Lepton flavour violation: a phenomenological overview. Ana M. Teixeira

Transcription

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

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

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

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

5 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 i New Physics l j BR(µ eγ) = (2 TeV/Λ) 4 (θ θ µe /0.01) 2 clfv New Physics (beyond SM mν m ν ) + Lepton Flavour Mixing Λ O(TeV) non-negligible θ li l j (testable at colliders?) (suggested by neutrino mixing...) Many reasons support considering BSM O(TeV) scenarios of New Physics Hierarchy - Higgs FT problem; dark matter candidate; neutrino mass generation (?);... Smallness of m ν (and nature - Majorana!?) new mechanism of mass generation Is Nature hidding clues of BSM in clfv processes? How to unravel them?

6 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 All clfv observables: l i l j γ, l i 3l j (and angular distributions, T-, P-odd asymmetries), µ e, N (different nuclei)..., meson decays,... Synergy of observables - peculiar patterns, dominances - id/exclude candidates... Approaches: 8 < : Effective approach Model dependent

7 Effective Approach

8 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 + higher order (non-renormalisable) terms L d 5 P n 5 1 Λ n 4 C n (g, Y,...) O n (l, q, H, γ,...) Λ n 4 Λ : mass scale of new physics C n : dimensionless couplings - gauge couplings, Yukawas, loop factors ((4π) m ),... O n : external legs of the diagrams - SM fields only! C ij n : matrices in flavour space!

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

10 clfv bounds and L eff Apply experimental bounds on clfv observables to constrain C 16π 2 ij 6 Λ 2 1. hypothesis on size of new couplings and/or 2. hypothesis on scale of new physics Natural values of the couplings C ij 6 O(1) BR(µ eγ) MEG Λ 50 TeV; BR(µ 3e) Λ 15 TeV BR(τ lγ) Λ 3 TeV; BR(τ 3l) 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 TeV BR(µ eγ) MEG Yµµ Yµe + Yτµ Yτe [from ] 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)

11 clfv bounds and L eff Apply experimental bounds on clfv observables to constrain C 16π 2 ij 6 Λ 2 1. hypothesis on size of new couplings and/or 2. hypothesis on scale of new physics Natural values of the couplings C ij 6 O(1) BR(µ eγ) MEG Λ 50 TeV; BR(µ 3e) Λ 15 TeV BR(τ lγ) Λ 3 TeV; BR(τ 3l) 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 TeV BR(µ eγ) MEG Yµµ Yµe + Yτµ Yτe [from ] Can we reconstruct the New Physics Lagrangian? not likely... Be prepared! - master theoretical expectations of model M376XV to falsify it!

12 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. Jäger, NA62 Workshop, 09] Here: consider examples of (well motivated?) models with potentially observable clfv implications! among many, many possibilities

13 Models of New Physics and clfv

14 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! Examples: Generic clfv extensions - general MSSM, Little Higgs, Xdim, 4th generation,... 8 < SM seesaw (TeV scale) - e.g. type II clfv from m ν : Extended frameworks - SUSY seesaw, GUTs,... Find clfv-footprints to probe the nature of the model!

15 clfv-footprints: unveiling the NP model In the absence of clfv (and other) signals: constraints on parameter space (scale and couplings) clfv observed: compare with peculiar features of given model predictions for low-energy clfv observables (& CPV, (g 2) µ,...) intrinsic patterns of correlations of observables possible high-energy (collider) clfv observables; further correlations! If present, explore links to ν data and dark matter One keyword: synergy of observables!

16 clfv-footprints: unveiling the NP model In the absence of clfv (and other) signals: constraints on parameter space (scale and couplings) clfv observed: compare with peculiar features of given model predictions for low-energy clfv observables (& CPV, (g 2) µ,...) intrinsic patterns of correlations of observables possible high-energy (collider) clfv observables; further correlations! If present, explore links to ν data and dark matter One keyword: synergy of observables! And at the end: If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.

17 clfv-footprints: unveiling the NP model In the absence of clfv (and other) signals: constraints on parameter space (scale and couplings) clfv observed: compare with peculiar features of given model predictions for low-energy clfv observables (& CPV, (g 2) µ,...) intrinsic patterns of correlations of observables possible high-energy (collider) clfv observables; further correlations! If present, explore links to ν data and dark matter One keyword: synergy of observables! And at the end: If it exhibits the observed pattern for clfv observables, explains the issues of the SM, is in agreement with everything... it might be the correct New Physics model!

18 Generic clfv extensions

19 Example: clfv in Little Higgs models (T-parity) [LHT] Higgs is a pseudo-goldstone boson of spontaneously broken global symmetry SU(5) SO(5) (@ TeV scale); augmented gauge group [SU(2) U(1)] 2 new (heavy) gauge bosons - A H, Z H, W ± H T parity prevents contributions to EW observables (tree-level) Lightest T-odd particle stable dark matter candidate T-odd sector: 3 doublets of mirror quarks and leptons (couple to SM via new gauge bosons) Only 10 new parameters in flavour sector, only SM operators relevant Sources of clfv: couplings of leptons - mirror leptons - heavy gauge bosons W H ±, A H, Z H ν i V Hν W H ±, A H, Z H l i V Hl V Hν V Hl = U PMNS l j H, νh ν j H ν j H, lh l H j [Many people,...]

20 clfv in Little Higgs models (T-parity): an example Strong correlation of some clfv observables: µ eγ and µ 3e Negligible dipole contributions [from Blanke et al, ] Chirality structure of LHT Asymmetries for polarised τ and µ decays [ ] Typically large contributions to clfv some fine-tuning required hierarchical mixing matrices (V Hl, V Hν ), quasi degenerate states,...

21 Geometric flavour violation: RS warped extra dimensions Embed 4dim space-time into higher dim AdS space (extra dims compactified on orbifold) Two branes (UV, IR) and bulk between; M TeV = M Planck e πl x Localise fields: Higgs close to IR brane (hierarchy problem); e.g. SM fermions and gauge bosons on bulk KK excitations of SM fields close to IR brane Interactions of fields: overlap of wave functions An example - Geometrical distribution of fermions in bulk: hierarchy in 4dim Yukawas for anarchic O(1) higher dim couplings Circumvent pheno issues: enlarge bulk symmetry (prevent violation of custodial SU(2)); additional rescue ingredients to avoid excessive FCNCs, protect EW precision observables,... [... also many people!]

22 Geometric flavour violation: RS warped extra dimensions [from Agashe et al, ] Electroweak precision observables: M KK 3 TeV [models with custodial sym.] Purely geometrical description (quarks εk ) M KK 20 TeV some FT M KK 3 TeV clfv processes mediated by KK-lepton excitations, new gauge fields clfv: M KK 10 TeV (5 TeV only marginally compatible) Possible ways out... flavour structure (non-geometrical), increase gauge symmetry,...

23 General Minimal Supersymmetric extension of the SM Supersymmetry is broken in Nature: different masses for SM particles and superpartners Generic soft-susy breaking terms introduce new sources of flavour violation (q and l) non-diagonal masses for sleptons and sneutrinos (M 2 l ) ij 0! (M 2 ν) ij 0! Misalignement of flavour and physical eigenstates: R l M 2 l R l = diag(m 2 li ) R l 1! {ẽ L, µ L, τ L, ẽ R, µ R, τ R } { l 1,..., l 6 } χ 0, χ ± manifest in neutral and charged lepton-slepton interactions l i l j, ν j R l ij R γ l ( ν) (M 2 l ) ij Sizable contributions to clfv observables δ ij l = (M2 l ) M 2 SUSY l i l j almost everything is possible - depending on the regime... χ 0 ( χ ± ) e.g. BR(µ µ eγ) α 4π MW sin 2 θẽ µ m 2 l 4 M sin 2 m 2 l θẽ µ SUSY M 2 SUSY «2 [... really a lot of people - a crowd!]

24 4th generation - and beyond! Extend the SM via a fourth family of quarks and leptons (Dirac or Majorana νs) LHC excluded?? Additional mixing angles and CP phases in the lepton sector Radiative and 3-body decays: all as large as current bounds (not simultaneously) Distinctive patterns for correlations of observables in SM4 [... still many people, decreasing?] And many other models... LR symmetric, multihiggs, Leptoquarks,... [... a whole population! ]

25 Comparing predictions - finding fingerprints ν ( l) ratio LHT MSSM (dipole) MSSM (Higgs) SM4 l i χ ± ( χ 0 ) l j BR(µ e e + e ) BR(µ eγ) BR(τ e e + e ) BR(τ eγ) BR(τ µ µ + µ ) BR(τ µγ) BR(τ e µ + µ ) BR(τ eγ) BR(τ µ e + e ) BR(τ µγ) BR(τ e e + e ) BR(τ e µ + µ ) BR(τ µ µ + µ ) BR(τ µ e + e ) R(µTi eti) BR(µ eγ) [from Buras et al, ] N q γ (Z, H) γ (Z, H) ν ( l) µ e χ ± ( χ 0 ) l j (l k ) l j (l k ) q N Most models predict/accommodate extensive ranges for observables (no new physics yet discovered, only bounds on new scale!) But... Peculiar patterns to correlation of observables (model-specific) Correlations might allow to disentagle models of clfv in the absence of discovery of new states!... or inability to identify mechanism of LFV!

26 clfv from ν mass generation mechanisms - seesaw

27 clfv and the SM seesaw mechanism Seesaw mechanism: explain small ν masses with natural couplings via new dynamics at heavy scale Y X clfv BRs, etc m ν M X Seesaw C5 New Physics scales clfv- C 6 clfv obs! Fermionic singlet Y T N 1 Y N O(1) M N GeV (type I) M Y N Y 1 N N M N M GUT??? M 1 M Y N... not enough... (?) N N! αβ Fermionic triplet Y T Σ 1 (type III) M Y Σ M Σ TeV Y 1 1 Σ Σ M Y Σ... not enough... (?) Σ Scalar triplet (type II) 4Y µ M 2 Y O(1) M TeV (µ 1!) M Σ 1 M 2 Y αβ Y γδ αβ maybe large... constrain model! clfv in type II seesaw: predictive (correlations), observable clfv! clfv bounds constraints on Y and M ; µ eee: Y O(1) M 300 TeV If M TeV (smaller Y ), possible discovery at LHC [from ] Inverse seesaw : similar decorrelation between m ν suppression and clfv - large BRs (?)... and many other variations! [... a very sizable community! ]

28 clfv from m ν in extended frameworks

29 The supersymmetric seesaw(s) and clfv Embed seesaw in the framework of (otherwise) flavour-conserving SUSY models (cmssm, supergravity-inspired, etc) In addition to Right-handed ν ν R [Type I] Scalar triplets triplinos [Type II] Fermion triplets s-triplets [Type III] with same couplings, same interactions! But! preserve nice SUSY feature of gauge coupling unification gauge non-singlets below M GUT running of g i embed superfields into complet GUT (e.g. SU(5)) representations SUSY introduces degrees of freedom active at seesaw scales indirect probe of the seesaw! Even if correlations, etc... - difficult to disentangle from generic MSSM clfv... On the other hand some scenarios are falsifiable! [... and many many many people!]

30 What is so special about the SUSY Seesaw? To accommodate data on ν-oscillations, Y ν cannot be diagonal! clfv originates from large size and non-trivial structure of Y ν! Even for universal soft-breaking M GUT (SUSY flavour problem), RGE running of Y ν from M GUT down to Seesaw scale M R induces flavour-violating terms in slepton soft-breaking masses M GUT M R m 0 ( m ij = 0) ν R l Y ij ν m ij ν R m L ij ν R decouple If Majorana νs, if seesaw scale O(10 15 GeV) Y ν can be O(1) Large flavour violation in slepton sector ( m 2 L) ij ij = 1 (3 m 2 8 π A 2 0)(Y ν L Y ν ) ij BR(l l i l j γ) (Y ν log M GUT M R Y ν ) ij 2 M R L = log(m GUT /M R ) M EW m L ij LFV observables Large SUSY contributions to clfv observables, within experimental reach!

31 One source of flavour violation in the lepton sector msugra-like SUSY seesaw: Y ν unique source of FV low-energies: l j l i γ, l j 3l i, µ e in Nuclei large rates potentially observable! (all observables strongly related) high-energies [LHC]: study charged sleptons from χ 0 2 l ± l χ 0 1 decays sizable ẽ µ mass differences, new edges in m ll : χ >< >: l i L l i l i R l i l j X l i 9 >= χ 0 1 >; l i l i high-energies - lepton colliders: clfv in e ± e e ± µ + E T miss possibily clfv-seesaw golden channel e e µ µ + 2χ 0 1 If LFV indeed observable (large BRs & CR), expect interesting slepton phenomena at colliders! [... a large group!]... strengthen / disfavour seesaw hypothesis!

32 LFV at low- and high-energies: general overview cmssm: CMS point HM1 {180, 850, 0, 10, +1} and ATLAS point SU1 {70, 350, 0, 10, +1} Seesaw: general R (vary θi, arg θi [ π, π]), MR3 = 1012,13,14 GeV; θ13 = 0.1 GeV GeV GeV ~,~ m~l / m~l (e L µl) M3 = 1012 GeV M3 = 1013 GeV M3 = 1014 GeV SU1 HM BR(τ µ γ) M3 = M3 = M3 = CR(µ-e, Ti) BR(µ e γ) ~,~ m~l / m~l (e L µl) [from AFRT, ] If type-i seesaw and SUSY LFV observables within experimental reach HM1: m(e L, µ L ) LHC 0.1 1% BR(µ eγ) MEG SU1: m(e L, µ L ) LHC 0.1 1% BR(τ µγ) & 10 9 (SuperB) Hint towards scale of new physics (MN3 & 1013 GeV)

33 LFV at the LHC: di-lepton distributions in χ 0 2 decays Impact of type-i SUSY seesaw for di-lepton distributions χ 0 2 l i l L,R i χ 0 1 l i l i Seesaw: R = 1 P ( ) M R R = 1, P ( ) ={10 10, (10 12 ), (10 15 )} GeV, θ 13 = 0.1 Γ -1 total dγ(χ0 2 χ0 1 µ µ) / dm µµ Point P1 P2 P3 SU m µµ [GeV] d(number of events) / dm µµ 7 TeV 14 TeV 7 TeV 14 TeV 7 TeV 14 TeV 7 TeV 14 TeV P1 P2 P3 SU [from AFRT, ] m l Displaced m µµ and m ee edges ( l L ) sizable m l Appearance of new edge in m µµ : intermediate τ 2 LFV at the LHC: χ 0 2 τ 2 µ χ 0 1 µ µ m l (ẽ L, µ L ) [ flavour non-universality (?)] [ flavour violation!]

34 clfv at Linear Colliders Seesaw-induced clfv final states from e ± e e ± µ +missing energy Potential backgrounds from SM mν m ν & SUSY mν m ν charged currents... explore electron and positron beam polarisation! Statistical significance of raw signal feasible observation of events! e e ± χ 0 l l ± l i χ 0 1 l ± j χ 0 1 S(e + e - (80% LL) e + µ - + 2χ 0 1 ) / (S+B) e + e e + µ + E T miss L = 0.5 ab -1 L = 3.0 ab -1 e e µ µ + E T miss M R [GeV] s [TeV] σ(e - e - µ - µ - + Missing Energy) [fb] Type A C-light Type A C-heavy Type B C-light Type B C-heavy Number events C-l 1000 (6000) C-H 500 (3000) L = 0.5 (3) ab 1 [from AFRT, ] Golden channel (?) : e e µ µ + missing energy Small background... signal clear probe type I of SUSY seesaw (if unique source of LFV!)

35 Beyond the type I SUSY seesaw: examples... Type II SUSY seesaw More predictive (up to overall scale) - ( m 2 L) ij m 2 ναu αi Uβj correlations between clfv observables controled by ν-parameters! Distinctive prospects for clfv at colliders [... large community!] σ(χ 2 0 ) BR [fb] m 0 =100 GeV m 0 =200 GeV m 0 =300 GeV m 0 =500 GeV m 1/2 [GeV] σ σprod prod (χ 0 2 ) BR(χ0 2 µτ) Type I SUSY seesaw Type II SUSY seesaw σ(χ 2 0 ) BR [fb] [from Esteves et al, ] m 1/2 [GeV] m 0 =100 GeV m 0 =200 GeV m 0 =300 GeV m 0 =500 GeV Non-singlet SUSY seesaw: force gauge coupling unification - embed into GUTs, etc Type III SUSY seesaw, Inverse SUSY seesaw, hybrid... [... really large community!]

36 Beyond the type I SUSY seesaw: examples... Supersymmetric Grand Unified Theories Reduce arbitrariness of Y ν [CKM- and U PMNS -inspired patterns... Symmetries...] SO(10) type II example (leptogenesis motivated) highly correlated clfv observables! [from Calibbi et al, ] BR(τ µ γ ) BR(µ e e e ) CR(µ e in Ti ) SU(5) + RH neutrinos SUSY GUTs MEG expected BR(µ e γ ) correlated CPV and FCNCs observables in lepton and hadron sectors! [from Buras et al, ]

37 Overview Flavour violated in neutral leptons (and quarks)... only logical and natural that charged lepton flavour also violated in Nature! and great! New Physics beyond SM + massive νs! Many (interesting) models predict clfv - some in relation with ν-mass generation clfv can play a unique rôle in disentangling models, info on ν-dynamics prefer those with some tension between theory and near future data! Nature has been kind - large Chooz angle... maybe 0ν2β? or NP at LHC? While waiting: explore new avenues, as many as possible! (here - just tip of iceberg! ) different models, clfv observables, correlations... and indirect links to other problems: dark matter, supernovae, BAU...

38 Overview Flavour violated in neutral leptons (and quarks)... only logical and natural that charged lepton flavour also violated in Nature! and great! New Physics beyond SM + massive νs! Many (interesting) models predict clfv - some in relation with ν-mass generation clfv can play a unique rôle in disentangling models, info on ν-dynamics prefer those with some tension between theory and near future data! Nature has been kind - large Chooz angle... maybe 0ν2β? or NP at LHC? While waiting: explore new avenues, as many as possible! (here - just tip of iceberg! ) different models, clfv observables, correlations... and indirect links to other problems: dark matter, supernovae, BAU... Joint effort of so many many people, working in so many interesting clfv models

39 Overview Flavour violated in neutral leptons (and quarks)... only logical and natural that charged lepton flavour also violated in Nature! and great! New Physics beyond SM + massive νs! Many (interesting) models predict clfv - some in relation with ν-mass generation clfv can play a unique rôle in disentangling models, info on ν-dynamics prefer those with some tension between theory and near future data! Nature has been kind - large Chooz angle... maybe 0ν2β? or NP at LHC? While waiting: explore new avenues, as many as possible! (here - just tip of iceberg! ) different models, clfv observables, correlations... and indirect links to other problems: dark matter, supernovae, BAU... we will come up with a theory And then one day... clfv is observed and so simple, so beautiful, so elegant - that it can only be true!

40 One day... - maybe 2013? Delivered to some British castle via a very Invisible g 3 -mail?... The new Standard Model of Particle Physics... [g 3 -mail : three-ghost mail (triplet, s-triplet, triplino representation!)]