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

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10-12

10-10

10-8

10-6

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Year

90%CLlimit�sensitivity

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[Marciano et al; Hoecker; Valle and Romao]