Theoretical aspects of charged Lepton Flavour Violation
a brief overview
Ana M. Teixeira
Laboratoire de Physique Corpusculaire, LPC - Clermont
Neutrino 2016
London, 6 July 2016τττ
µµµeee
Beyond the Standard Model
◮ Neutrino oscillations provided the 1st laboratory evidence of New Physics
⇒⇒⇒ SM must be clearly extended (or embedded in a larger framework)!
Several possible models successfully account for ννν data
such extensions might even allow to address SM caveats
hints to the flavour puzzle ? BAU via leptogenesis ? DM candidates ?
[ presentations by A. De Gouvea, F. Feruglio, C. Hagedorn and P. Di Bari ]
◮ Gateway to new experimental signals (deviation from SM) in the lepton sector:
Lepton Number Violation (if Majorana) - 0ν2β0ν2β0ν2β, meson decays, colliders, ...
[ presentation by F. Deppisch ]
Lepton flavour universality violation - weak boson and meson decays.. (e.g. RKRKRK)
Electric dipole moments and Anomalous magnetic moments
Violation of lepton flavour - in charged sector as well?
LFV observables as a sign of New Physics
◮ Lepton sector: Charged currents also violate lepton flavour! UPMNS W± ℓ ν
◮ Extend the SM to accommodate να ! νβνα ! νβνα ! νβ
Assume most minimal extension SMmνmνmν
W±W±W±
•
ℓiℓiℓi
νανανα
• ∝ UPMNSαiUPMNSαiUPMNSαi
mν 6= 0mν 6= 0mν 6= 0
να =∑
i Uαiνβνα =∑
i Uαiνβνα =∑
i Uαiνβ
[SMmνmνmν= “ad-hoc” mν , UPMNS]
SMmνmνmν - cLFV possible??
W−
γ
ℓi ℓj
νLUik U∗
jk
BR(µ → eγ)BR(µ → eγ)BR(µ → eγ) ∝
∣
∣
∣
∣
∑
U∗µiUei
m2νi
M2W
∣
∣
∣
∣
2
∼ 10−5410−5410−54
[Petcov, ’77]
Possible - yes... but not observable!!
◮ “Observable” cLFV ⇒ New Physics in the lepton sector - beyond SMmνmνmν
Are neutral and charged LFV related?
Does cLFV arise from ν-mass mechanism? Or entirely different nature?
◮◮◮ Lepton flavour violation: from observables to NP models
Signals of Lepton Flavour Violation
◮ Neutrino oscillations [ννν-dedicated experiments]
◮ Rare leptonic decays and transitions [high-intensity facilities]
ℓi → ℓjγℓi → ℓjγℓi → ℓjγ, ℓi → 3ℓjℓi → 3ℓjℓi → 3ℓj , mesonic τττ decays...
e
γ
µ
NP
nucleus assisted µ− eµ− eµ− e transitions, Muonium channels...
◮ Meson decays: violation of lepton flavour universality (e.g. RKRKRK)
lepton Number violating decays - B → Dµ−µ−B → Dµ−µ−B → Dµ−µ−, ...
lepton flavour violating decays - B → τµB → τµB → τµ, ... [high-intensity; LHCb]
◮ Rare (new) heavy particle decays (typically model-dependent) [colliders]
SM boson decays: H → τµH → τµH → τµ, Z → ℓiℓjZ → ℓiℓjZ → ℓiℓj
SUSY ℓi → ℓjχ0ℓi → ℓjχ0ℓi → ℓjχ0; FV KK-excitation decays; ...
LFV final states: for example, e±e− → e±µ− + Emisse±e− → e±µ− + Emisse±e− → e±µ− + Emiss
◮ And many others ... all absent in the SM!
Searches for cLFV: where do we stand?
Observable Bound (90% C.L.) future sensitivity
BR(µ → eγµ → eγµ → eγ) 4.2 × 10−13
4.2 × 10−13
4.2 × 10−13
4 × 10−14
4 × 10−14
4 × 10−14 [ MEG II ]
BR(µ → 3eµ → 3eµ → 3e) 1.0 × 10−12
1.0 × 10−12
1.0 × 10−12
10−15
10−15
10−15 [ Mu3e Phase I ]
BR(µ − eµ − eµ − e,N) 7 × 10−13
7 × 10−13
7 × 10−13 (Au)
10−14
10−14
10−14 [ SiC, DeeMe ]
10−17
10−17
10−17 [ Al, Mu2e/COMET ]
BR(µ−e− → e−e−µ−e− → e−e−µ−e− → e−e−) — 10−17
10−17
10−17 [ Al, COMET ? ]
P(Mu − MuMu − MuMu − Mu) 8.3 × 10−11
8.3 × 10−11
8.3 × 10−11
10−14
10−14
10−14 [FNAL ? ]
e
γ
µ
NP
e
µ
NP
q
q0
NP
e�
e�
µ�
e�
e+
e�
µ�
µ+
NP
γ - eγ - µ0 π - e0 π - µη - eη - µ'η - e'η - µ
0 S K- e
0 S K- µ
0 f- e0 f- µ0ρ - e
0ρ - µ K
*- e K
*- µK
* - eK
* - µ
φ - eφ - µω - eω - µ
- e+
e- e-
e+ e- µ
- µ + µ - e- µ + µ - µ-
e+ µ - e- µ +
e- µ- π
+ π - e- π + π - µ-
K+ π - e
- K+ π - µ
- π + K- e
- π + K- µ
- K+
K- e-
K+ K- µ
0 S K
0 S K- e
0 S K
0 S K- µ
- π + e- π
- π + µ - π-
K+ e- π
- K+ µ - π
- K+
e-K
- K+ µ -
KΛ - πΛ - πΛ -
KΛ -
K+ µ - µ p- µ - µ
p
dec
ays
τ90
% C
.L. u
pper
lim
its fo
r LF
V
-810
-710
-610
-510
γl 0lP 0lS 0lV lll lhh BNV
CLEOBaBarBelleLHCb
HFAG-TauSummer 2014
Further bounds: BR(Z → ℓiℓjZ → ℓiℓjZ → ℓiℓj), ..., BR(K,D,B → (h) ℓiℓjK,D,B → (h) ℓiℓjK,D,B → (h) ℓiℓj), ... [ presentation by W. Ootani ]
Interpreting experimental data (bounds & measurements)
◮ What is required of a SM extension to have “observable” cLFV?li lj
γ
New
Physics
Pheno approaches:
Effective approach (model-independent)
Model dependent (specific NP scenario)
◮ From an “effective approach”, NP can lead to “observable cLFV”, introducing:
(i) new sources of flavour violation ⇒ new effective couplings
(ii) new Lorentz structure other than “standard” interactions ⇒ new operators
◮ Preferred NP model? most lead to extensive ranges for cLFV observables...
More than a NP signal, cLFV can be a powerful probe to test NP realisations:
1. Probe NP scales beyond collider reach
2. Hint on fundamental properties and/or parameters of the model
3. Allow to disentangle between candidate NP models
4. Ultimately lead to disfavouring (exclusion) of a BSM candidate
◮◮◮ cLFV: effective approach
cLFV: the effective approach
◮ Leff
Leff
Leff - “vestigial” (new) interactions of “heavy” fields with SM at low-energies
Leff = L
SM +∑
n≥5L
eff = LSM +
∑
n≥5Leff = L
SM +∑
n≥51
Λn−41
Λn−41
Λn−4 Cn(g, Y, ...) On(ℓ, q,H, γ, ...)Cn(g, Y, ...) On(ℓ, q,H, γ, ...)Cn(g, Y, ...) On(ℓ, q,H, γ, ...)
◮ Dimension 5 - ∆L5∆L5∆L5 (Weinberg): neutrino masses (LNVLNVLNV, ∆L = 2)
a unique operator O5ijO5ijO5ij ∼ (Li H)(H Lj)∼ (Li H)(H Lj)∼ (Li H)(H Lj)
◮ Dimension 6 - ∆L6 :∆L6 :∆L6 : kinetic corrections, cLFV (dipole and 3-body), EWP tests, t physics...
3 “types” of operators relevant for cLFV
Dipole: O6ℓiℓjγ
O6ℓiℓjγ
O6ℓiℓjγ
∼ LiσµνejHFµν∼ LiσµνejHFµν∼ LiσµνejHFµν radiative decays ℓi → ℓjγℓi → ℓjγℓi → ℓjγ
4 fermion: O6ℓiℓjℓkℓl
O6ℓiℓjℓkℓl
O6ℓiℓjℓkℓl
∼ (ℓiγµPL,Rℓj)(ℓkγµPL,Rℓl)∼ (ℓiγµPL,Rℓj)(ℓkγµPL,Rℓl)∼ (ℓiγµPL,Rℓj)(ℓkγµPL,Rℓl) 3-body decays ℓi → ℓjℓkℓlℓi → ℓjℓkℓlℓi → ℓjℓkℓl, ...
O6ℓiℓjqkql
O6ℓiℓjqkql
O6ℓiℓjqkql
∼ (ℓiγµPL,Rℓj)(qkγµPL,Rql)∼ (ℓiγµPL,Rℓj)(qkγµPL,Rql)∼ (ℓiγµPL,Rℓj)(qkγµPL,Rql) µ− eµ− eµ− e in Nuclei, meson decays, ...
Vector/scalar: O6HHℓiℓj
O6HHℓiℓj
O6HHℓiℓj
∼ (H†i↔
DµH)(ℓiγµℓj)∼ (H†i↔
DµH)(ℓiγµℓj)∼ (H†i↔
DµH)(ℓiγµℓj) 3-body decays ℓi → ℓjℓkℓlℓi → ℓjℓkℓlℓi → ℓjℓkℓl, ...
cLFV bounds and Leff
◮ Apply experimental bounds on cLFV observables to constrainC6
ijC6
ijC6
ij
Λ2
Hypotheses on:
1. size of “new couplings”
⇒⇒⇒ Natural couplings
C6ij ∼ O(1)C6ij ∼ O(1)C6ij ∼ O(1)
2. scale of “new physics”
⇒⇒⇒ Natural scale - delicate..
direct discovery Λ ∼Λ ∼Λ ∼ TeV
Effective coupling
(example)
Bounds on ΛΛΛ (TeV)
(for |C6ij | = 1)
Bounds on |C6ij ||C6ij ||C6ij |
(for Λ = 1 TeV)Observable
Cµeeγ 6.3 × 10
42.5 × 10
−10 µ → eγ
Cτeeγ 6.5 × 10
22.4 × 10
−6 τ → eγ
Cτµeγ 6.1 × 10
22.7 × 10
−6 τ → µγ
Cµeee
ℓℓ,ee207 2.3 × 10
−5 µ → 3e
Ceτeeℓℓ,ee 10.4 9.2 × 10
−5 τ → 3e
Cµτµµ
ℓℓ,ee11.3 7.8 × 10
−5 τ → 3µ
Cµe
(1,3)Hℓ, Cµe
He160 4 × 10
−5 µ → 3e
Cτe(1,3)Hℓ, C
τeHe ≈ 8 1.5 × 10
−2 τ → 3e
Cτµ
(1,3)Hℓ, Cτµ
He≈ 9 ≈ 10
−2 τ → 3µ
[Feruglio et al, 2015]
◮ Despite its generality, caution in interpreting limits from effective approach!
- limits assume dominance of one operator; NP leads to several (interference...)
- contributions from higher order operators may be non-negligible if ΛΛΛ is low...
- multiple “new physics” scales: Leff = LSM+1
ΛLNVΛLNVΛLNVC5(mν)+
1Λ2LFV
Λ2LFVΛ2LFV
C6(ℓi ↔ ℓj) + ...
◮◮◮ New Physics models: cLFV
◮ cLFV can be a powerful probe to test NP realisations:
1. Probe NP scales beyond collider reach
2. Hint on fundamental properties and/or parameters of the model
3. Allow to disentangle between candidate NP models
4. Ultimately lead to disfavouring (exclusion) of a BSM candidate
◮ Only a few illustrative examples! Extensive contributions in literature...
Models of New Physics and cLFV: some examples
◮ Generic cLFV extensions of the SM - supersymmetric (SUSY) extensions of the SM
cLFV observables at low- and high-energies (interplay) to constrain LSUSYsoft
correlation of cLFV observables ⇒ hint on the nature (dipole vs scalar) of NP operator
◮ “Geometric” cLFV - extra dimensional Randall-Sundrum models
e− µ bounds constrain NP scale beyond LHC reach: TKK & 4 TeV ( KK(1st) & 10 TeV)
future sensitivities: exclude (general) anarchic RS models up to 8 TeV ( mKK-g & 20 TeV)
[Beneke et al, 1508.01705]
◮ cLFV and compositness - Little(st) Higgs
distinctive patterns for ratios of observables (testability!)
[Blanke et al, ’09]
- Holographic composite Higgs
BR(µ → eγ) - constrain the size of boundary kinetic terms
⇒ relevant information on fundamental parameters from cLFV!
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-1.0 -0.5 0.0 0.5 1.0∆z`10-16
10-15
10-14
10-13
10-12
10-11
BRHΜ®e ΓL
[Hagedorn and Serone, ’11-’12]
Models of New Physics and cLFV: some examples
◮ Simple SM extensions and cLFV - Multi-Higgs doublet, Leptoquarks, additional Z′Z′Z′, ...
◮ Additional symmetries and cLFV - Flavour symmetries
reduce arbitrariness, strengthen predictivity (testability!)
- Left-Right symmetric models
distinctive correlations of observables (testability!)
cLFV & LNV: strong interplay at low-energy and colliders
dilepton cLFV signatures pp → WR → e±µ∓,± + 2pp → WR → e±µ∓,± + 2pp → WR → e±µ∓,± + 2 jets
[Das et al, 1206.0256]
1 2 3 4 50
1
2
3
mWR!TeV"
mN!TeV"
5Σ 90"
10
102
103
Br#Μ$eΓ$&2.4'10(12
RAu#Μ$e$&8'10(13
Br#Μ$eee$&10(12
Br#Μ$eΓ$)10(13
RAl#Μ$e$)10(16
FIG. 12: Dependence of the rates of low energy
- Extended gauge groups and GUTs
augmented predictivity (falsifying probes)
many naturally incorporate ν-mass generation (seesaw)
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-14 10-13 10-12 10-11 10-10
BR(µ → e γ )
MEG expected
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-14 10-13 10-12 10-11 10-10
BR(µ → e γ )
MEG expected
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-14 10-13 10-12 10-11 10-10
BR(µ → e γ )
MEG expected
BR(τ → µ γ )
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-14 10-13 10-12 10-11 10-10
BR(µ → e γ )
MEG expected
BR(τ → µ γ )BR(µ → e e e )
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-14 10-13 10-12 10-11 10-10
BR(µ → e γ )
MEG expected
BR(τ → µ γ )BR(µ → e e e )
CR(µ → e in Ti )
SUSY SO(10) type II [Calibbi et al, ’09]
◮◮◮ cLFV and mechanisms of ννν mass generation
cLFV: low scale seesaws and beyond
“Standard” fermionic seesaws: Y ν∼ O(1)Y ν∼ O(1)Y ν∼ O(1) ⇒ Mnew ≈ 1013−15
⇒ Mnew ≈ 1013−15⇒ Mnew ≈ 1013−15 GeV!
Suppression of LFV rates due to the large mass of the mediators!
Low scale seesaws
Seesaw & new mediators
rich phenomenology (also at LHC), observable cLFV!
[ presentation by M. Patel ]
Well motivated frameworks (some examples):
⇒⇒⇒ Low-scale Type I Seesaw [and its many variants...]
Ltype I = −Y ℓ LL H eR − Y ν νR H νL −12νR MN νc
RLtype I = −Y ℓ LL H eR − Y ν νR H νL −12νR MN νc
RLtype I = −Y ℓ LL H eR − Y ν νR H νL −12νR MN νc
R ⇒⇒⇒mν ∼v2 Y 2
ν
MNmν ∼
v2 Y 2ν
MNmν ∼
v2 Y 2ν
MN
⇒⇒⇒ Inverse Seesaw realisations
LISS = −Y ν νR H L−MR νR X −12µX Xc X + 1
2µR νR νc
RLISS = −Y ν νR H L−MR νR X −12µX Xc X + 1
2µR νR νc
RLISS = −Y ν νR H L−MR νR X −12µX Xc X + 1
2µR νR νc
R ⇒⇒⇒mν ∼v2 Y 2
ν
MR
µX
MRmν ∼
v2 Y 2ν
MR
µX
MRmν ∼
v2 Y 2ν
MR
µX
MR
⇒⇒⇒ SUSY seesaws (type I, II, sISS), ..., R-parity violating SUSY, ...
cLFV: low scale type I seesaw
◮ Addition of 3 “heavy” Majorana RH neutrinos to SM; MeV . mNi . 10fewTeVMeV . mNi . 10fewTeVMeV . mNi . 10fewTeV
◮ Spectrum and mixings: UUUTM
6×6ν UUU = diag(mi) mνmνmν ≈ −v2Y T
ν M−1N Yν≈ −v2Y T
ν M−1N Yν≈ −v2Y T
ν M−1N Yν
UUU =
(
UννUννUνν UνNUνNUνN
UNν UNN
)
UννUννUνν ≈ (1− ε)UPMNSUPMNSUPMNS Non-unitary leptonic mixing UPMNSUPMNSUPMNS!
◮ Heavy states do not decouple ⇒ modified neutral and charged leptonic currents
◮ Rich phenomenology at high-intensity and searches at colliders - probe seesaw hypothesis
(see also Dinh et al, ’12-’14)
[Alonso et al, 1209.2679]
cLFV: Inverse Seesaw (ISS) realisations
◮ Addition of 3 “heavy” RH neutrinos and 3 extra “sterile” fermions XXX to SM ISS(3,3) ISS(3,3) ISS(3,3)
M9×9ISSM9×9ISSM9×9ISS =
0 YνvYνvYνv 0
Y Tν vY Tν vY Tν v 0 MRMRMR
0 MRMRMR µXµXµX
⇒
3 light ννν : mν ≈(Yνv)2
M2R
mν ≈(Yνv)2
M2R
mν ≈(Yνv)2
M2R
µXµXµX
3 pseudo-Dirac pairs : mN±mN±mN± ≈MR ± µXMR ± µXMR ± µX
Theoretically appealing: “naturally” small LNV parameter µXµXµX ∼ O(0.01 eV− MeV)∼ O(0.01 eV− MeV)∼ O(0.01 eV− MeV)
◮ New (virtual) states & modified couplings: cLFV, non-universality, signals at colliders!
◮ cLFV in muonic atoms: µ−e− → e−e−µ−e− → e−e−µ−e− → e−e− (���) vs µ− eµ− eµ− e conversion (���) in Aluminium
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
log BR(µe → eeµe → eeµe → ee)
excluded
COMET
[Abada, De Romeri, AMT, ’15]
cLFV: Inverse Seesaw (ISS) realisations
◮ cLFV ZZZ decays at FCC-ee vs 3 body decays ℓi → 3ℓjℓi → 3ℓjℓi → 3ℓj (sizeable MR & ΛEWMR & ΛEWMR & ΛEW)
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)
◮ 3-body: dominated by ZZZ penguin contributions[Abada et al, ’15]
LC
FCC-ee excludedµ
µ
W �
Z
τ µνi
ℓ1
ℓ2
W
νj
νiZ
◮ Allows to probe µ− τµ− τµ− τ cLFV beyond SuperB reach
◮ 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]
SUSY (type I) seesaw: cLFV at low- and high energies
◮ Large Y νY νY ν : sizable contributions to cLFV observables
cLFV driven by the exchange of virtual SUSY particles
l (ν)
γ
ℓi ℓj
χ0 (χ±)
MEG 2013 BR
(µ →
e γ
)
CR
(µ-e
, T
i)
∆ml~ / ml~ (e~
L, µ~L)
10-18
10-17
10-16
10-15
10-14
10-13
10-12
10-5
10-4
10-3
10-2
10-1
10-20
10-19
10-18
10-17
10-16
10-15
MR (GeV)
��� [1014, 1015]
��� [1013, 1014]
��� [1012, 1013]
[Antusch, Arganda, Herrero, AMT, ’06 - ’07] [Figueiredo and AMT, ’13]
◮ Y νY νY ν unique source of LFV: synergy of high- and low-energy observables
◮ Isolated cLFV manifestations ⇒⇒⇒ disfavours SUSY seesaw hypothesis
◮ “Correlated” cLFV observations ⇒⇒⇒ strengthen SUSY seesaw hypothesis !∆m
ℓm
ℓ
(eL, µ
L)
∆mℓ
mℓ
(eL, µ
L)
∆mℓ
mℓ
(eL, µ
L) & O(0.5%) and µ → eγ|MEGµ → eγ|MEGµ → eγ|MEG ✔ !! Hints on the seesaw scale: MR ∼ 1014MR ∼ 1014MR ∼ 1014 GeV
◮◮◮ Concluding remarks
Charged lepton flavour violation: outlook
◮◮◮ Flavour violation observed in quarks & neutral leptons...
why should Nature “conserve” charged lepton flavour?
◮◮◮ Lepton flavour violation and New Physics
cLFV observables can provide (indirect) information on the underlying NP model
⇒⇒⇒ Probe scales beyond collider reach, falsify NP candidates,
hint on fundamental parameters and/or new scales, ...
◮◮◮ Models of ννν-mass generation: well-motivated frameworks for cLFV
⇒⇒⇒ Several realisations lead to very rich phenomenology
cLFV and direct searches could substantiate the seesaw hypothesis !...
Charged lepton flavour violation: outlook
◮◮◮ In the lepton sector ννν oscillations provided 1st laboratory evidence of New Physics
New Physics can be manifest via cLFV even before any direct discovery!
Numerous observables currently being searched for!
⇒⇒⇒ very intensive worldwide experimental programme
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1940 1960 1980 2000 2020
10-18
10-16
10-14
10-12
10-10
10-8
10-6
10-4
10-2
Year
90%CLlimit�sensitivity
ô Τ®3Μì Τ®ΜΓ
ò ΜN®eNæ Μ®3eà Μ®eΓ
MEGSINDRUM SINDRUM-II
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çProject X?
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[Marciano et al; Hoecker; Valle and Romao]