Lepton flavour violation: a phenomenological overview Ana M. - PowerPoint PPT Presentation

Lepton flavour violation: a phenomenological overview Ana M. Teixeira Laboratoire de Physique Corpusculaire, LPC Clermont “What is ν ν ν ?” INVISIBLES 2012 GGI, Firenze, 26 June 2012

Lepton Flavour Violation: LFV@2012 ⋆ ⋆ ⋆ What we do know about Lepton Flavour Violation [experiment] ν α � ν β ◮ Neutral leptons � neutrino oscillations ν α � ν β ν α � ν β θ @ , θ 13 θ 13 θ 13 [ ∆ m 2 3 mixing angles ( U PMNS U PMNS ) - solar, atmospheric, reactor θ ⊙ θ ⊙ θ ⊙ , θ @ θ @ i ] U PMNS ◮ Charged leptons � so far, only upper bounds ... on “possible” observables! LFV process Present bound Future sensitivity LFV process Present bound Future sensitivity 2 . 4 × 10 − 12 10 − 13 BR( µ → eγ ) 4 . 3 × 10 − 12 O (10 − 16( − 18) ) CR( µ − e , Ti) 3 . 3 × 10 − 8 10 − 9 BR( τ → eγ ) 7 × 10 − 13 CR( µ − e , Au) 4 . 4 × 10 − 8 10 − 9 BR( τ → µγ ) O (10 − 16 ) CR( µ − e , Al) 1 . 0 × 10 − 12 O (10 − 16 ) BR( µ → 3 e ) BR( ¯ K 0 4 . 7 × 10 − 12 L → µe ) 2 . 7 × 10 − 8 2 × 10 − 10 BR( τ → 3 e ) BR( B + → K + τµ ) 7 . 7 × 10 − 5 2 . 1 × 10 − 8 8 × 10 − 10 BR( τ → 3 µ ) ... and many others! BR( τ → ℓP ) (2 − 5) × 10 − 3 But a huge experimental commitment! (Y. Kuno’s review) ◮ ◮ ◮ Will cLFV be observed soon? How to accommodate such a signal? Which origin?

A first look at flavours in the SM W ± ¯ ◮ Quark sector: flavour violated by charged current interactions V CKM q i q j ij Observed in many oscillation/decay processes: very good agreement with SM! Little room for “beyond SM” contributions (eg B s → µµ ) SM QFV: Th vs Exp ⇒ strong constraints on “beyond SM” dynamics!

A first look at flavours in the SM W ± ¯ ◮ Quark sector: flavour violated by charged current interactions V CKM q i q j ij Observed in many oscillation/decay processes: very good agreement with SM! ◮ Lepton sector: neutral & charged lepton flavours strictly conserved ⇒ ν α � ν β ⇒ ⇒ Extend the SM to accommodate ν α � ν β ν α � ν β [ SM m ν m ν = “ad-hoc” m ν , U PMNS ] m ν ℓ i ℓ i ℓ i W ± W ± W ± m ν � = 0 m ν � = 0 m ν � = 0 • ∝ U PMNS U PMNS U PMNS • Charged currents violate lepton flavour! αi αi αi ν α = P ν α = P ν α = P i U αi ν i i U αi ν i i U αi ν i ν α ν α ν α γ W − 2 ˛ ˛ m 2 P U ∗ ˛ ˛ νi 10 − 54 ∼ 10 − 54 10 − 54 BR ( µ → eγ ) BR ( µ → eγ ) BR ( µ → eγ ) ∝ µi U ei ˛ ˛ ℓ j ℓ i M 2 SM m ν m ν - cLFV viable?? ˛ ˛ m ν W ˛ ˛ U ∗ ν L U ik jk Viable - yes... but not observable!! ◮ “Observable” cLFV ⇒ New Physics in the lepton sector - beyond SM m ν m ν m ν

A few thoughts on lepton flavour violation ⋆ Huge experimental effort: MEG, PRISM/PRIME, SuperB, JPARC, ... What is required of a SM extension to have “observable” cLFV? γ l j l i ( µ → eγ ) = 10 − 12 × (2 TeV / Λ Λ) 4 × ( θ µe θ µe / 0 . 01) 2 New � BR ( µ → eγ ) ( µ → eγ ) Λ θ µe Physics New Physics (beyond SM m ν + Lepton Flavour Mixing m ν ) m ν ◮ cLFV ⇔ ⇔ ⇔ Λ θ ℓ i ℓ j Λ Λ ∼ O ( TeV ) non-negligible θ ℓ i ℓ j θ ℓ i ℓ j (testable at colliders ?) (suggested by neutrino mixing ...) ◮ Many reasons support considering BSM O O O (TeV) scenarios of New Physics Hierarchy - Higgs FT problem; dark matter candidate; neutrino mass generation (?); ... ◮ Smallness of m ν m ν m ν (and nature - Majorana!? ) � � � new mechanism of mass generation ◮ Is Nature hidding clues of BSM in cLFV processes? How to unravel them?

cLFV beyond the SM - road map ◮ Assume existence of New Physics (couplings, dynamics, states) and ◮ Evaluate impact of New Physics for all possible signatures: “SM” collider signals, cascade decays, EW precision tests, CP violation, anomalous moments ( � E , � B ), qFV, LFV, unitarity, dark matter... at high-energies, high-intensities and astro/cosmo frontier ℓ i → ℓ j γ ℓ i → 3 ℓ j ◮ All cLFV observables: ℓ i → ℓ j γ ℓ i → ℓ j γ , ℓ i → 3 ℓ j ℓ i → 3 ℓ j (and angular distributions, T-, P-odd asymmetries) , µ − e, N µ − e, N µ − e, N (different nuclei) ..., meson decays , ... ◮ Synergy of observables - peculiar patterns, dominances - id/exclude candidates... 8 Effective approach < ◮ Approaches: Model dependent :

◮ Effective Approach ◮ ◮

cLFV: the effective approach ◮ At higher scales (TeV? M GUT ? M Planck ?) additional “heavy” degrees of freedom ◮ Integrate out “new heavy fields” (e.g. as possibly required to generate ν masses) ◮ Effective Lagrangian: “vestigial” (new) interactions with SM fields at low-energies L eff = L SM + L eff = L SM + L eff = L SM + higher order (non-renormalisable) terms 1 ∆ L d ≥ 5 ∼ P ∆ L d ≥ 5 ∼ P ∆ L d ≥ 5 ∼ P 1 1 Λ n − 4 C n ( g, Y, ... ) O n ( ℓ, q, H, γ, ... ) C n ( g, Y, ... ) O n ( ℓ, q, H, γ, ... ) C n ( g, Y, ... ) O n ( ℓ, q, H, γ, ... ) Λ n − 4 Λ n − 4 n ≥ 5 n ≥ 5 n ≥ 5 Λ : Λ : Λ : mass scale of new physics C n : C n : C n : dimensionless couplings - gauge couplings, Yukawas, loop factors ( (4 π ) m ) , ... C n ⇒ C n C n ⇒ ⇒ ij : ij : ij : matrices in flavour space! O n : O n : O n : “external legs” of the diagrams - SM fields only!

cLFV: the effective approach H H H H H H e R e R e R 1 1 ∆ L d ≥ 5 = Weinberg 1 1 1 1 ∆ L d ≥ 5 ∆ L d ≥ 5 C 5 C 5 C 5 + C 6 C 6 C 6 e L e L e L Λ × Λ 2 × + ... µeee Λ 2 Weinberg µeee µeee Λ 2 Weinberg Λ Λ µ R µ R µ R e L e L e L ν j ν i ν j ν j ν i ν i L L L L L L ∆ L 5 (Weinberg): neutrino masses ( ∆ L = 2 ) ◮ Dimension 5 ∆ L 5 ∆ L 5 Common to all models with Majorana neutrinos [seesaws, radiative (Zee, RpV), ...] ◮ Dimension 6 ∆ L 6 : ∆ L 6 : ∆ L 6 : kinetic corrections, cLFV (dipole and 3-body) , EW precision, t physics... Differs from model to model - used to disentangle scenarios... ∆ L 7 , 8 ,.. : ◮ Higher order ∆ L 7 , 8 ,.. : ∆ L 7 , 8 ,.. : ν (transitional) magnetic moments, NSI, ...

cLFV bounds and L eff 1 ij 1 1 C 6 16 π 2 C 6 1 1 1 C 6 ◮ Apply experimental bounds on cLFV observables to constrain ∼ ij Λ 2 16 π 2 16 π 2 ij Λ 2 Λ 2 1. hypothesis on size of “new couplings” 2. hypothesis on scale of “new physics” and/or ◮ Natural values of the couplings C 6 C 6 C 6 ij ∼ O (1) ij ∼ O (1) ij ∼ O (1) BR( µ → eγ ) | MEG ⇒ Λ Λ Λ � 50 TeV; BR( µ → 3 e ) ⇒ Λ Λ Λ � 15 TeV Λ Λ BR( τ → ℓγ ) ⇒ Λ Λ � 3 TeV; BR( τ → 3 ℓ ) ⇒ Λ Λ � 1 TeV [from La Thuile ’12] ◮ Natural scale? more delicate - well motivated: direct discovery, ... Example: discovery of type II seesaw (scalar triplet) mediator at LHC, M ∆ ∼ 1 M ∆ ∼ 1 M ∆ ∼ 1 TeV 2 × 10 − 3 BR( µ → eγ ) | MEG ⇒ | Y ∆ † µµ Y ∆ µe + Y ∆ † τµ Y ∆ τe | � 2 × 10 − 3 2 × 10 − 3 [from 0707.4058] ◮ Can we reconstruct the New Physics Lagrangian? not likely... We can identify operators (combining distinct observables) and learn about flavour structure (same observable, different flavours)

cLFV bounds and L eff ij 1 1 1 16 π 2 C 6 1 C 6 C 6 1 1 ◮ Apply experimental bounds on cLFV observables to constrain ∼ Λ 2 16 π 2 ij ij Λ 2 Λ 2 16 π 2 1. hypothesis on size of “new couplings” 2. hypothesis on scale of “new physics” and/or ◮ Natural values of the couplings C 6 C 6 C 6 ij ∼ O (1) ij ∼ O (1) ij ∼ O (1) BR( µ → eγ ) | MEG ⇒ Λ Λ Λ � 50 TeV; BR( µ → 3 e ) ⇒ Λ Λ Λ � 15 TeV BR( τ → ℓγ ) ⇒ Λ Λ Λ � 3 TeV; BR( τ → 3 ℓ ) ⇒ Λ Λ Λ � 1 TeV [from La Thuile ’12] ◮ Natural scale? more delicate - well motivated: direct discovery, ... Example: discovery of type II seesaw (scalar triplet) mediator at LHC, M ∆ ∼ 1 M ∆ ∼ 1 M ∆ ∼ 1 TeV BR( µ → eγ ) | MEG ⇒ | Y ∆ † µµ Y ∆ µe + Y ∆ † τµ Y ∆ τe | � 2 × 10 − 3 2 × 10 − 3 2 × 10 − 3 [from 0707.4058] ◮ Can we reconstruct the New Physics Lagrangian? not likely... ◮ Be prepared! - master “theoretical expectations” of model M376XV to falsify it!

Models of New Physics But “theoretical expectations” is an oxymoron: different theorists expect different New Physics at the TeV scale because it is - motivated by the naturalness of the weak scale - motivated by precision unification of couplings - not motivated, but why not - to their personal taste or prejudice! [cf. J¨ ager, NA62 Workshop, ’09] ◮ Here: consider examples of (well motivated?) models � � � with potentially observable cLFV implications! among many, many possibilities

◮ Models of New Physics and cLFV ◮ ◮

cLFV: models of New Physics ◮ New physics at TeV: Higgs fine-tuning - hierarchy problem Dark matter candidates Within experimental reach! ◮ SM extensions introduce new particles , new flavour violating couplings.. ◮ Recall: contributions to quark FV strongly constrained (dominated by SM) No “SM background” for cLFV contributions! Generic cLFV extensions - general MSSM, Little Higgs, Xdim, 4th generation, ... 8 ◮ Examples: SM seesaw (TeV scale) - e.g. type II < cLFV from m ν m ν m ν Extended frameworks - SUSY seesaw, GUTs, ... : ◮ Find cLFV-footprints to probe the nature of the model!