lpt-orsay clfv and neutrino mass models lpt · 2019-06-19 · still undetermined oscillation data:...
TRANSCRIPT
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
❍
✵�✁ ✵�✁✂ ✵�✄ ✵�✄✂ ✵�☎
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 = 0.58sin2 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