[PPT] - LPT-Orsay CLFV and Neutrino Mass Models LPT Orsay Neutrino data PowerPoint Presentation

SLIDE 1

LPT Orsay

LPT-Orsay CLFV and Neutrino Mass Models

☞ Neutrino data calls for New Physics ☞ Which BSM? Neutrino mass models ☞ BSM (with mν): impact on LFV observables CLFV 2019, Fukuoka, 17-20 June 2019 Asmaa Abada

SLIDE 2

☞ Facts: ν change flavours after propagating a finite distance

Solar νe → νµ,τ ∆m2

sol ≃ 7.6 × 10−5 eV2

sin2 θsol ≃ 0.30

SNO, BOREXino, Super-Kamiokande, GALLEX/GNO, SAGE, Homestake, Kamiokande

Atmospheric νµ → ντ LBL Accelerator νµ disappearance LBL Accelerator νµ → ντ ∆m2

atm ≃ 2.4 × 10−3 eV2

sin2 θatm ≃ 0.50

IMB, MAcro, Soudan-2, Kamiokande, Super-Kamiokande K2K, T2K, MINOS Opera

LBL Accelerator νµ → νe LBL Reactor ¯ νe disappearance ∆m2

atm

sin2 θChooz ≃ 0.023

T2K, MINOS Daya Bay, RENO Double Chooz

SBL Accelerator νµ(¯ νµ) → νe(¯ νe) SBL Reactor ¯ νe disappearance ∆m2 ≃ 1eV2 (?) sin2 θ ≃ 0.1 (?)

LSND, MiniBooNE ++ Solar: GALLEX, SAGE++ Bugey, ILL, Rovno,...

SLIDE 3

Lepton mixing & neutrino data: current status

❍ ✵ ✁ ✵

✁

✂ ✵

✄

✵

✄ ✂

✵

☎

s✆ ✝ ✷ q ✶ ✷ ✻ ✂ ✼ ✼ ✂ ✽ ❉ ♠ ✞ ✞ ✟ ✥ ✠ ✡ ✲ ☛ ☞ ✌ ✞ ❪ ❍ ✵ ✵ ✍ ✂ ✵

✵

✁ ✵ ✵ ✁ ✂ ✵ ✵ ✄ s✆ ✝ ✷ q ✶✎ ❍ ✵

✄

✵

☎

✵ ✂ ✵

✻

✵

✼

s✆ ✝ ✷ q ✷ ✎ ✵ ✾ ✵ ✍ ✽ ✵ ✁ ✼ ✵ ✄ ✻ ✵ ❞ ❈ ✏ ❍ ✑ ✁

✽

✑ ✁

✻

✑ ✁

☎

✑ ✁

✁

❍ ✁ ✁ ✁ ☎ ✁

✻

✁

✽

❉ ♠ ✞ ✸ ✞ ✥ ✠ ✡ ✲ ✸ ☞ ✌ ✞ ❪ ❉ ♠ ✞ ✸ ✟ ❍ ◆ ✒ ✓✔ ✕ ✖ ✗ ✘ ✙ ✚ ✘ ✛ ✜ ✢

⇒ ⇒ ⇒

✞ ✝ ☎ ✆

◮ “Precision era” for neutrino physics ◮ Only three oscillation parameters unknown... θ23 octant; δCP; ν-mass ordering (preference: sin2 θ23 = 0.58 sin2 θ23 = 0.58 sin2 θ23 = 0.58 (b.f) 2nd octant; δCP = 217 δCP = 217 δCP = 217 (b.f);) ◮ Exciting experimental road ahead!

SLIDE 4

Still undetermined

◮ Oscillation data: only two squared-mass differences Undetermined mass ordering! normal [mν1 < mν2 ≪ mν3] inverted [mν3 ≪ mν1 mν2] Unknown absolute mass scale! need direct measurment

m2

solar~7×10−5eV2 atmospheric ~2×10−3eV2 atmospheric ~2×10−3eV2 m1

2

m2

2

m3

2

m2

2

m1

2

m3

2

νe νµ ντ ? ? solar~7×10−5eV2

☞ Resolving the absolute mass scale for light neutrinos

Tritium decays (3H →3He +νe + e−): mνe 2.1

mνe 2.1 mνe 2.1 eV [Troitsk]

☞

June 11 2018, the KATRIN experiment has been inaugurated!

0ν2β

0ν2β 0ν2β decays ➙ Majorana nature : |mee| 0.3 |mee| 0.3 |mee| 0.3 eV

[GERDA, KamLAND-Zen]

Cosmology (CMB, LSS, Lyα):

i mνi 0.23 → 0.12

i mνi 0.23 → 0.12
i mνi 0.23 → 0.12 eV

ν

m K (T) Q T

✥ ❱✮ ❧ ✐ ❣ ✁✂ ❡ s ✂ ♠ ✹ ✶ ✄ ✸ ✶ ✄ ✷ ✶ ✄ ☎ ✶ ✄ ✆ ✝ ✞ ✟ ✠ ✸ ✶ ✄ ✷ ✶ ✄ ☎ ✶ ✄ ✶ ■ ✡ ◆ ✡ ❳ ☛☞ ✌ ✍ ✎ ❑ ❛✏ ▲ ❆ ◆ ❉ ✲ ✑ ☛♥ ✒ ✓ ✺ ✔ ✕ ✔ ✔ ✕ ✺ ✔ ❈✖

✗

❙ ✗ ❩ ✘ ▼ ✙ ❈ ✚ ❚ ✗ ❚ ✗ ✛ ✗ ✜ ✚

SLIDE 5

☞ Indisputable: νs are massive and mix

➙

The minimal SM is incomplete!

➙

✞ ✝ ☎ ✆

An observational caveat that is also a theoretical one!

SLIDE 6

◮ Is ν ν ν mass generation mechanism = = = the one of quarks/charged leptons ? ◮ ν mixings "add fuel to the fire": add to the fermion flavour puzzle!

VCKM =     1 − λ2/2 λ Aλ3(ρ − iη) −λ 1 − λ2/2 Aλ2 Aλ3(1 − ρ − iη) −Aλ2 1     , λ ∼ 0.2, A ≃ 0.8, ρ ≃ 0.1, η ≃ 0.4 VCKM =     1 − λ2/2 λ Aλ3(ρ − iη) −λ 1 − λ2/2 Aλ2 Aλ3(1 − ρ − iη) −Aλ2 1     , λ ∼ 0.2, A ≃ 0.8, ρ ≃ 0.1, η ≃ 0.4 VCKM =     1 − λ2/2 λ Aλ3(ρ − iη) −λ 1 − λ2/2 Aλ2 Aλ3(1 − ρ − iη) −Aλ2 1     , λ ∼ 0.2, A ≃ 0.8, ρ ≃ 0.1, η ≃ 0.4

Quarks: small mixing angles, 1 Dirac CPV phase

UP MNS =     c13c12 c13s12 s13e−iδ −c23s12 − s23s13c12eiδ c23c12 − s23s13s12eiδ −s23c13 s23s12 − c23s13c12eiδ −s23c12 − c23s13s12eiδ c23c13    ×diag

eiα1, eiα2, 1
UP MNS =

    c13c12 c13s12 s13e−iδ −c23s12 − s23s13c12eiδ c23c12 − s23s13s12eiδ −s23c13 s23s12 − c23s13c12eiδ −s23c12 − c23s13s12eiδ c23c13    ×diag

eiα1, eiα2, 1
UP MNS =

    c13c12 c13s12 s13e−iδ −c23s12 − s23s13c12eiδ c23c12 − s23s13s12eiδ −s23c13 s23s12 − c23s13c12eiδ −s23c12 − c23s13s12eiδ c23c13    ×diag

eiα1, eiα2, 1
Leptons: 2 large mixing angles, 1 Dirac (+ 2 Majorana) CPV phase(s)

⇒ Very different mixing pattern for Leptons and Quarks

☞

✞ ✝ ☎ ✆ Is this related to neutrino mass generation mechanism?

SLIDE 7

◮ Light ν ν ν mass scale ? ◮ ν data worsens fermion hierarchy problem!

☞

✞ ✝ ☎ ✆ Why ν so light?

☞

✞ ✝ ☎ ✆ and what absolute neutrino mass scale?

SLIDE 8

◮ Neutrino oscillation reactor and accelerator anomalies ◮ Are there some extra fermionic gauge singlets (steriles)?

3-ν mixing scheme 3+?-ν mixing schemes

☞

✞ ✝ ☎ ✆ Does this mean that UP MNS is incomplete? Non-Unitary?

☞

✞ ✝ ☎ ✆ Do they play a role in the neutrino mass generation mechanism?

SLIDE 9

☞

Bonus: strong Potential for CP violation! ◮ Unitarity triangle surface ∝ Jlepton

CP

: Jlepton

CP,max ≃ 1000 × Jquark CP

Jquark

CP

= 2.96 × 10−5, JCP,max ≃ 3.29 × 10−2 J ≡ Im

Ue3U ∗

e1U ∗ µ3Uµ1

J = Jmax

CP sin δ

Unitarity Triangle (in e, µ) Jarlskog Invariant

☞

✞ ✝ ☎ ✆ New possibility for having BAU from Leptogenesis ? Contribution to EDMs?

SLIDE 10

mν = 0 ⇒ New Physics Scale

Standard Model ◮ νL only and no νR = ⇒ No Dirac mass term: LmD = mD (νLνR + νRνL) ◮ No Higgs triplet = ⇒ No Majorana mass term: LmM = 1

2Mνc LνL + h.c.

Majorana field: Ψν = νL + νc

L ➙

Ψν = Ψc

ν ➙

νc

LνL = νT L CνL,

C = iγ2γ0

◮ Lepton number symmetry is accidental = ⇒ Non-renormalisable operators dim 5, 6 .. ✞ ✝ ☎ ✆ SM ≡ Effective theory of a larger one valid at a scale Λ

➙

δLd=5 = cd=5Od=5, Od=5 = 1

Λ

φℓ

T φℓ

+ h.c.

φ=v − → mν ∼ v2/Λ for cd=5 ∼ O(1), mν ∼

∆m2

atm ∼

2 × 10−3eV2 ⇒ Λ ∼ 1015 GeV (near ΛGUT!)

✞ ✝ ☎ ✆ Depending on cd=5 (thus on NP model) ⇒ Λ ∈ [..., MeV, GeV, TeV, ..., GUT, ...]

SLIDE 11

◮ Lepton mixing & massive neutrinos: unique signal for NP

☞ SM has other issues that call for BSM

◮ observational problems (ν masses & mixings): BAU and Dark Matter ◮ theoretical caveats: fine-tuning, hierarchy and flavour problems ....

☞ ν-SM = New Physics just to explain ν masses and mixings

◮ New d.o.f, for example Right-Handed Neutrinos, H Y ν νL νR + ...➙ mν H Y ν νL νR + ...➙ mν H Y ν νL νR + ...➙ mν ◮ What is the neutrino mass generation mechanism? ◮ ν ↔ ¯ ν ν ↔ ¯ ν ν ↔ ¯ ν the only particle that can have both Dirac or Majorana descriptions ◮ If ν is a Majorana particle ➙ New physics scale, LNV observables, ...

☞ ν-SM will allow for many new phenomena

◮ LFV in neutral sector. Why not in the charged sector? ℓi → ℓj ℓk ℓl, ℓi → ℓjγ, ... ◮ Contributions to g − 2, Lepton EDMs ◮ Signatures of the new heavy states at colliders, ...

☞

✞ ✝ ☎ ✆

Determination of ν-SM/BSM model requires combinations of many = observables

SLIDE 12

☞ Determination of ν-SM/BSM requires to combine = observables: how to proceed?

◮ Inputs:

a mass generation mechanism (seesaw, radiative corrections, extra dim, ...)
and/or, extension of SM: SM + new d.o.f, or BSM (e.g. SUSY, ...)

◮ Observables (peculiar to these extensions):

Produce directly new d.o.f at LHC (if accessible)
Or/and study impact of 1. (and 1. + 2.) on e.g. cLFV observables at low-

energy/high intensity (MEG, ...) and high-energy (LHC, Future colliders) ◮

✞ ✝ ☎ ✆

Probe of New Physics: interplay of low- and high-energy observables [cLFV]

SLIDE 13

◮ Observables: charged lepton flavour violation ✞ ✝ ☎ ✆ No SM theoretical background!

☞ Many candidate observables! and many experiment/projects!

MEG, Mu3e, COMET, Mu2e, Belle II, LHCb, TauFV, Super Charm-Tau Factory, FCC-ee, ... upgrades, ... ◮ leptonic decays and transitions µ − e conversion in nuclei, µ → eγ, µ → eee, τ → µµµ, mesonic τ decays (τ → ππµ), ... ◮ Meson decays: lepton Number violating decays - B → D µ−e−, ... lepton flavour violating decays- B → τµ, ... ◮ (New) heavy particle decays (model-dependent)

➙

[colliders] ˜ ℓi → ℓjχ0, χ0

2 → χ0 1 τ µ, H → τµ, ∆±± → µ± i τ ± j , ...

LFV final states: e±e− → e±µ− + ET

miss, ...

SLIDE 14

Lepton Flavour Violation ☞ A world-wide experimental effort > 60 years!

90% C.L. upper-limit Future Sensitivity BR(µ → eγ µ → eγ µ → eγ) 4.2 × 10−13 4.2 × 10−13 4.2 × 10−13 (MEG, ’16) 4 × 10−14 4 × 10−14 4 × 10−14 (MEG) BR(τ → µγ) 4.4 × 10−8 (BaBar, ’10) 10−(9−10) (Belle II) BR(τ → eγ) 3.3 × 10−8 (BaBar, ’10) 10−(9−10) (Belle II) CR(µ-e, Au) 7.0 × 10−13 (SINDRUM II, ’06) – CR(µ-e, Al) – 10−(16−18) (Mu2e/COMET) BR(µ → 3e) 1.0 × 10−12 (SINDRUM, ’88) 10−16 (Mu3e)

SLIDE 15

cLFV: observables of New Physics

◮ In the absence of cLFV [and other] signals:

➙ ➙ ➙ constraints on parameter space [scale and couplings] ➙ ➙ ➙ i.e. constraint the neutrino mass generation mechanism

◮ if cLFV observed: compare with peculiar features of given model

➙ ➙ ➙ predictions for cLFV observables ➙ ➙ ➙ intrinsic patterns of correlations of observables

SLIDE 16

☞ Several New Physics Scenarios

◮ cLFV from generic BSM models: SUSY, Extra dimensions, leptoquarks, extended Higgs

sector, ...; OkadaYasuhiro

◮ cLFV from ν ν ν-mass models:    SM seesaw (@ = scales) - type I, II, inverse seesaw, ... , radiative models, Extended frameworks - SUSY seesaw, GUTs, ... ◮ Use Effective Approach to study a given cLFV observable - [example: type II seesaw]

☞ Effective Approach to cLFV: Sacha Davidson

SLIDE 17

Effective approach

◮ BSM (or SM + mν ) requires new fields (or extremely tiny Yν) ◮ Effects at low energy: effective theorie approach Effective operators obtained when expanding the heavy field propagators in 1

M

☞ heavy fermion:

1 D /−M ∼ − 1 M − 1 M D

/ 1

M + ...

☞ heavy scalar :

1 D2−M2 ∼ − 1 M2 − D2 M4 + ...

➙

Leff = LSM + 1

M cd=5Od=5 + 1 M 2cd=6Od=6 + · · ·

Leff = LSM + 1

M cd=5Od=5 + 1 M2cd=6Od=6 + · · ·

Leff = LSM + 1

M cd=5Od=5 + 1 M2cd=6Od=6 + · · ·

∆Ld≥5 ∆Ld≥5 ∆Ld≥5 =

cd=5 M cd=5 M cd=5 M

×

H H H H H H νi

L

νi

L

νi

L

νj

L

νj

L

O6

ℓiℓjqkql∼(ℓiγµPL,Rℓj)(qkγµPL,Rql)

∼(ℓiγµPL,Rℓj)(qkγµPL,Rql) ∼(ℓiγµPL,Rℓj)(qkγµPL,Rql) µ − e

µ − e µ − e in Nuclei, meson decays, (☞ Higher order Od=7,8,.. : Od=7,8,.. : Od=7,8,.. : ν (transitional) magnetic moments, NSI, unitarity violation, ...)

☞

A specific example: Seesaw type II

SLIDE 19

Neutrino mass models

Typically 3 possible ways to generate mν = 0 mν = 0 mν = 0 (and lepton mixings):

☞ Seesaw mechanism can be achieved via bosonic or fermionic exchange

◮ type I with RH neutrino exchange ◮ type II with scalar triplet exchange ◮ type III with fermionic triplet exchange

☞ Radiative corrections ➙ MSSM extended +Rp

/ , Zee model, · · ·

☞ Extra dimensions ➙ alternative to the seesaw

SLIDE 20

Radiative masses

☞ Models at low energy ➙ mν mν mν and lepton mixing

◮ Example: SUSY with Rp / Rp = (−1)L+3B+2S = +1(−1) for particles (superparticles) ◮ Extended Higgs sector, like in the Zee Model Namura Takaaki

➙

mν =     α β α ǫ β ǫ    

ǫ≪α∼β

☞

✞ ✝ ☎ ✆

(Minimal) Zee model predictions already in conflict with neutrino data ➙ excluded!!

SLIDE 21

☞ Scotogenic model [Ma 2006] ➙ mν mν mν masses, dark matter

SM + inert scalar doublet (η η η) + RH neutrinos Ni Ni Ni, SU(3)×SU(2)×U(1)× Z2

Z2 Z2

◮ ◮ ◮ Neutrino masses at 1-loop

η0 = (ηR + iηI)/ √ 2 η0 = (ηR + iηI)/ √ 2 η0 = (ηR + iηI)/ √ 2 EWSB ➙

m2

R = µ2 η + (λ3 + λ4 + λ5) H2 ,

m2

I

= µ2

η + (λ3 + λ4 − λ5) H2 ,

(mν)αβ = 2

i=1 yiαyiβ mi 2(4π)2

m2

R m2 R−m2 i

log

m2

R m2 i

−

m2 I m2 I −m2 i

log

m2

I m2 i

◮

◮ ◮ Neutrino masses + fermionic (Ni Ni Ni) or bosonic (η η η) DM candidate

10

✦6

10

✦4

10

✦2

100 102 104 106 10

✦20

10

✦18

10

✦16

10

✦14

10

✦12

10

✦10

10

✦8

10

✦6

10

✦4 ✧ ✁m N ✂m ✩ ✪ ★ 2

Br

✄ ✫ ☎

3e

✆

Br

✄ ✫ ☎

e

✭ ✆

10

✦6

10

✦4

10

✦2

100 102 104 106 10

✦20

10

✦18

10

✦16

10

✦14

10

✦12

10

✦10

10

✦8

10

✦6

10

✦4 ✧ ✁m N ✂m ✩ ✪ ★ 2

Br

✄ ✫ ☎

3e

✆

Br

✄ ✫ ☎

e

✭ ✆

[Vicente, Toma ’13]

SLIDE 22

☞ Scotogenic model [Ma 2006] ➙ mν mν mν masses, dark matter

SM + inert scalar doublet (η η η) + RH neutrinos Ni Ni Ni, SU(3)×SU(2)×U(1)× Z2

Z2 Z2

◮ ◮ ◮ Neutrino masses at 1-loop

η0 = (ηR + iηI)/ √ 2 η0 = (ηR + iηI)/ √ 2 η0 = (ηR + iηI)/ √ 2 EWSB ➙

m2

R = µ2 η + (λ3 + λ4 + λ5) H2 ,

m2

I

= µ2

η + (λ3 + λ4 − λ5) H2 ,

(mν)αβ = 2

i=1 yiαyiβ mi 2(4π)2

m2

R m2 R−m2 i

log

m2

R m2 i

−

m2 I m2 I −m2 i

log

m2

I m2 i

◮

◮ ◮ Neutrino masses + fermionic (Ni Ni Ni) or bosonic (η η η) DM candidate

✶ ✶

✶
✶
❉ ✁✂✄

☎ ✁ ✆ ✆ ✝ ✂ ☎ ✁✞ ✞ ✟✠ ✝✡ ☛ ✶☞✌ ✶✍ ✶☞✌ ✶✎ ✶☞✌

✏

✶☞✌

✑

❇ ✒ ✓ ✦ ✧ ✥★ ✮ ❇ ✒ ✓ ✦ ✧ ❡ ★ ✮ ✔ ✔ ✕ ✔ ✕✕ ✔ ✕✕✕ ✖ ✗✘✙ ✚ ✗ ✛ ✛ ✜ ✘ ✚ ✗✢ ✢ ✣✤ ✜✩ ✪ ✔ ✫✬ ✔ ✭ ✔ ✫✬ ✔✯ ✔ ✫✬ ✕ ✰ ✔ ✫✬ ✕ ✱ ✲ ✳ ✴ ✵ ✷ ✸ ➭✹ ✲ ✳ ✴ ✵ ✷ ✺ ✻✼

[Vicente, Yaguna ’15]

SLIDE 23

✞ ✝ ☎ ✆ Scotogenic model: DM and cLFV phenomenology strongly related

☞ If N1

N1 N1 is the DM candidate, DM constraints (N1N1 → ℓαℓβ N1N1 → ℓαℓβ N1N1 → ℓαℓβ) ➙

➙ ➙ Yukawa O(1)

O(1) O(1) ◮ ξ < 1 ξ < 1 ξ < 1: CR(µ − e µ − e µ − e,N )& ℓα → 3ℓβ ℓα → 3ℓβ ℓα → 3ℓβ > ℓα → ℓβγ ℓα → ℓβγ ℓα → ℓβγ ✞ ✝ ☎ ✆ cLFV impact/constraints : 4-fermion being the most stringent ◮ Rates highly sensitive to mν1 mν1 mν1 (large mν1 mν1 mν1 enhances box diagrams) ◮ ◮ ◮ Bonus: sizable electron EDM

ACME 2018 ACME 2018

Scalar DM Fermionic DM, within ACME reach [Abada, Toma ’18]

SLIDE 24

☞ Leptoquarks ➙ mν mν mν masses, dark matter, B anomalies

◮ ◮ ◮ Neutrino masses at 3-loops SM + scalar leptoquarks (h1,2 h1,2 h1,2) + RH lepton triplets ΣR ΣR ΣR; SU(3)×SU(2)×U(1)×ZDM

2

ν

L

ν

L

NR d

L

d

R

d

R

d

L

◮ ◮ ◮ Leptoquarks and triplets: within LHC reach!

[Hati, Kumar, Orloff, Teixeira ’18]

SLIDE 25

Tree-Level: Seesaw mechanism(s)

☞ See-Saw mechanism, SM + νR

νR νR L = LSM + λν

Jk ¯

LkνRJ H − 1

2 ¯

νRJ MRJ νc

RJ + λαHc¯

eRαℓα , mD = λν v Majorana Eigenstates(3 × 3) :    ν = L + Lc= νc ,

➙

˜ mL ∼ −mD

1 MR mT D

N = R + Rc=N c,

➙

˜ MR ∼ MR    mD ∼ 200 GeV MR ∼ 1015GeV → mν ∝

∆m2

atm ∼ (10−2 − 10−1)eV

➙

λν ∼ O(1) λν ∼ λe

➙

MR ∼ few TeV

✄ ✂

✁

Testable! low scale seesaw

SLIDE 26

◮ Dimension 5 for mν mν mν δLd=5 = 1

2 cd=5 αβ

ℓc

Lα ˜

φ∗ ˜ φ† ℓLβ

+ h.c.

SLIDE 28

Seesaw I, II, III

.

× × × Y Y MR NR NR Y∆ ∆ µ µ µ

.

× × × Yt Yt MΣ ΣR ΣR

type I (fermionic singlet) type II (scalar triplet) type III (fermionic triplet)

mν mν mν = − 1

2v2 Y T N 1 MN YN

mν mν mν = −2v2Y∆

µ∆ M 2

∆

mν mν mν = − v2

2 Y T Σ 1 MΣ YΣ

Minkowski, Gell-Man, Magg, Wetterich, Ma, Hambye et al. Ramond, Slansky Nussinov Bajc, Senjanovic, Lin Yanagida, Glashow Mohapatra, Senjanovic A.A., Biggio, Bonnet, Gavela, Mohapatra, Senjanovic Schechter, Valle Notari, Strumia, Papucci, Dorsner Ma, Sarkar Fileviez-Perez, Foot, Lew...

SLIDE 29

Dimension 6 operators

Effective Lagrangian Leff = ciOi Model cd=5 cd=6

i

Od=6

i

Fermionic Singlet Y T

N 1 MN YN

Y †

N 1 M†

N

1 MN YN

αβ
ℓLα

φ

i∂

/

φ†ℓLβ
LFV

1 M2

∆ Y∆αβY †

∆γδ

ℓLα−

→ τ ℓLβ ℓLγ− → τ ℓLδ LFV Scalar Triplet 4Y∆

µ∆ M2

∆

|µ∆|2 M4

∆

φ†−

→ τ φ ← − Dµ − → Dµ

φ†−

→ τ φ

Higgs-Gauge

−2 (λ3 + λ5) |µ∆|2

M4

∆

φ†φ

3

Higgs

Fermionic Triplet Y T

Σ 1 MΣ YΣ

Y †

Σ 1 M†

Σ

1 MΣ YΣ

αβ
ℓLα−

→ τ φ

iD

/

φ†−

→ τ ℓLβ LFV

☞ Fermions: no observable effects from Od=6

i

∼ (cd=5)2 Od=6

i

∼ (cd=5)2 Od=6

i

∼ (cd=5)2, not the case for scalars!

SLIDE 30

Case of scalar triplet (type II)

Y∆ ∆ µ µ µ

∆ =     ∆++ ∆+ ∆0     ∼ (1, 3, 2) L∆ = −2 Yukawa couplings: Scalar coupling: Y∆ij Y∆ij Y∆ij(lL)c

ia (lL)jb (iτ2τα)ab ∆α + h.c.

µ µ µ φT

a φb (iτ2τα)

∆†α + h.c.

−M∆ M∆ M∆2∆†∆ − 1

2λ2

∆†∆

2 −λ3

φ†φ

∆†∆

+ ...

d=5 Operator (Mass)

mν = v2 Y∆

µ M∆

2

mν = v2 Y∆

µ M∆

2

mν = v2 Y∆

µ M∆

2

➙ 2 different scales µ

µ µ, M∆ M∆ M∆ possible to have Y∆ ∼ O(1) Y∆ ∼ O(1) Y∆ ∼ O(1) M∆ ∼ 1 M∆ ∼ 1 M∆ ∼ 1 TeV (µ ∼ 100 µ ∼ 100 µ ∼ 100 eV)

SLIDE 31

Low energy effects of dimension 6 operators:

1 2M2

∆Y∆ijY †

∆kl

lLiγµlLk

lLjγµlLl

→ LFV, g − 2, EDMs

constraints not suppressed by small mν ∝ µ −2 µ2

M4

∆∂µ

φ†φ
∂µ

φ†φ

2λ3

µ2 M4

∆

φ†φ

3 4 µ2

M4

∆

φ†Dµφ

† φ†Dµφ



                  → EW precision data, couplings to gauge bosons, ... −2 µ2

M 4

∆

φ†φ

YeleRφ + Ydqdφ − Yuqiτ2uφ + h.c.

→ top physics...

SLIDE 32

Constraining the type II seesaw

⋆ Scalar triplet: bounds from low energy constraints

☞ ☞ ☞ Y∆ < ∼ 10−1 × M∆

1 TeV

Y∆ <

∼ 10−1 × M∆

1 TeV

Y∆ <

∼ 10−1 × M∆

1 TeV

r stronger

☞ ☞ ☞ If observation of µ → eγ µ → eγ µ → eγ at MEG (sensitivity of 10−14)

for Y∆ ∼ O(1)

➙

30 TeV < M∆ < 90 TeV

for Y∆ ∼ O(10−2)

➙

0.3 TeV < M∆ < 0.9 TeV

⋆ Scalar triplet: bounds from LHC

☞ If M∆ M∆ M∆ turns out to be as low as O O O(TeV) ➙ possibility of clean signals at colliders

SLIDE 33

LHC constraints on scalar triplet

⋆ Production of ∆++ and ∆−−, decaying into pairs of same-sign leptons

➙ striking signals, free from SM backgrounds

⋆ Drell-Yann Production    M∆++ ∼ 200 GeV ⇒ σ(γ∗, Z∗ → ∆++∆−−) ∼ 100 fb M∆++ ∼ 900 GeV ⇒ σ(γ∗, Z∗ → ∆++∆−−) ∼ 0.1 fb ⋆ Decay product    Γ(∆±± → W ±W ±) ∼ µ2M 3

∆

Γ(∆±± → ℓ±

i ℓ± j ) ∼ Y∆ijM∆

➙ LHC: so far, only negative search results ⇒ constraints on parameter space (M∆, µ, Y∆)

!""#$%& ''( ')*+,+- %. '/( ')*+0+- %. ')*+12+- %. 34#5+!5#3!"#46+3!75%89:+3#3%58

+ ✁+%+ ✂ ✄+;!<!3%8%<

Antusch et.al., arXiv:1811.03476

✞ ✝ ☎ ✆ vT = µv2/M 2

T

SLIDE 34

LFV predictions for ν mass spectrum

◮ LFV in high-energy (LHC) + low-energy observables (e.g µ → eee) ⇒ ⇒ ⇒ predictions for ν mass spectrum, CP phases ...

Garayoa, Schwetz, arXiv:0712.1453

☞ If ∆ observed, must verify whether a scalar-mediated seesaw is at work

⇒ ⇒ ⇒ observe in addition at least three LFV processes (to measure and disentangle the individual Y∆ij couplings)

SLIDE 35

☞

✞ ✝ ☎ ✆ CLFV plays important rôle in disentangling between models [Construction of the Lagrangian at best only partially...]

SLIDE 36

✞ ✝ ☎ ✆

Back to the type I seesaw ☞ Testable Seesaw type I mechanism?

SLIDE 37

☞ Seesaw mechanism at different scales

◮ Extending the SM with other “sterile fermions": singlets under SU(3)c×SU(2)L×U(1)Y Interactions with SM fields: through mixings with active neutrinos A priori, no bound on the number of sterile states, no limit on their mass scale(s) ◮ Interest/phenomenological implications of new “neutrinos" (νR νR νR) dependent on their mass! eV scale ↔ ↔ ↔ extra neutrinos suggested by reactor (& short baseline?) ν-oscil. anomalies keV scale ↔ ↔ ↔ warm dark matter candidates; explain pulsar velocities (kicks); 3.5 keV line.. MeV - TeV scale ↔ ↔ ↔ experimental testability, i.e! cLFV/colliders (and BAU, DM, ...) Beyond 109 109 109 GeV ↔ ↔ ↔ theoretical appeal: standard seesaw, BAU, GUTs

SLIDE 38

☞ Extending the SM with “sterile" fermions: phenomenological consequences

◮ Modified charged (W ± W ± W ±) and neutral (Z0 Z0 Z0) current interactions: LW ± LW ± LW ± ∼ − gw

√ 2 W − µ

α=e,µ,τ

νj

Uαi Uαi Uαi ➙ modified lepton mixing - now encodes also active-sterile mixings (for Ns = 0, Uαi Uαi Uαi = UPMNS)

◮ If sufficiently light, sterile νS can be produced as final states

☞ Many new searches proposed➙ Huge impact for numerous observables!

But also abundant constraints on new mixings and masses!!

[Deppisch et al, ’15, ] [updated 2018: AA et al, 1712.03984 ]

SLIDE 39

☞ Updated constraints

[AA, De Romeri, Lucente, Toma, Teixeira, 1712.03984]

SLIDE 40

☞ Extending the SM with sterile fermions: (testable!) theoretical frameworks

◮ Incorporating νR νR νR - low scale seesaws: type I seesaw [ TeV ] ➙ small Yν Yν Yν type I seesaw variants ➙ "large" Yν Yν Yν ν ν νMSM [ GeV ] ➙ tiny Yν Yν Yν Mν Mν Mν =

v Y T

ν

Y T

ν

Y T

ν

v Yν Yν Yν MR MR MR

✞

✝ ☎ ✆

mν mν mν ≈ −v2Y T

ν 1 MR MR MR Yν

≈ −v2Y T

ν 1 MR MR MR Yν

≈ −v2Y T

ν 1 MR MR MR Yν

◮ ν ν νMSM: Minimal “type I seesaw-like” extension: SM + 3 νR νR νR New states account for neutrino data, offer DM candidate, allow BAU via leptogenesis

☞ tiny Yukawa couplings; heavily constrained parameter space (th, cosmo, exp..)

[Canetti et al, ’13]

0.2 0.5 1.0 2.0 5.0 10.0 1012 1010 108 106 M GeV U2 B A U BAU S e e s a w B B N P S 1 9 1 NuTeV CHARM

☞ ν

ν νMSM: very difficult prospects for cLFV (many orders below exp. sensitivity)

SLIDE 41

☞ Extended seesaw: Inverse and Linear Seesaw

◮ Incorporating νR νR νR and additional steriles νS νS νS: Inverse seesaw (ISS) ➙ sizeable Yν Yν Yν Linear seesaw (LSS) ➙ sizeable Yν Yν Yν

[in the basis

νL, νc

R, νS

T ]

MISS MISS MISS =

    Y T

ν v

Y T

ν v

Y T

ν v

Yνv Yνv Yνv MR MR MR MT

R

MT

R

MT

R

µX µX µX    

mν ≈ (Yνv)2

MR

mν ≈ (Yνv)2

MR

mν ≈ (Yνv)2

MR µX

µX µX MLSS MLSS MLSS =

    Y T

ν v

Y T

ν v

Y T

ν v

MT

L

MT

L

MT

L

Yνv Yνv Yνv MR MR MR ML ML ML MT

R

MT

R

MT

R

   

mν ≈ (vYν) (MLMR

−1)T + (MLMR −1) (vYν)T

mν ≈ (vYν) (MLMR

−1)T + (MLMR −1) (vYν)T

mν ≈ (vYν) (MLMR

−1)T + (MLMR −1) (vYν)T

◮ Heavy physical states ➙ pseudo-Dirac pairs: mN± mN± mN± ≈ MR ± µX MR ± µX MR ± µX

[see, e.g., Mohapatra et al, 1986, Gonzalez-Garcia et al, 1988, Deppisch et al, ’04, Asaka et al, ’05, Gavela et al, ’09, Ibarra, Petcov et al, ’10, AA, Lucente, ’14, ...]

SLIDE 42

☞ Low scale seesaw: cLFV in radiative decays ℓi → ℓjγ

ℓi → ℓjγ ℓi → ℓjγ and 3-body decays ℓi → 3ℓj ℓi → 3ℓj ℓi → 3ℓj

10-35 10-30 10-25 10-20 10-15 10-10 10-5 100 10-6 10-4 10-2 100 102 104 106

BR (µ → e γ) m4 (GeV)

“3+1” toy model, [AA, De Romeri and Teixeira, ’15] “(2,2) ISS realisation” [AA and Lucente, ’14]

◮ Consider µ → eγ µ → eγ µ → eγ: for ms 10 − 100 GeV sizeable νs contributions

W ± γ µ e

νi

... but precluded by invisible Z Z Z width And by other cLFV observables! ◮ Particularly constraining: BR(µ → 3e), CR(µ − e, N) Dominated by Z penguin contributions for ms MZ

µ µ W ± Z τ µ

νi

SLIDE 43

☞ Interplay: cLFV at high- and low-energies

[AA, De Romeri, Monteil, Orloff, Teixeira, ’15]

10-25 10-20 10-15 10-10 10-5 10-6 10-4 10-2 100 102 104 106

BR (Z → µ τ) m4 (GeV)

LC FCC-ee (Z pole) FCC-ee

3+1 toy model 3+1 toy model

10-25 10-20 10-15 10-10 10-5 10-20 10-18 10-16 10-14 10-12 10-10 10-8 10-6

BR (Z → µ τ) BR(τ → µ µ µ)

FCC-ee LC FCC-ee (Z pole)

10-30 10-28 10-26 10-24 10-22 10-20 10-18 10-16 10-14 10-12 10-10 0.1 1 10 100

BR (Z → e µ) M (GeV)

(3,3) ISS νMSM

◮ Complementarity probes of νs νs νs cLFV at low- and high energies! (and in LNV...) ◮ Z → µτ Z → µτ Z → µτ at FCC-ee: allows to probe µ − τ µ − τ µ − τ cLFV beyond Belle II reach

[see also AA, Becirevic, Lucente, Sumensari ’15, and De Romeri et al, ’16]

SLIDE 44

☞ cLFV in muonic atoms

◮ Muonic atoms: 1s bound state formed when µ− stopped in target Interesting laboratory to study cLFV! µ − e µ − e µ − e conversion ◮ Muonic atom decay: µ−e− → e−e− µ−e− → e−e− µ−e− → e−e− ( Chen Wu)

[Koike et al, ’10]

Initial µ− µ− µ− and e− e− e−: 1s state bound in Coulomb field of the muonic atom’s nucleus ◮ Experimental status: New observable! Hopefully included in Physics programmes of COMET & Mu2e (?) ◮ Coulomb interaction increases overlap between Ψµ− and Ψe− wave functions Γ(µ−e− → e−e−, N) ∝ σµe→eevrel [(Z − 1) α me]3/π

NP

e− e− µ− e−

◮ Rate strongly enhanced in large Z Z Z atoms Γ/Γ0 10×(Z − 1)3 Γ/Γ0 10×(Z − 1)3 Γ/Γ0 10×(Z − 1)3

[Uesaka et al, ’15-’16]

Consider experimental setups for Pb, U !?

SLIDE 45

☞ cLFV muonic atom decays

[AA, De Romeri, Teixeira, ’15] 3+1 toy model

10-25 10-20 10-15 10-10 10-5 10-1 100 101 102 103 104 105 106 10-25 10-20 10-15 10-10 10-5

BR (µ- e- → e- e-, Al) CR (µ - e, Al) m4 (GeV)

CR(µ - e, Al) BR (µ- e- → e- e-, Al)

|Uµ 4|2 m4 (GeV)

10-12 10-10 10-8 10-6 10-4 10-2 100 10-1 100 101 102 103 104 105 106

21
20
19
18
17
16
15

SHIP FCC-ee OTHER BOUNDS BBN DUNE LHC14

10-25 10-20 10-15 10-10 10-5 10-1 100 101 102 103 104 105 106 10-25 10-20 10-15 10-10 10-5

BR (µ- e- → e- e-, Al) CR (µ - e, Al) < m4-9 > (GeV)

CR(µ - e, Al) BR (µ- e- → e- e-, Al)

|Uµ 5|2 m5 (GeV)

10-12 10-10 10-8 10-6 10-4 10-2 100 10-1 100 101 102 103 104 105 106

21
20
19
18
17
16
15

SHIP FCC-ee OTHER BOUNDS BBN DUNE LHC14

(3,3) ISS Log BR(µe → ee µe → ee µe → ee)

◮ Sizeable values for BR(µ−e− → e−e− µ−e− → e−e− µ−e− → e−e−) - potentially within experimental reach! ◮ For Aluminium, CR(µ − e µ − e µ − e) appears to have stronger experimental potential .. consider “heavy” targets to probe BR(µ−e− → e−e− µ−e− → e−e− µ−e− → e−e−)

SLIDE 46

☞ Searches at the LHC and beyond Michael Schmidt, Amandeep Kaur Kalsi

◮ Searches for νs by ATLAS and CMS “smoking-gun” (LNV) channel:

p p → W ∗ → N ℓ± → ℓ± + ℓ± + 2 jets

◮ Promising prospects for FCC-ee, ILC, CEPC...

[Banerjee et al, 1503.05491]

◮ Further searches carried for LFV final states and/or

ther exotic channels

◮ cLFV exotic events at the LHC ◮ Searches for heavy N N N at the LHC q q′ → τ µ + 2 jets q q′ → τ µ + 2 jets q q′ → τ µ + 2 jets (no missing ET !) ◮ After cuts, significant number of events!

[Arganda et al, 1508.05074]

◮ Resonant mono-Higgs production at FCC-ee N → H ν N → H ν N → H ν sizeable deviations from SM mono-Higgs ◮ Sensitive probe of νs at high-energies!

[Antusch et al, ’15]

SLIDE 47

Conclusions

◮ Neutrino oscillations call for BSM ◮ Flavour violation in quarks and neutral leptons..., expected in the charged lepton sector ◮ New Physics can be manifest via cLFV even before any direct discovery! ◮ cLFV observables can provide information on the ν ν ν mass generation mechanism at work! ◮ Numerous observables of different origin, infer pattern, correlation if unique LFV source