC DY (NLO)

NC DY (NLO)

LL)3

GF (N

14 TeV LHC

[GeV]NmHeavy Neutrino Mass,

200 400 600 800 1000

LO

σ/σ

=K

0

1

2

3

VBF (NLO)

NC DY (NLO) CC DY (NLO)LL

3N 500 1000 1500 2000

[fb

]

2

lNV

) /

NX

→

pp

(σ

1

10

210

310

410

VBF (NLO)

CC DY (NLO)

NC DY (NLO)

LL)

3

GF (N

27 TeV HELHC

[GeV]NmHeavy Neutrino Mass,

500 1000 1500 2000

LO

σ/σ

=K

0

1

2

3

VBF (NLO)

NC DY (NLO) CC DY (NLO)LL

3N

Plotted: Flavor-independent heavy N production rate (σ/|V |2) vs massGF and VBF dominate at larger

√s, mN

At√

s = 100 TeV and |VℓN |2 ∼ 10−3, about one N(10 TeV)/ab−1

If roughly BR×ε×A× L ∼ 13 × 30 ab−1, then

√NObs. > 3σ



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310 410Heavy Neutrino Mass [GeV]

5−10

4−10

3−10

2−10

1−102 | 4τ

= |V

2 |e4

|V

µe / 2e / 3Xelhτ →95% Sensitivity - pp

[1802.02965]-113 TeV, 35.9 fb

2|e4

CMS upper limit on |V

=02|4µ|V

-1

LHC 14, 300 fb

-1

LHC 14, 3 ab

-1

LHC 27, 3 ab

-1

LHC 27, 15 ab-1

LHC 100, 15 ab

-1

LHC 100, 30 ab

| [1605.08774]*4τVe4on |V

Indirect upper limit

> 5%NmNΓ

After 3 yrs, total rewrite of pp → 3ℓX search for Dirac N!10 − 11× improved sensitivity to cLFV at LHC Pascoli, RR, et al, [1805.09335, 1812.08750]




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LHC Searches for N

See Talk by D. Trocino


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Tests of Type II Seesaw

H++ (H+)γ∗/Z∗q

H−− (H−)

H++

H−−

q (a)

(d)

W±

W±

H±±

H∓

W±∗

H++

H−−

Z∗/h∗ H++ (H+)

H−− (H−)

g

g

γ

γ

(b) (c)

q

q′(e)

H0

H±±

(f)


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The Type II Seesaw Mechanism is very special: solves neutrino massproblem without hypothesizing right-handed neutrinos

Important example that mν = 0 ⇒ that νR exist

Add one scalar multiplet with SU(2)L⊗U(1)Y quantum numbers (3, 2)

Lν Yuk. = −y∆Lc(iσ2)∆L = −y∆(νc

L ℓcL)(⟨∆⟩+ δ0 δ+

δ+ δ++

)(νLℓL

)= −y∆⟨∆⟩︸︷︷︸

=mν

νcLνL + . . . , ⟨∆⟩ < few GeV

Light νm possess tiny LH Majorana mass (NO νR NEEDED!)Neutrino mixing matrix is precisely the 3 × 3 PMNS matrix

After mixing with SM Higgs sector, characterized by existence of scalarswith exotic charges: H0, H±, H±±

Couple to W ,Z ,γ via gauge couplings, NOT through mixing!Interact through new L-violating and cLF-violating couplings


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The Type II Seesaw Mechanism is very special: solves neutrino massproblem without hypothesizing right-handed neutrinos

Important example that mν = 0 ⇒ that νR exist

Add one scalar multiplet with SU(2)L⊗U(1)Y quantum numbers (3, 2)

Lν Yuk. = −y∆Lc(iσ2)∆L = −y∆(νc

L ℓcL)(⟨∆⟩+ δ0 δ+

δ+ δ++

)(νLℓL

)= −y∆⟨∆⟩︸︷︷︸

=mν

νcLνL + . . . , ⟨∆⟩ < few GeV

Light νm possess tiny LH Majorana mass (NO νR NEEDED!)Neutrino mixing matrix is precisely the 3 × 3 PMNS matrix

After mixing with SM Higgs sector, characterized by existence of scalarswith exotic charges: H0, H±, H±±

Couple to W ,Z ,γ via gauge couplings, NOT through mixing!Interact through new L-violating and cLF-violating couplings


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Limited number of parameters =⇒ rich experimental predictionsFileviez Perez, Han, Li, et al, [0805.3536], Crivellin, et al [1807.10224] + others

E.g., Higgs branching rates that encode inverse (L) vs normal (R)ordering of light neutrino masses

BR(H±± → ℓ±i ℓ±j ) ∼ (U∗

PMNSmdiagν U†

PMNS)ij




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What is new?


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Theory studies and LHC searches for H++H−− pairs use Pythia6×KNLO

Okay but limited to Drell-Yan (DY) / (qq)-annihilation channel,=⇒ no EW boson fusion (VBF) or gluon fusion (GF)

Unnecessarily suffer from leading order theory unc., O(15 − 40%)

H++ (H+)γ∗/Z∗q

H−− (H−)

H++

H−−

q (a)

(d)

W±

W±

H±±

H∓

W±∗

H++

H−−

Z∗/h∗ H++ (H+)

H−− (H−)

g

g

γ

γ

(b) (c)

q

q′(e)

H0

H±±

(f)


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NEW: NLO- software libraries (UFO model files) Nemevsek, RR, [1909.yyyyy]

Fully exclusive event generation up to NLO(QCD)+PS usingmainstream generators: HERWIG, mg5amc@nlo, SHERPA

0.5 1 1.5

4−10

3−10

2−10

1−10

1

10

210

310

X)

[fb

] ±

±∆

→p

p(

σ

14 TeV LHC

PRELIMINARY

(NLO)

±∆±±∆

(NLO)

∆++∆

(LO)

∆++∆→γγ

jj (NLO)

0∆±±∆

(LO)

∆++∆→gg

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

[TeV]∆mTriplet Scalar Mass,

0

1

2

3

LO

σ /

σ

=

K

jj (NLO)0

∆±±∆

(NLO)

∆++∆ (NLO)

±

∆±±∆

1 2 3 4

4−10

2−10

1

210

410

X)

[fb

] ±

±∆

→p

p(

σ

100 TeV VLHC

PRELIMINARY

(NLO)

±∆±±∆

(NLO)

∆++∆

(LO)∆

++∆→γγ

jj (NLO)

0∆±±∆

(LO)

∆++∆→gg

0.5 1 1.5 2 2.5 3 3.5 4 4.5

[TeV]∆mTriplet Scalar Mass,

0

1

2

3

LO

σ /

σ

=

K

jj (NLO)0

∆±±∆

(NLO)

∆++∆ (NLO)

±

∆±±∆

Watch this space! (or see the review and references therein!!)


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Type III Seesaw

γ

T+

T−(0)

T+(±)

(a)(b)

γ∗/Z∗ (W±∗) gZ∗ h∗

q

q (q′)

(c)γ

T−

T± T±

ℓ∓ ℓ∓


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Type III Seesaw combines main features of Types I and II Seesaws:Idea: add SU(2)L fermion triplet (Y = 0) with mass mΣ

Key to reconciling GUTs with proton decay E.g., Bajc, Senjanovic [hep-ph/0612029], . . .

Lν Yuk. = −yΣLΣΦSM = −yΣ(νL ℓL

)( Σ0 √2Σ+

√2Σ− −Σ0

)(⟨ΦSM⟩+ h

0

)= −yΣ⟨ΦSM⟩︸︷︷︸

=mD

νLΣ0 + ...

Assuming that mΣ (Majorana mass) ≫ yΣ⟨Φ⟩ (Dirac mass)

mlight ≈ y2Σv2/2mΣ, mheavy ≈ −mΣ

For mlight = 0.1 eV, if yΣ ∼ O(ye) ∼ 1 · 10−6, mheavy ≈ 300 GeV!

After rotating into the mass basis, mixing-induced cLFV:

|T 0⟩ = cos θ |Σ0⟩+ sin θ |νℓ⟩ ≈ (1 − ε2/2) |Σ0⟩+ ϵ |νℓ⟩|T±⟩ = cosϕ |Σ±⟩+ sinϕ |ℓ±⟩ ≈ (1 − ε2/2) |Σ±⟩+ ϵ |ℓ±⟩



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Type III Seesaw combines main features of Types I and II Seesaws:Idea: add SU(2)L fermion triplet (Y = 0) with mass mΣ

Key to reconciling GUTs with proton decay E.g., Bajc, Senjanovic [hep-ph/0612029], . . .

Lν Yuk. = −yΣLΣΦSM = −yΣ(νL ℓL

)( Σ0 √2Σ+

√2Σ− −Σ0

)(⟨ΦSM⟩+ h

0

)= −yΣ⟨ΦSM⟩︸︷︷︸

=mD

νLΣ0 + ...

Assuming that mΣ (Majorana mass) ≫ yΣ⟨Φ⟩ (Dirac mass)

mlight ≈ y2Σv2/2mΣ, mheavy ≈ −mΣ

For mlight = 0.1 eV, if yΣ ∼ O(ye) ∼ 1 · 10−6, mheavy ≈ 300 GeV!

After rotating into the mass basis, mixing-induced cLFV:

|T 0⟩ = cos θ |Σ0⟩+ sin θ |νℓ⟩ ≈ (1 − ε2/2) |Σ0⟩+ ϵ |νℓ⟩|T±⟩ = cosϕ |Σ±⟩+ sinϕ |ℓ±⟩ ≈ (1 − ε2/2) |Σ±⟩+ ϵ |ℓ±⟩



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Collider prediction: heavy charged (T±) and neutral (T 0) leptons:Production through gauge couplings to W ,Z , γ

Decays to SM leptons through mixing, e.g., T± → ℓ±ν

) [f

b]

±

l± o

r T

-T

+T

→pp(

σ

2−10

1−10

1

10

210

310

LL)3

- GF (N±

l±T

LL)3

GF (N

- DY (NLO)-T+T

(LO)-T+ T→γγ

(LO)γγ

= 500 GeVTm

= 1 TeVTm

-2 = 102TlV

[TeV]sCollider Energy, 0 20 40 60 80 100

LOσ/

σ 0123

LL)3GF (N

DY (NLO)

[TeV]E = mNm0 1 2 3 4 5

]1

Lu

min

osi

ty [

fb

1

10

210

310

410

Discovery

E+ + E±NE

Type III Seesaw

14 TeV 27 TeV

13 ab

15 ab

115 ab

σ5

σ2σ5

σ2

TeV-scale heavy charged and neutral leptons discoverable at LHCR. Ruiz - CP3, Universite Catholique de Louvain “Other Seesaws” - Vietnam 2019 21 / 35

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Grand Unified Theories and

Theories with Gauged Lepton Number5

No time! Arise when UV completing simplified Seesaw Models

5Many, many omissions: e.g., SO(10), U(1)B−L, etcR. Ruiz - CP3, Universite Catholique de Louvain “Other Seesaws” - Vietnam 2019 22 / 35

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Gauged Left-Right Parity[Pati, Salam, Mohapatra, Senjanovic, etc., (’74-’79)]

ui

dj

WR

N

ℓ1

um

dn

ℓ2

W∗

R


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Left-Right Symmetric ModelLRSM asks what is the origin of (V − A) structure in the SM?

Why is nature weird and differentiates between LH and RH particles?

Idea: suppose nature was once parity symmetric:

G =SU(3)c⊗SU(2)L

⊗SU(2)R⊗U(1)B−L⊗PLR

Ask about parity and automatically learn about B − L!Larger Higgs sector needed to breakdown “right-handed” sector to SMLight neutrino masses are complicated

mνlight = yL⟨∆L⟩︸︷︷︸

Type II

−(

yDy−1R yT

D

)⟨Φ⟩2⟨∆R⟩−1︸︷︷︸

Type I a la Type II

Collider predictions: Majorana N, ZR ,WR guage bosons, Type II ScalarsAll enable collider-scale LNV and cLFV


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G =SU(3)c⊗SU(2)L⊗SU(2)R

⊗U(1)B−L⊗PLR



Type II

−(

yDy−1R yT

D

)⟨Φ⟩2⟨∆R⟩−1︸︷︷︸

Type I a la Type II



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G =SU(3)c⊗SU(2)L⊗SU(2)R⊗U(1)B−L⊗PLR



Type II

−(

yDy−1R yT

D

)⟨Φ⟩2⟨∆R⟩−1︸︷︷︸

Type I a la Type II



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Hallmark Collider Test: Searching for pp → W±R → Nℓ± → ℓ±ℓ±jj

Keung, Senjanovic PRL(’83)

Signature: same-sign ℓ±1 ℓ±2 +2j+ no MET, with pℓ,j

T ≳ O(MWR )

ui

dj

WR

N

ℓ1

um

dn

ℓ2

W∗

R


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Hallmark Collider Test: Searching for pp → W±R → Nℓ± → ℓ±ℓ±jj

Keung, Senjanovic PRL(’83)

Signature: same-sign ℓ±1 ℓ±2 +2j+ no MET, with pℓ,j

T ≳ O(MWR )

For (mN/MWR ) ≪ 1, i.e., boosted N, searches are losing sensitivity!R. Ruiz - CP3, Universite Catholique de Louvain “Other Seesaws” - Vietnam 2019 26 / 35

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For a 1 → 2 decay, m2ij = (pi + pj)

2 ≈ 2EiEj(1 − cos θij) ≈ EiEjθ2ij

⇒ Angle between e and (qq′)-system = θe(qq′) ∼mN√Ei Ej

∼ 4mNMWR

As (mN/MWR ) shrinks, N is more boosted, and its decay more collimated:

For(

mNMWR

)< 0.1, θe(qq′) falls below det. isolation threshold, θmin

ℓX = 0.4

ui

dj

WR

N

ℓ1

um

dn

ℓ2

W∗

R


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For a 1 → 2 decay, m2ij = (pi + pj)

2 ≈ 2EiEj(1 − cos θij) ≈ EiEjθ2ij

⇒ Angle between e and (qq′)-system = θe(qq′) ∼mN√Ei Ej

∼ 4mNMWR

As (mN/MWR ) shrinks, N is more boosted, and its decay more collimated:

For(

mNMWR

)< 0.1, θe(qq′) falls below det. isolation threshold, θmin

ℓX = 0.4

q′

e±

N → jN

|~pN | ∼ MWR≫ mN

qW±

R

Fun Idea: Why not treat second e± like any other poorly isolatedparticle bathed in QCD radiation and label it as constituent of a jet?w/ Mitra, Scott, Spannowsky, PRD (’17) [1607.03504], w/ Mitra, Mattelaer [1607.03504]




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Search for Neutrino Jets

See Talk by D. Trocino


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Can a gauge boson be too heavy for the LHC?


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If new gauge mediators are too heavy, light N are still accessible

q

q′

W±

R N

ℓ+q′

q N

ℓ+

When MWR ≫√

s but mN ≲ O(1) TeV, pp → Nℓ+ X production in theLRSM and minimal Type I Seesaw are not discernibleHan, Lewis, RR, Si, [1211.6447]; RR, [1703.04669]

Signature: pp → ℓ±ℓ± + nj + X +pℓ

T ≳ O(mN) + no MET

At 14 (100) TeV with L = 1 (10)ab−1, MWR ≲ 9 (40) TeV probed

DO NOT STOP SEARCHINGFOR HEAVY MAJORANA N 10 20 30 40 50

[TeV]RWM

500

1000

1500

2000

[G

eV]

Nm

Channel±µ±µ95% CLs Exclusion

(Expected)-1100 TeV, 30 ab

(Expected)

-127 TeV, 15 ab


←

(Expected)-1 14 TeV, 100 fb←

-18 TeV, 20.3 fbATLAS Observed←

-18 TeV, 19.7 fbCMS Observed

←

RW = MN m←


http://arxiv.org/abs/1211.6447


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If new gauge mediators are too heavy, light N are still accessible

q

q′

W±

R N

ℓ+q′

q N

ℓ+

When MWR ≫√

s but mN ≲ O(1) TeV, pp → Nℓ+ X production in theLRSM and minimal Type I Seesaw are not discernibleHan, Lewis, RR, Si, [1211.6447]; RR, [1703.04669]

Signature: pp → ℓ±ℓ± + nj + X +pℓ

T ≳ O(mN) + no MET

At 14 (100) TeV with L = 1 (10)ab−1, MWR ≲ 9 (40) TeV probed

DO NOT STOP SEARCHINGFOR HEAVY MAJORANA N 10 20 30 40 50

[TeV]RWM

500

1000

1500

2000

[G

eV]

Nm

Channel±µ±µ95% CLs Exclusion


(Expected)

-127 TeV, 15 ab


← (Expected)-1 14 TeV, 100 fb←

-18 TeV, 20.3 fbATLAS Observed←

-18 TeV, 19.7 fbCMS Observed

←

RW = MN m←


http://arxiv.org/abs/1211.6447


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LNV at Higgs FactoriesIf Higgs that breaks U(1)B−L is too heavy, light N are still accessible

N

N

ΦSM

ΦSM ∆B−L

〈ΦSM〉

hSM

N

N

SM-invariant effective field theories with sterile neutrinos exist!Heavy Neutrino Effective Field Theory (NEFT) Aparici, et al [0904.3244]

LNEFT = LType I +∑

5∑

iα(d)i

Λ(d−4)O(d)i , O(5)

S =(Φ†

SMΦSM

) (Nc

RNR)

One subtlety: NR here is chiral/interaction state RR [1703.04669]

Must decompose into mass basis: NR =∑

Xℓmνm +∑

Yℓm′Nm′

After EWSB, NEFT operators map onto light neutrino NSI operators!Can mediate hSM → NN decays! See, e.g., Caputo, et al [1704.08721]





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N

N

ΦSM

ΦSM ∆B−L

〈ΦSM〉

hSM

N

N



5∑

iα(d)i

Λ(d−4)O(d)i , O(5)

S =(Φ†

SMΦSM

) (Nc

RNR)



Xℓmνm +∑

Yℓm′Nm′






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N

N

ΦSM

ΦSM ∆B−L

〈ΦSM〉

hSM

N

N



5∑

iα(d)i

Λ(d−4)O(d)i , O(5)

S =(Φ†

SMΦSM

) (Nc

RNR)



Xℓmνm +∑

Yℓm′Nm′






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Summary


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Lack of clear guidance from data and theory means we must take a broad,open approach to uncovering the origin of tiny ν masses.

1 Colliders are incredibly complementary to oscillation facilities:▶ Direct production of Seesaw particles▶ Test UV realizations of low-scale neutrino EFTs / NSIs

2 e+e− and DIS machines explore new depths for light N▶ Searches for B, τ → N + X , Z → Nν, h → NN▶ Baseline luminosities at

√s = 240 GeV sufficient to go beyond LHC

3 pp machines offers many opportunites:▶ New analysis techniques =⇒ new territory for cLFV and LNV at LHC▶ N, H±± ZB−L, T 0,± masses up to 10-15 TeV scale at

√s = 100 TeV

4 Lots not covered today, so see the review [1711.02180]

5 Be encouraged! More data soon! Be prepared for a discovery.



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Thank you.


Documents

Tests of “Other” Seesaws