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

☞ Facts: ν change flavours after propagating a finite distance

Solar

νe → νµ,τ

∆m2sol ≃ 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

∆m2atm ≃ 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

∆m2atm

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,...

Lepton mixing & neutrino data: current status

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◆✒✓✔✕ ✖✗✘ ✙✚✘✛✜✢

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☎

✆

◮ “Precision era” for neutrino physics

◮ Only three oscillation parameters unknown...

θ23 octant; δCP; ν-mass ordering

(preference: sin2 θ23 = 0.58sin2 θ23 = 0.58sin2 θ23 = 0.58 (b.f) 2nd octant; δCP = 217δCP = 217δCP = 217 (b.f);)

◮ Exciting experimental road ahead!

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

0

solar~7×10−5eV2

atmospheric

~2×10−3eV2

atmospheric

~2×10−3eV2

m12

m22

m32

m2

0

m22

m12

m32

νe

νµντ

? ?

solar~7×10−5eV2

☞ Resolving the absolute mass scale for light neutrinos

- Tritium decays (3H →3He +νe + e−): mνe . 2.1mνe . 2.1mνe . 2.1 eV [Troitsk]

☞June 11 2018, the KATRIN experiment has been inaugurated!

- 0ν2β0ν2β0ν2β 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

νm

K (T)

QT

✥�❱✮❧✐❣✁✂❡s✂♠

✹

✶✄

✸

✶✄

✷

✶✄

☎

✶✄

✆✝✞

✟✠

✸

✶✄✷

✶✄☎

✶✄✶

■✡◆✡

❳☛☞✌✍✎❑❛✏▲❆◆❉✲✑☛♥ ✒

✓

✺✔ ✕✔✔ ✕✺✔

❈✖●✗

❙✗❩✘

▼✙❈✚

❚✗❚✗

✛✗✜✚

☞ Indisputable: νs are massive and mix

➙

The minimal SM is incomplete!

➙

✞

✝

☎

✆An observational caveat that is also a theoretical one!

◮ Is ννν mass generation mechanism 6=6=6= 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 ≃ 0.4VCKM =

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 ≃ 0.4VCKM =

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

UPMNS =

c13c12 c13s12 s13e−iδ

−c23s12 − s23s13c12eiδ c23c12 − s23s13s12e

iδ −s23c13

s23s12 − c23s13c12eiδ −s23c12 − c23s13s12e

iδ c23c13

×diag(

eiα1 , eiα2 , 1)

UPMNS =

c13c12 c13s12 s13e−iδ

−c23s12 − s23s13c12eiδ c23c12 − s23s13s12e

iδ −s23c13

s23s12 − c23s13c12eiδ −s23c12 − c23s13s12e

iδ c23c13

×diag(

eiα1 , eiα2 , 1)

UPMNS =

c13c12 c13s12 s13e−iδ

−c23s12 − s23s13c12eiδ c23c12 − s23s13s12e

iδ −s23c13

s23s12 − c23s13c12eiδ −s23c12 − c23s13s12e

iδ 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?

◮ Light ννν mass scale ?

◮ ν data worsens fermion hierarchy problem!

☞

✞

✝

☎

✆Why ν so light?

☞

✞

✝

☎

✆and what absolute neutrino mass scale?

◮ 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 UPMNS is incomplete? Non-Unitary?

☞

✞

✝

☎

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

☞ Bonus: strong Potential for CP violation!

◮ Unitarity triangle surface ∝ J leptonCP : J lepton

CP,max ≃ 1000× JquarkCP

JquarkCP = 2.96× 10−5, JCP,max ≃ 3.29× 10−2

J ≡ Im(

Ue3U∗e1U

∗µ3Uµ1

)

J = JmaxCP sin δ

Unitarity Triangle (in e, µ) Jarlskog Invariant

☞

✞

✝

☎

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

mν 6= 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

2MνcLνL + h.c.

Majorana field: Ψν = νL + νcL ➙ Ψν = Ψcν ➙ νcLνL = νTLCνL, 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 ∼√

∆m2atm ∼

√

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

✞

✝

☎

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

◮ 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 + ...➙ mνH Y ν νL νR + ...➙ mνH Y ν νL νR + ...➙ mν

◮ What is the neutrino mass generation mechanism?

◮ ν ↔ νν ↔ νν ↔ 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 6= observables

☞ Determination of ν-SM/BSM requires to combine 6= 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]

◮ 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 → Dµ−e−, ...

lepton flavour violating decays- B → τµ, ...

◮ (New) heavy particle decays (model-dependent) ➙ [colliders]

ℓi → ℓjχ0, χ0

2 → χ01 τ µ, H → τµ, ∆±± → µ±

i τ±j , ...

LFV final states: e±e− → e±µ− + ETmiss, ...

Lepton Flavour Violation

☞ A world-wide experimental effort > 60 years!

90% C.L. upper-limit Future Sensitivity

BR(µ → eγµ → eγµ → eγ) 4.2 × 10−134.2 × 10−134.2 × 10−13 (MEG, ’16) 4 × 10−144 × 10−144 × 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)

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

☞ Several New Physics Scenarios

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

sector, ...; OkadaYasuhiro

◮ cLFV from ννν-mass models:

SM seesaw (@ 6= 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

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 in1M

☞ heavy fermion: 1D/−M

∼ − 1M− 1

MD/ 1

M+ ...

☞ heavy scalar : 1D2−M2 ∼ −

1M2 −

D2

M4 + ...

➙ Leff = LSM + 1Mcd=5Od=5 + 1

M2 cd=6Od=6 + · · ·Leff = LSM + 1

Mcd=5Od=5 + 1

M2 cd=6Od=6 + · · ·Leff = LSM + 1

Mcd=5Od=5 + 1

M2 cd=6Od=6 + · · ·

∆Ld≥5∆Ld≥5∆Ld≥5 =cd=5

Mcd=5

Mcd=5

M ×

HHH HHH

νiLνiLνiL ν

jLνjLνjL

+cd=6µeee

M2

cd=6µeee

M2

cd=6µeee

M2 ×

eReReR

eLeLeL

eLeLeL

µRµRµR

+cd=6ℓiℓjγ

M2

cd=6ℓiℓjγ

M2

cd=6ℓiℓjγ

M2 ...

Higher order operators

☞ O5ijO5ijO5ij (Weinberg) operator: O5

ijO5ijO5ij ∼ (Li H)(H Lj)∼ (Li H)(H Lj)∼ (Li H)(H Lj) ➙ LNV ∆L = 2 processes

Common to all SM extensions incorporating massive Majorana neutrinos

☞ 3 “types” of Dimension 6 operators relevant for cLFV (dipole and 3-body)

◮ 2 lepton-Higgs-photon: O6ℓiℓjγ

∼ LiσµνejHFµν∼ LiσµνejHFµν∼ LiσµνejHFµνO6

ℓiℓjγ∼ Liσ

µνejHFµν∼ LiσµνejHFµν∼ LiσµνejHFµνO6

ℓiℓjγ∼ Liσ

µνejHFµν∼ LiσµνejHFµν∼ LiσµνejHFµν

O6ℓiℓiγ ➙ anomalous magnetic or electric moments (∝ Re or Im C6

ℓiℓiγ/Λ2)

O6ℓiℓjγ

O6ℓiℓjγ

O6ℓiℓjγ ➙ radiative decays ℓi → ℓjγℓi → ℓjγℓi → ℓjγ (∝ C6

ℓiℓjγ/Λ2)

◮ 4 lepton: O6ℓiℓjℓkℓl

O6ℓiℓjℓkℓl

O6ℓiℓjℓkℓl

∼ (ℓiγµPL,Rℓj)(ℓkγµPL,Rℓl)∼ (ℓiγµPL,Rℓj)(ℓkγµPL,Rℓl)∼ (ℓiγµPL,Rℓj)(ℓkγµPL,Rℓl) 3-body decays ℓi → ℓjℓkℓlℓi → ℓjℓkℓlℓi → ℓjℓkℓl, ...

◮ 2 lepton-2 quarks: O6ℓiℓjqkql

O6ℓiℓjqkql

O6ℓiℓjqkql

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

Neutrino mass models

Typically 3 possible ways to generate mν 6= 0mν 6= 0mν 6= 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

Radiative masses

☞ Models at low energy ➙ mνmνmν 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 =

0 α β

α 0 ǫ

β ǫ 0

ǫ≪α∼β

☞

✞

✝

☎

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

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

SM + inert scalar doublet (ηηη) + RH neutrinos NiNiNi, SU(3)×SU(2)×U(1)× Z2Z2Z2

◮◮◮ Neutrino masses at 1-loop

η0 = (ηR + iηI )/√2η0 = (ηR + iηI)/

√2η0 = (ηR + iηI)/

√2 EWSB ➙

m2R = µ2

η + (λ3 + λ4 + λ5) 〈H〉2 ,

m2I = µ2

η + (λ3 + λ4 − λ5) 〈H〉2 ,

(mν)αβ =∑2

i=1

yiαyiβmi

2(4π)2

[

m2R

m2R

−m2i

log

(

m2R

m2i

)

−m2

I

m2I−m2

i

log

(

m2I

m2i

)]

◮◮◮ Neutrino masses + fermionic (NiNiNi) or bosonic (ηηη) DM candidate

10

✦610

✦410

✦210

010

210

410

6

10

✦2010

✦18

10

✦16

10

✦14

10

✦12

10

✦10

10

✦8

10

✦6

10

✦4

✧�✁m N ✂m ✩✪ ★

2

Br

✄✫

☎

3e

✆

Br

✄✫

☎

e

✭✆

10

✦610

✦410

✦210

010

210

410

6

10

✦2010

✦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]

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

SM + inert scalar doublet (ηηη) + RH neutrinos NiNiNi, SU(3)×SU(2)×U(1)× Z2Z2Z2

◮◮◮ Neutrino masses at 1-loop

η0 = (ηR + iηI )/√2η0 = (ηR + iηI)/

√2η0 = (ηR + iηI)/

√2 EWSB ➙

m2R = µ2

η + (λ3 + λ4 + λ5) 〈H〉2 ,

m2I = µ2

η + (λ3 + λ4 − λ5) 〈H〉2 ,

(mν)αβ =∑2

i=1

yiαyiβmi

2(4π)2

[

m2R

m2R

−m2i

log

(

m2R

m2i

)

−m2

I

m2I−m2

i

log

(

m2I

m2i

)]

◮◮◮ Neutrino masses + fermionic (NiNiNi) or bosonic (ηηη) DM candidate

✶ ✶� ✶�� ✶���

❉✁✂✄ ☎✁✆✆✝✂ ☎✁✞✞ ✟✠✝✡☛

✶☞✌✶✍

✶☞✌✶✎

✶☞✌�✏

✶☞✌�✑

❇✒✓✦ ✧ ✥★✮

❇✒✓✦ ✧ ❡ ★✮

✔ ✔✕ ✔✕✕ ✔✕✕✕

✖✗✘✙ ✚✗✛✛✜✘ ✚✗✢✢ ✣✤✜✩✪

✔✫✬✔✭

✔✫✬✔✯

✔✫✬✕✰

✔✫✬✕✱

✲✳✴✵ ✷ ✸➭✹

✲✳✴✵ ✷ ✺✻✼

[Vicente, Yaguna ’15]

✞

✝

☎

✆Scotogenic model: DM and cLFV phenomenology strongly related

☞ If N1N1N1 is the DM candidate, DM constraints (N1N1 → ℓαℓβN1N1 → ℓαℓβN1N1 → ℓαℓβ) ➙➙➙ Yukawa O(1)O(1)O(1)

◮ ξ < 1ξ < 1ξ < 1: CR(µ− eµ− eµ− e,N )& ℓα → 3ℓβℓα → 3ℓβℓα → 3ℓβ > ℓα → ℓβγℓα → ℓβγℓα → ℓβγ

✞

✝

☎

✆cLFV impact/constraints : 4-fermion being the most stringent

◮ Rates highly sensitive to mν1mν1mν1

(large mν1mν1mν1

enhances box diagrams)

◮◮◮ Bonus: sizable electron EDM

ACME 2018ACME2018

Scalar DM Fermionic DM, within ACME reach

[Abada, Toma ’18]

☞ Leptoquarks ➙ mνmνmν masses, dark matter, B anomalies

◮◮◮ Neutrino masses at 3-loops

SM + scalar leptoquarks (h1,2h1,2h1,2) + RH lepton triplets ΣRΣRΣR; SU(3)×SU(2)×U(1)×ZDM2

νL νLNRdL dR dR dL

h2 h2

h1 h1 ◮◮◮ Radiatively induced mνmνmν (3-loop); Σ0Σ0Σ0 ↔ DM candidate

◮◮◮ Non-trivial structure in leptoquark Yukawa couplings yyy

⇒⇒⇒ account for R(∗)KR(∗)KR(∗)K anomalies!

yyy ∼

ǫ4 ǫ5 ǫ2

ǫ3 ǫ3 ǫ4

ǫ4 ǫ ǫ

✞

✝

☎

✆◮◮◮ Huge impact/constraints from cLFV and meson decays:

CR(µ− eµ− eµ− e,N), K → πννK → πννK → πνν the most stringent

◮◮◮ Oscillation data (perturbative couplings)

viable DM candidate

◮◮◮ Explain RK(∗)RK(∗)RK(∗) anomalies [no RD(∗)RD(∗)RD(∗) , (g − 2)µ(g − 2)µ(g − 2)µ]

◮◮◮ Leptoquarks and triplets: within LHC reach![Hati, Kumar, Orloff, Teixeira ’18]

Tree-Level: Seesaw mechanism(s)

☞ See-Saw mechanism, SM + νRνRνR

L = LSM + λνJkLkνRJH −

12νRJMRJ ν

cRJ

+ λαHceRαℓα , mD = λν v

Majorana Eigenstates(3× 3) :

ν = L+ Lc= νc , ➙ mL ∼ −mD1

MRmT

D

N= R+ Rc=Nc, ➙ 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

◮ Dimension 5 for mνmνmν

δLd=5 = 12cd=5αβ

(ℓcLα

φ∗)(

φ† ℓLβ

)+ h.c.

mν = v2Y †YMR

mν = cd=5v2, cd=5 = Y †YMR

◮ Dimension 6 for cLFV

☞ cd=6 ∼ (cd=5)2cd=6 ∼ (cd=5)2cd=6 ∼ (cd=5)2 small mνmνmν preclude observable effects from Od=6iOd=6iOd=6i

☞ Need variants or other seesaw mechanisms?

☞ Tree-level ννν mass generation mechanism, other options?

➙

✞

✝

☎

✆Other realisations of the seesaw mechanism

Seesaw I, II, III

.

×××

Y

Y

MR

NR

NR

Y∆

∆µµµ

.

×××

Yt

Yt

MΣ

ΣR

ΣR

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

mνmνmν = −12v2 Y T

N1

MNYN mνmνmν = −2v2Y∆

µ∆

M2∆

mνmνmν = − v2

2Y TΣ

1MΣ

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...

Dimension 6 operators

Effective Lagrangian Leff = ciOi

Model cd=5 cd=6i Od=6

i

Fermionic Singlet Y TN

1MN

YN

(Y †N

1

M†N

1MN

YN

)

αβ

(ℓLαφ

)i∂/

(φ†ℓLβ

) LFV

1M2

∆Y∆αβY

†∆γδ

(ℓLα−→τ ℓLβ

)(ℓLγ−→τ ℓLδ

) LFV

Scalar Triplet 4Y∆µ∆

M2∆

|µ∆|2M4

∆

(φ†−→τ φ

)(←−Dµ−→Dµ

)(φ†−→τ φ

)Higgs-Gauge

−2 (λ3 + λ5)|µ∆|2M4

∆

(φ†φ

)3 Higgs

Fermionic Triplet Y TΣ

1MΣ

YΣ

(Y †Σ

1

M†Σ

1MΣ

YΣ

)

αβ

(ℓLα−→τ φ

)iD/

(φ†−→τ ℓLβ

) LFV

☞ Fermions: no observable effects from Od=6i ∼ (cd=5)2Od=6i ∼ (cd=5)2Od=6i ∼ (cd=5)2, not the case for scalars!

☞ Direct Lepton Violation pattern: Od=5iOd=5iOd=5i suppressed by a small scale ∝ mν∝ mν∝ mν but not the Od=6

iOd=6iOd=6i

Case of scalar triplet (type II)

Y∆

∆µµµ ∆ =

∆++

∆+

∆0

∼ (1, 3, 2) L∆ = −2

Yukawa couplings: Scalar coupling:

Y∆ijY∆ijY∆ij(lL)cia (lL)jb (iτ2τα)ab ∆

α + h.c. µµµ φTa φb (iτ2τα)

(

∆†)α

+ h.c.

−M∆M∆M∆2∆†∆− 1

2λ2

(

∆†∆)2

−λ3

(

φ†φ) (

∆†∆)

+ ...

d=5 Operator (Mass) mν = v2 Y∆µ

M∆2mν = v2 Y∆

µ

M∆2mν = v2 Y∆

µ

M∆2 ➙ 2 different scales µµµ, M∆M∆M∆

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

Low energy effects of dimension 6 operators:

12M2

∆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)

2λ3µ2

M4∆

(

φ†φ)3

4 µ2

M4∆

[

φ†Dµφ]† [

φ†Dµφ]

→EW precision data,couplings to gauge bosons, ...

−2 µ2

M4∆

(

φ†φ) {

YeleRφ+ Ydqdφ− Yuqiτ2uφ+ h.c.}

→ top physics...

Constraining the type II seesaw

⋆ Scalar triplet: bounds from low energy constraints

☞ ☞ ☞ Y∆<∼ 10−1 ×

(

M∆

1TeV

)

Y∆<∼ 10−1 ×

(

M∆

1TeV

)

Y∆<∼ 10−1 ×

(

M∆

1TeV

)

or stronger

☞ ☞ ☞ If observation of µ → eγµ → eγµ → 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 OOO(TeV) ➙ possibility ofclean signals at colliders

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±) ∼ µ2M3∆

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/M2

T

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)

☞

✞

✝

☎

✆CLFV plays important rôle in disentangling between models

[Construction of the Lagrangian at best only partially...]

✞

✝

☎

✆Back to the type I seesaw

☞ Testable Seesaw type I mechanism?

◮ Economical

◮ Majorana Nature

◮ Aiming at having challenging prospect for cLFV :

Direct Lepton Violation pattern:

Od=5iOd=5iOd=5i suppressed by a small scale ∝ mν∝ mν∝ mν and not the Od=6

iOd=6iOd=6i

☞ 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" (νRνRνR) 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 109109109 GeV↔↔↔ theoretical appeal: standard seesaw, BAU, GUTs

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

◮ Modified charged (W±W±W±) and neutral (Z0Z0Z0) current interactions:

LW±LW±LW± ∼ − gw√2W−

µ

∑α=e,µ,τ

∑3+NSi=1 UαiUαiUαi ℓα γµ PL νi

LZ0LZ0LZ0 ∼ − gw2 cos θw

Zµ

∑3+NSi,j=1 νi γ

µ[PL (U†

U)ij(U†U)ij(U†U)ij − PR (U†

U)∗ij(U†U)∗ij(U†U)∗ij

]νj

UαiUαiUαi ➙ modified lepton mixing - now encodes also active-sterile mixings

(for Ns = 0, UαiUαiUαi = 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 ]

☞ Updated constraints

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

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

◮ Incorporating νRνRνR - low scale seesaws: type I seesaw [ TeV ] ➙ small YνYνYν

type I seesaw variants ➙ "large" YνYνYν

νννMSM [ GeV ] ➙ tiny YνYνYν

MνMνMν =

(

0 vY TνYTνYTν

vYνYνYν MRMRMR

)

✞

✝

☎

✆mνmνmν ≈ −v

2Y Tν

1MRMRMR

Yν≈ −v2Y Tν

1MRMRMR

Yν≈ −v2Y Tν

1MRMRMR

Yν

◮ νννMSM: Minimal “type I seesaw-like” extension: SM + 3 νRνRνR

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 10.010-12

10-10

10-8

10-6

M @GeVD

U2

BAU

BAU

Seesaw

BBN

PS191

NuTeV

CHARM

☞ νννMSM: very difficult prospects for cLFV (many orders below exp. sensitivity)

☞ Extended seesaw: Inverse and Linear Seesaw

◮ Incorporating νRνRνR

and additional steriles νSνSνS

: Inverse seesaw (ISS) ➙ sizeable YνYνYν

Linear seesaw (LSS) ➙ sizeable YνYνYν

[in the basis(

νL, νc

R, ν

S

)T]

MISSMISSMISS =

0 Y Tν vY Tν vY Tν v 0

YνvYνvYνv 0 MRMRMR

0 MTRMTRMTR µXµXµX

mν ≈(Yνv)2

MRmν ≈

(Yνv)2

MRmν ≈

(Yνv)2

MRµXµXµX

MLSSMLSSMLSS =

0 Y Tν vY Tν vY Tν v MT

LMTLMTL

YνvYνvYνv 0 MRMRMR

MLMLML MTRMTRMTR 0

mν ≈ (vYν) (MLMR−1)T + (MLMR

−1) (vYν)Tmν ≈ (vYν) (MLMR

−1)T + (MLMR−1) (vYν)

Tmν ≈ (vYν) (MLMR−1)T + (MLMR

−1) (vYν)T

◮ Heavy physical states ➙ pseudo-Dirac pairs: mN±mN±mN± ≈MR ± µXMR ± µXMR ± 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, ...]

☞ Low scale seesaw: cLFV in radiative decays ℓi → ℓjγℓi → ℓjγℓi → ℓjγ and 3-body decays ℓi → 3ℓjℓi → 3ℓjℓi → 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→ eγµ→ eγµ→ eγ:

for ms & 10− 100 GeV sizeable νs contributions

W± γ

µ eνi

... but precluded by invisible ZZZ 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 µνi

☞ 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(Zpole)

FCC-ee3+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

→µτ)

BR(τ → µ µ µ)

FCC-ee

LC

FCC-ee(Zpole)

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 νsνsνs cLFV at low- and high energies! (and in LNV...)

◮ Z → µτZ → µτZ → µτ at FCC-ee: allows to probe µ− τµ− τµ− τ cLFV beyond Belle II reach[see also AA, Becirevic, Lucente, Sumensari ’15, and De Romeri et al, ’16]

☞ cLFV in muonic atoms

◮ Muonic atoms: 1s bound state formed when µ− stopped in target

Interesting laboratory to study cLFV! µ− eµ− eµ− 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)αme]3/π

NP

e−

e−

µ−

e−

◮ Rate strongly enhanced in large ZZZ atoms

Γ/Γ0 & 10×(Z − 1)3Γ/Γ0 & 10×(Z − 1)3Γ/Γ0 & 10×(Z − 1)3 [Uesaka et al, ’15-’16]

Consider experimental setups for Pb, U !?

☞ 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 10610-25

10-20

10-15

10-10

10-5

BR

(µ- e

- → e

- e- , A

l)

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

DU

NE

LHC14

10-25

10-20

10-15

10-10

10-5

10-1 100 101 102 103 104 105 10610-25

10-20

10-15

10-10

10-5

BR

(µ- e

- → e

- e- , A

l)

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

DU

NE

LHC14

(3,3) ISS

Log BR(µe → eeµe → eeµe → 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− eµ− eµ− 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−)

☞ 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

other exotic channels

◮ cLFV exotic events at the LHC

◮ Searches for heavy NNN at the LHC

q q′ → τ µ+ 2 jetsq q′ → τ µ+ 2 jetsq 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 νN → H νN → H ν sizeable deviations from SM mono-Higgs

◮ Sensitive probe of νs at high-energies! [Antusch et al, ’15]

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 ννν mass generation mechanism at work!

◮ Numerous observables of different origin, infer pattern, correlation if unique LFV source✞

✝

☎

✆Common tool: Interplay between high and low-energy observables

Rich phenomenology from neutrino mass generation

models