(Charged) Lepton Flavor Violation

Transcription

1 (Charged) Lepton Flavor Violation University Neutrino Oscillation Workshop Conca Specchiulla, Otranto, Italia, September 6 13, 2008

2 Outline 1. Brief Introduction; 2. Old and ν Standard Model Expectations; 3. A Model Independent Approach; 4. Interplay with ν Masses, Leptogenesis and the LHC via Examples; 5. Conclusions. Advertisement: there are detailed theory and experiment talks on today! [F. Cei (MEG, next); F. Joaquim, L. Merlo, P. Cattaneo (tetrahedron)].

3 Ever since it was established that µ eν ν, people have searched for µ eγ, which naively could arise at one-loop: ν µ e γ The fact that µ eγ did not happen, led one to postulate that the two neutrino states produced in muon decay were distinct, and that µ eγ, and other similar processes, were forbidden due to symmetries. To this date, these so-called individual lepton-flavor numbers seem to be conserved in the case of charged lepton processes, in spite of many decades of (so far) fruitless searching...

4 Searches for Lepton Number Violation (µ and e) UL Branching Ratio (Conversion Probability) µ e γ µ - N e - N µ + e - µ - e + µ e e e K L π + µ e K L µ e K L π 0 µ e Year [hep-ph/ ]

5 SM Expectations In the old SM, the rate for charged lepton flavor violating processes is trivial to predict. It vanishes because individual lepton flavor number is conserved: N α (in) = N α (out), for α = e, µ, τ. However, the old SM is wrong: NEUTRINOS change flavor after propagating a finite distance. ν µ ν τ and ν µ ν τ atmospheric experiments ν e ν µ,τ solar experiments ν e ν other reactor neutrinos ν µ ν other from accelerator experiments [ indisputable ]; [ indisputable ]; [ indisputable ]; [ indisputable ]. The simplest and only satisfactory explanation of all this data is that neutrinos have distinct masses, and leptons mix. Lepton Flavor Number not a good quantum number.

6 Hence, in the New Standard Model (νsm, equal to the old Standard Model plus operators that lead to neutrino masses) µ eγ is allowed (along with all other charged lepton flavor violating processes). These are Flavor Changing Neutral Current processes, observed in the quark sector (b sγ, K 0 K 0, etc). Unfortunately, we do not know the νsm expectation for charged lepton flavor violating processes we don t know the νsm Lagrangian! [M-C Chen]

7 One contribution known to be there: active neutrino loops (same as quark sector). In the case of charged leptons, the GIM suppression is very efficient... e.g.: Br(µ eγ) = 3α 32π i=2,3 U µi U ei m2 1i M 2 W [U αi are the elements of the leptonic mixing matrix, 2 < m 2 1i m 2 i m 2 1, i = 2, 3 are the neutrino mass-squared differences]

8 e.g.: SeeSaw Mechanism [minus Theoretical Prejudice ] MAX B() τ µγ τ µµµ µ e conv in 48 Ti µ eγ µ eee m 4 (GeV) arxiv: [hep-ph]

9 Independent from neutrino masses, there are strong theoretical reasons to believe that the expected rate for flavor changing violating processes is much, much larger than naive νsm predictions and that discovery is just around the corner. Due to the lack of SM backgrounds, searches for rare muon processes, including µ eγ, µ e + e e and µ + N e + N (µ-e conversion in nuclei) are considered ideal laboratories to probe effects of new physics at or even above the electroweak scale. Indeed, if there is new physics at the electroweak scale (as many theorists will have you believe) and if mixing in the lepton sector is large everywhere the question we need to address is quite different: Why haven t we seen charged lepton flavor violation yet?

10 Model Independent Approach As far as charged lepton flavor violating processes are concern, new physics effects can be parameterized via a handful of higher dimensional operators. For example, say that the following effective Lagrangian dominates phenomena: L = m µ (κ + 1)Λ 2 µ Rσ µν e L F µν + κ (1 + κ)λ µ Lγ 2 µ e L (ūl γ µ u L + d ) L γ µ d L First term: mediates µ eγ and, at order α, µ eee and µ + Z e + Z Second term: mediates µ + Z e + Z and, at one-loop, µ eγ and µ eee Λ is the scale of new physics. κ interpolates between transition dipole moment and four-fermion operators. Which term wins? Model Dependent

11 µ e-conv at guaranteed deeper probe than µ eγ at Λ (TeV) B(µ e conv in 48 Ti)>10-18 We don t think we can do µ eγ better than µ e conv only way forward after MEG B(µ e conv in 48 Ti)>10-16 If the LHC does not discover new states µ e-conv among very few process that can access TeV new physics scale: tree-level new physics: κ 1, 1 Λ 2 g2 θ eµ Mnew 2. B(µ eγ)>10-13 B(µ eγ)> EXCLUDED κ

12 Other Example: µ ee + e L = m µ (κ+1)λ 2 µ R σ µν e L F µν + + κ (1+κ)Λ 2 µ L γ µ e L ēγ µ e Λ (TeV) B(µ eγ)>10-13 B(µ eee)>10-16 B(µ eee)>10-15 µ eee-conv at guaranteed deeper probe than µ eγ at B(µ eee)>10-14 µ eee another way forward after MEG? If the LHC does not discover new states µ eee among very few process that can access TeV new physics scale: tree-level new physics: κ 1, 1 Λ 2 g2 θ eµ Mnew EXCLUDED κ

13 What is This Good For? While specific models (to be discussed) provide estimates for the rates for processes, the observation of one specific process cannot determine the underlying physics mechanism (this is always true when all you measure is the coefficient of an effective operator). Real strength lies in combinations of different measurements, including: kinematical observables (e.g. angular distributions in µ eee); other channels; neutrino oscillations; measurements of g 2 and EDMs; collider searches for new, heavy states; etc.

14 [Kitano, Koide, Okada, PRD66, (2002)]

15 Example: Anomalous Magnetic Moment of the Muon, (g 2)/2 a µ Current 3.4 sigma discrepancy. Is it first evidence of new physics at the TeV scale? SM prediction more robust than in recent past. Way forward more or less clear: new e + e data to improve precision of hadronic contribution (BaBar), light-by-light scattering ultimate obstacle lattice(?). NOTE: new experimental effort would encourage theorists to improve on SM value. The effective operators that mediate µ eγ and contribute to a µ are virtually identical: m µ m µ Λ 2 µσµν µf µν θ eµ Λ 2 µσµν ef µν If θ eµ 1, µ eγ is a much more stringent probe of Λ... If the current discrepancy in a µ is due to new physics, θ eµ < A very strong constraint (already) on the flavor violating nature of the new physics, whatever it may be! [Hisano, Tobe, hep-ph/ ]

16 Bread and Butter SUSY plus High Energy Seesaw θ eµ m2 ẽ µ m 2 κ 1 while 1 Λ 2 g2 e 16π 2 m 2 θ eµ, where m 2 is a typical supersymmetric mass. θ eµ measures the amount of flavor violation. For m around 1 TeV, θẽ µ is severely constrained. Very big problem. Natural solution: θ eµ = 0 modified by quantum corrections.

17 L y iα L i HN α M αβ N y iα The Seesaw Mechanism N 2 α N β + H.c., N α gauge singlet fermions, (very large) mass parameters. dimensionless Yukawa couplings, M αβ N At low energies, integrate out the right-handed neutrinos N α : ( ) 1 + H.c. L ( ym 1 N y t) ij Li HL j H + O M 2 N y are not diagonal right-handed neutrino loops generate non-zero m 2 ẽ µ ( m 2 ll)αβ 3m2 0 + A 2 0 8π 2 k (y) kα (y) kβ ln M UV M Nk, M UV = M Planck, M GUT,... If this is indeed the case, would serve as another channel to probe neutrino Yukawa couplings, which are not directly accessible experimentally. Fundamentally important for testing the seesaw, leptogenesis, GUTs, etc.

18 What are the neutrino Yukawa couplings ansatz needed! B(µ eγ) title10 tan β = CKM SO(10) inspired model. 10 Now remember B scales with y 2. y 0.01 MEG B(µ eγ) M 2 R [ln(m P l/m R )] e-05 1e-06 1e x M 1/2 (GeV) [Calibbi, Faccia, Masiero, Vempati, hep-ph/ ]

19 µ e conversion is at least as sensitive as µ eγ B(µTi eti) title10 tan β = CKM MNS SO(10) inspired model. 10 Now y remember B scales with y 2. B(µ eγ) M 2 R [ln(m P l/m R )] 2 1e-04 1e-05 PRIME 1e-06 1e x M 1/2 (GeV) [Calibbi, Faccia, Masiero, Vempati, hep-ph/ ]

20 Input From/To Leptogenesis In the case of the seesaw mechanism, the matter-antimatter asymmetry generated via leptogenesis is (yet another) function of the neutrino Yukawa couplings: [M. Plumacher] If one is to hope to ever reconstruct the seesaw Lagrangian and test leptogenesis, LFV needs to be measured. Note that this is VERY ambitious, and we need to get lucky a few times: Weak scale SUSY has to exist; Precision measurement of µ e, τ µ, τ e; Precision measurement of SUSY masses; Very good understanding of mechanism of SUSY breaking; There are no other relevant degrees of freedom between the weak scale and > 10 9 GeV; etc Other ways to do this would be much appreciated!

21 Randall-Sundrum Model (fermions in the bulk) - dependency on UV-completion(?) - dependency on Yukawa couplings - complementarity between µ eγ, µ e conv [Agashe, Blechman, Petriello, hep-ph/ ]

22 Little Higgs Models: M. Blanke, et al, JHEP 0705, 013 (2007). R ΜTi eti Br Μ eγ

23 SUSY with R-parity Violation The MSSM Lagrangian contains several marginal operators which are allowed by all gauge interactions but violate baryon and lepton number. A subset of these (set λ to zero to prevent proton decay, and ignore bi-linear terms, which do not contribute as much to ) is: L = λ ijk ( ν Lie c Lj ẽ Rk + ē Rk ν Li ẽ Lj + ē Rk e Lj ν Li ) + λ ijkv jα c KM ( ν Li d Lα d Rk + d Rk ν Li dlα + d ) Rk d Lα ν Li λ ijk (ūc j e Li d Rk + d Rk e Li ũ Lj + d Rk u Lj ẽ Li ) + h.c., The presence of different combinations of these terms leads to very distinct patterns for. Proves to be an excellent laboratory for probing all different possibilities. [AdG, Lola, Tobe, hep-ph/ ] Bottom Line: This is simple scenatio where: κ 1, 1 Λ 2 λ2 m 2

24 Br(µ + e + γ) Br(µ + e + e e + ) = ( ) 2 1 m2 ντ 2m 2 ẽ R β (β 1) R(µ e in Ti (Al)) Br(µ + e + e e + ) = 2 (1) 10 5 β ( m2 ντ 12m 2 ẽ R + log m2 e m 2 ντ + δ) 2 2 (1) 10 3, µ + e + e e + most promising channel! [AdG, Lola, Tobe, hep-ph/ ]

25 Br(µ + e + γ) Br(µ + e + e e + ) = 1.1 (m dr = m cl = 300 GeV) R(µ e in Ti (Al)) Br(µ + e + e e + ) = 2 (1) 10 5 µ e-conversion only hope! [AdG, Lola, Tobe, hep-ph/ ]

26 Short Comment of Processes Involving τ Leptons Current Bound On Selected τ Processes (All from the B-Factories): B(τ eγ) < ; B(τ µγ) < B(τ eπ) < ; B(τ µπ) < B(τ eee) < ; B(τ eeµ) < , (µ eγ) (µ e conversion) (µ eee) B(τ eµµ) < ; B(τ µµµ) < Relation to µ e violating processes is model dependent. Typical enhancements, at the amplitude-level, include: Chirality flipping: m τ m µ ; Lepton mixing effects: U τ3 U e3 ; Mass-Squared Difference effects: m 2 13 m 2 12; etc

27 Rate ε=0.003, Λ=1 TeV, (λ =0.54) ε=0.003, Λ=10 TeV, (λ =5.4) P(ν µ ν τ ) P(ν µ ν τ ) P(ν µ ν e ) P(ν µ ν e ) τ µγ τ µγ e.g.: Large Extra-Dimensions -no ambiguity in y (neutrinos Dirac) µ eγ µ-e conv µ eee µ-e conv µ eee µ eγ dependency on UV-completion Rate ε=0.0003, Λ=1 TeV, (λ =0.17) ε=0.0003, Λ=10 TeV, (λ =1.7) τ µγ P(ν µ ν τ ) P(ν µ ν e ) τ µγ P(ν µ ν τ ) P(ν µ ν e ) Other example: neutrino masses from Higgs triplets [F. Joaquim] µ-e conv µ eγ µ eγ µ-e conv µ eee µ eee U e3 U e [AdG, Giudice, Strumia, Tobe, hep-ph/ ]

28 UL Branching Ratio (Conversion Probability) Searches for Lepton Number Violation µ e γ µ - N e - N µ + e - µ - e + µ e e e K L π + µ e K L µ e K L π 0 µ e Year [hep-ph/ ]

29 Brief: where is going (experiments)? [P. Cattaneo] MEG will aim at B(µ eγ) > several Can anyone do better? Looks very challenging! Different new initiatives in Fermilab (µ2e) and in Japan (COMET) will aim at B(µZ ez) > No showstopper for doing (much?) better. Concrete discussions at Fermilab (with Project X) and Japan (PRISM). See also NuFact study at CERN, hep-ph/ Recent discussions of new µ eee effort at PSI. Perhaps B(µ eee) > or Is it possible to do better? How much? Sensitivity to involving taus can improve past the 10 8 level with Super-B factories. B(τ lx) > 10 9 seems feasible. Naively unlikely that LHC can contribute (in spite of huge τ event sample).

30 Summary and Conclusions We know that charged lepton flavor violation must occur. Naive expectations are really tiny in the νsm (neutrino masses too small). If there is new physics at the electroweak scale, we must see very soon (MEG the best bet stay tuned?). Why haven t we seen it yet? It is fundamental to probe all channels. While in many scenarios µ eγ is the largest channel, there is no theorem that guarantees this (and many exceptions). may be intimately related to new physics unveiled with the discovery of non-zero neutrino masses. It may play a fundamental role in our understanding of the seesaw mechanism, GUTs, the baryon-antibaryon asymmetry of the Universe. We won t know for sure until we see it!

31 Complementary to LHC and other searches for new physics. Guaranteed to lean something regardless of scenario: New d.o.f. at LHC and positive signal for next-generation : best case scenario. Differentiate new scenarios for the new physics. Connections to neutrino masses? Neutrino masses at the TeV scale? New d.o.f. at LHC and negative signal for next-generation : New physics flavor blind. Why? Neutrino masses are very high energies? Leptogenesis disfavored? No new d.o.f. at LHC and positive signal for next-generation : New physics beyond the reach of LHC. Can we learn more? How? No new d.o.f. at LHC and negative signal for next-generation : Next-next generation (possibly µ e-conversion) among very few probes of new physics scales (along with neutrino oscillation experiments, astrophysics, cosmology, etc). How do we learn more?