Charged Lepton Flavor Violation: an EFT perspective

Transcription

1 2010 Amherst Phenomenology Workshop, Amherst, Oct Charged Lepton Flavor Violation: an EFT perspective Vincenzo Cirigliano Los Alamos National Laboratory

2 Outline Charged LFV: general considerations, experimental searches EFT framework Model discriminating power of LFV processes probe UV structure (spectrum, dominant operators, etc): μ 3e vs μ eγ vs μ e conversion (Z) Flavor structure (MFV and beyond): μ e vs τ μ vs τ e

3 Charged LFV: general considerations Evidence of ν osc. implies that individual lepton family numbers are not conserved (after all Le,μ,τ are accidental symmetries of SM) In SM + massive ν, charged LFV rates are tiny (GIM-suppression) νi γ Petcov 77, Marciano-Sanda Great discovery channels. Extremely clean probe of BSM physics

4 Experimental status (90% CL): muons 10-13/14 (MEG at PSI, now running) 10-14/16 (PSI or MuSIC?) 10-16/17-18 (Mu2e, COMET, PRISM) μ-to-e conversion rate (normalized to total muon capture rate)

5 Experimental status: taus (90% BR limits from PDG) /10 sensitivities at future super-b factory (KEK)

6 Effective theory framework Dynamics below scale Λ [~ mass of new particles] described by Leff E Dynamics involving particles with m > Λ Λ (~TeV) M W,Z LFV processes probe a combination of effective scale and flavor structure of the various operators generated by SM extensions

7 Several operators generated at dim6: rich phenomenology Dominant in SUSY- GUT and SUSY seesaw scenarios

8 Several operators generated at dim6: rich phenomenology Dominant in SUSY- GUT and SUSY seesaw scenarios Dominant in RPV SUSY and RPC SUSY for large tan(β) and low ma q q

9 Several operators generated at dim6: rich phenomenology Dominant in SUSY- GUT and SUSY seesaw scenarios Dominant in RPV SUSY and RPC SUSY for large tan(β) and low ma q q... Z-penguin Enhanced in triplet models, Left-Right symmetric models e e δ lepton operators

10 EFT framework: ask a number of questions on LFV dynamics before getting married to a specific model (answers will eventually help discriminating among models) 0) What combination of scale Λ + couplings produces observable LFV effects? 1) What is the relative strength of various operators (αd vs αs... )? What experiments are needed to disentangle operators? 2) What is the flavor structure of the couplings ([αd] eμ vs [αd] τμ...)? How can we probe it? How does it relate to lepton mixing? ( what are the sources of flavor breaking in underlying model)

11 0th order question What combination of scale Λ + couplings produces observable rates? BRα β ~ (vew/λ) 4 (αn)αβ 2 Observable 10-1? new physics between weak and GUT scale Current limit from μ eγ implies even after taking into account loop factors New physics at TeV scale (and reasonable mixing pattern) LFV signals are within reach of planned searches

12 Remaining part of this talk Be optimistic: assume weak-scale BSM physics induces observable rates. Ask questions that probe more deeply LFV dynamics What is the relative strength of various operators (αd vs αs... )? Explore discriminating power of μ 3e vs μ eγ vs μ e conversion measurements in different target nuclei VC, R. Kitano, Y. Okada, P. Tuzon PRD (2009) What is the flavor structure of the couplings ([αd] eμ vs [αd] τμ...)? Review Minimal Flavor Violation ideas / patterns and discuss discriminating role of μ eγ vs τ μγ searches VC, B. Grinstein, G. Isidori, M. Wise NPB 728, 121 (2005) VC, B. Grinstein, G. Isidori, M. Wise NPB 763, 35 (2006)

13 Relative strength of operators: μ 3e vs μ eγ vs μ e

14 μ eγ vs μ 3e Relative rate of μ eγ and μ 3e knows about UV dynamics

15 μ eγ vs μ 3e Relative rate of μ eγ and μ 3e knows about UV dynamics Dramatic deviation if contact terms are generated at tree level RPV SUSY: DeGouvea-Lola-Tobe 00 LRSM: VC-Kurylov-RamseyMusolf-Vogel 04 Great diagnostic tool, but no new μ 3e search underway

16 Discriminating power of μ eγ and μ e conversion μ eγ and μ e conversion probe different combinations of operators x In principle, by measuring the target dependence of μ e conversion (and ratio to μ eγ BR) we can infer the relative strength of effective operators

17 Test hypothesis of single-operator dominance One unknown parameter ([αd,v,s] eμ /Λ 2 ) predict ratios of LFV BRs Test dipole-dominance model with μ eγ and one μ e rate Kitano-Koike-Okada 02 VC-Kitano-Okada-Tuzon 09 B(µ e,z) B(µ eγ) Pattern: 1) Behavior of overlap integrals** 2) Total capture rate (sensitive to nuclear structure) 3) Deviations would indicate presence of scalar / vector terms O(α/π) Z

18 Test any single-operator model via target-dependence of μ e rate VC-Kitano-Okada-Tuzon Al Ti Pb V(Z) Z couples predominantly to neutrons - γ couples to protons V(γ) 1 D S Z - Essentially free of theory uncertainty (largely cancels in ratios) - Discrimination: need ~5% measure of Ti/Al or ~20% measure of Pb/Al - Ideal world: use Al and a large Z-target (D,V,S have largest separation): challenge for experimental programs (Mu2e, COMET,...)

19 Test two-operator models If single-operator dominance hypothesis fails, consider next simplest case: two-operator dominance (DV, DS, SV) Unknown parameters: [α1] eμ /Λ 2, [α2] eμ /Λ 2 Hypothesis can be tested with two double ratios (three LFV measurements!!). For example: DV, DS SV B(µ e,al) B(µ eγ) B(µ e,ti) B(µ e,al) B(µ e,ti) B(µ e,al) B(µ e,pb) B(µ e, Al)

20 Consider S and D: realized in SUSY via competition between dipole and scalar operator (mediated by Higgs exchange) Relative sign: + VC-Kitano-Okada-Tuzon 2009 scalar dipole - Uncertainty from strange form factor largely reduced by lattice QCD [0, 0.4] [0, 0.05] JLQCD 2008 fat error band thin error band realistic discrimination

21 Consider S and D: realized in SUSY via competition between dipole and scalar operator (mediated by Higgs exchange) Relative sign: - VC-Kitano-Okada-Tuzon 2009 scalar dipole - Uncertainty from strange form factor largely reduced by lattice QCD [0, 0.4] [0, 0.05] JLQCD 2008 fat error band thin error band realistic discrimination

22 Consider S and D: realized in SUSY via competition between dipole and scalar operator (mediated by Higgs exchange) In summary: Relative sign: - dipole - Theoretical scalar hadronic uncertainties under control (OK for 1-operator dominance, need Lattice QCD for 2-operator models) - Realistic model discrimination requires measuring Ti/Al at <5% or Pb/Al at <20% - In principle, can perform similar analysis for hadronic vs radiative tau - decays Uncertainty at super-b from factory strange form factor largely reduced by lattice QCD [0, 0.4] [0, 0.05] JLQCD 2008 fat error band thin error band realistic discrimination

23 Explicit realization: SUSY see-saw scenario See-saw scenario: mixing in L-slepton mass matrices Dipole vs scalar operator, mediated by Higgs exchange Kitano-Koike-Komine-Okada 2003 /msl 2 /ma 2

24 Explicit realization: SUSY see-saw scenario See-saw scenario: mixing in L-slepton mass matrices Dipole vs scalar operator, mediated by Higgs exchange Learn about SUSY parameters VC-Kitano-Okada-Tuzon 2009

25 Flavor structure of couplings: MFV and beyond

26 Probe underlying sources of flavor violation? Within any given model, the (lepton) flavor symmetry breaking couplings leave their imprint in the matrix structure of [αd,v,..] ab E Λ FB» Λ λ λ Breaking of G F occurs via λ insertions Flavor-blind interactions of particles with m > Λ Λ (~TeV) λ λ Local operator involving SM fields and λ

27 Probe underlying sources of flavor violation? Within any given model, the (lepton) flavor symmetry breaking couplings leave their imprint in the matrix structure of [αd,v,..] ab Effective theoretical approach: given an ansatz on flavor symmetry group and sources of breaking (insensitive to UV details of the model) use group theory + EFT to analyze pattern of predictions Most predictive ansatz: Minimal Flavor Violation Other example: GUT-motivated ansatz... Experimentally, need information on transitions between different families: μ e vs τ μ vs τ e

28 MFV ansatz Flavor-breaking structures (SM & BSM) are aligned with fermion mass matrices - Introduced in the quark sector to solve flavor problem** Georgi-Chivukula 87, Hall-Randall 90, Buras 01, D ambrosio-giudice-isidori-strumia 02 - MFV extension to leptons defines a constrained class of models. Tool to investigate nature / structure of flavor breaking sources ** Problem exists in lepton sector as well:

29 MFV in lepton sector what is the origin of neutrino masses? Origin of Neutrino mass Dirac Majorana Replica of quark MFV λ D λ e λ U λ ν m ν /v < Identify flavor breaking sources: λ e and??

30 MFV in lepton sector what is the origin of neutrino masses? Origin of Neutrino mass Dirac Majorana Replica of quark MFV λ D λ e λ U λ ν m ν /v < Identify flavor breaking sources: λ e and?? g ν irreducible (SM lepton field content) H H T L i gν ij L j

31 MFV in lepton sector what is the origin of neutrino masses? Origin of Neutrino mass Dirac Majorana Replica of quark MFV λ D λ e λ U λ ν m ν /v < Identify flavor breaking sources: λ e and?? g ν irreducible (SM lepton field content) H H T g ν reducible (models with heavy ν R ) g ν ~ λ ν T M R -1 λ ν H M R -1 H L i gν ij L j L i λ ν T ν R ν R λ ν L j MFV alignment only if M R = M ν I and λ ν = λ ν *

32 MFV in lepton sector what is the origin of neutrino masses? Origin of Neutrino mass Dirac Majorana Replica of quark MFV λ D λ e λ U λ ν m ν /v < Identify flavor breaking sources: λ e and?? g g ν irreducible (SM lepton field content) ν reducible (models with heavy ν R ) g ν ~ λ T ν M -1 R λ ν - Other less H minimal H definitions are possible (see Davidson-Palorini 07) H H T M -1 - Other realizations (with different field content) different R LFV pattern (Gavela-Hambye-Hernandez-Hernandez 09) L i gν ij L j L i λ ν T ν R ν R λ ν Embed in GUT? MFV alignment only if M R = M ν I and λ ν = λ ν * L j

33 VC-Grinstein-Isidori-Wise 05 MLFV: simplest implementation GLF = SU(3)L x SU(3)E broken only by λ e and g ν Formally invariant under if

34 VC-Grinstein-Isidori-Wise 05 MLFV: simplest implementation GLF = SU(3)L x SU(3)E broken only by λ e and g ν Formally invariant under if Implications for radiative decays: - Normalization unknown (mν = v 2 gν/λln ): observable effects only if Λ LN /Λ > Ratios of l i l j BRs are predicted in terms of Δm ν 2 and U PMNS

35 Scenario is falsifiable: ideal test-ground is μ eγ vs τ μγ Reach of Super-B factories Reach of B factories [ ] Shading corresponds to different values of the phase δ and normal/inverted spectrum τ μγ is observable at B factories s 13 < 0.05

36 GUT-motivated ansatz (see extra slides) induces very different pattern: B(μ eγ) / B(τ μγ) ~ Vus 6 Reach of Super-B factories Reach of B factories PMNS pattern - PMNS pattern: τ μγ is observable at B factories only if s 13 < 0.05 CKM pattern - GUT-induced pattern: τ μγ is within reach of (super-)b factories VC-Grinstein-Isidori-Wise 06

37 Conclusions Charged LFV: golden modes to probe physics BSM - In TeV extensions of the SM, signals can be easily within reach of current / planned searches Observation of more than one mode model discriminating power: Relative strength of operators through μ 3e vs μ eγ vs μ e conversion in different nuclei Structure of flavor breaking sources through μ vs τ LFV BRs. Illustration with MFV and GUT ansatze

38 Visit T-division at Los Alamos (lots of interesting things to do after your talk...)

39 Extra Slides I: MFV and GUTs

40 VC-Grinstein-Isidori-Wise 06 Flavor group GUT-motivated ansatz (SU(5)) Symmetry breaking terms

41 VC-Grinstein-Isidori-Wise 06 Flavor group GUT-motivated ansatz (SU(5)) Symmetry breaking terms (consistent with fermion spectrum) Fix mass relations

42 VC-Grinstein-Isidori-Wise 06 Flavor group GUT-motivated ansatz (SU(5)) Symmetry breaking terms (consistent with fermion spectrum) Spurion transformation laws

43 Strength of radiative leptonic FCNC: two competing structures PMNS mixing pattern CKM mixing pattern [~ Barbieri-Hall-Strumia 95] What s going on? - Radiative corrections [Λ Planck > μ > Λ GUT ] induce cross-talk between quark & lepton sector - CKM mixing pattern appears in leptonic transitions - Do not recover MFV(quark) + MFV(lept)

44 Strength of radiative leptonic FCNC: two competing structures PMNS mixing pattern CKM mixing pattern [~ Barbieri-Hall-Strumia 95] - Normalization cannot be suppressed by lowering Mν (λν) - New (more hierarchical) pattern of BRs emerges

45 Again, μ eγ vs τ μγ can discriminate B(μ eγ) / B(τ μγ) ~ Vus 6 Reach of Super-B factories Reach of B factories PMNS pattern - PMNS pattern: τ μγ is observable at B factories only if s 13 < 0.05 CKM pattern - GUT-induced pattern: τ μγ is within reach of (super-)b factories

46 Extra Slides II: mu-to-e conversion

47 Definition of models: D, S, V(Z), V(γ) Dipole model Vector model: V(γ) Scalar model Vector model: V(Z)

48 Dependence of conversion amplitude on target nucleus: distinguish D,S,V underlying operators Czarnecki-Marciano- Melnikov Kitano-Koike-Okada - Lepton wave-functions in EM field generated by nucleus - Relativistic components of muon wavefunction give different contributions to D,S,V overlap integrals. For example: - Sensitive to hadronic and nuclear properties - Expect largest discrimination for heavy target nuclei

49 Qualitative behavior of overlap integrals free outgoing electron wf (average value)