1. Neutrinoless double beta decay and Lepton Flavor Violation Or, in other words, how the study of LFV can help us to decide what mechanism is responsible for the 0  decay

2. Based on “Lepton number violation without supersymmetry” hep-ph/0404233, Phys.Rev.D accepted V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V. And on “Neutrinoless double beta decay and lepton flavor violation” hep-ph/0406199, V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V.

3. Observation of 0  would establish the existence of massive Majorana neutrinos. However, only if the process is mediated by the light neutrino exchange can one extract the effective mass from the rate since only then  2. In most cases it is impossible to decide which mechanism is responsible for 0  since the electron spectra, angular distributions, polarizations, etc. are independent of it.

5. The relative size of heavy (A H ) vs. light particle (A L ) exchange to the decay amplitude is (a crude estimate) A L ~ G F 2 m  /, A H ~ G F 2 M W 4 /  , Where  is the heavy scale and k ~ 50 MeV is the virtual neutrino momentum. For  TeV and m  ~ 0.1 – 0.5 eV A L /A H ~ 1, hence both mechanism contribute equally.

6. In the following we suggest that Lepton flavor violation (LFV) involving charged leptons provides a “diagnostic tool” for establishing the mechanism of  decay.

7. In the standard model lepton flavor conservation is as a consequence of vanishing neutrino masses. However, the observation of neutrino oscillations shows that neutrinos are massive and that the flavor is not conserved. Hence a more general theory must contain LFV of charged leptons generated probably at some high scale. There is a long history of searches for LFV with charged leptons, like  e +  muon conversion    e  + (Z,A), or    e + + e + + e . Impressive limits for the branching ratios have been established: < 1.2x10 -11 < 8x10 -13

8. There are ambitious new proposals with much better sensitivities: MECO: B  e < 5x10 -17 on Al MEG: B  e  < 5x 10 -14 i.e. improvement by a factor of ~ 1000 - 10000. The direct effect of neutrino mass is “GIM suppressed” by a factor of (  m  /M W 2 ) 2 ~ 10 -50 hence unobservable.

9. In the most popular SUSY-GUT scenario (for SU(5) GUT) one has the branching ratios Thus a) MEG and MECO should see an effect, and b)  e  is enhanced by a factor ~  compared to  e conversion. The feature b) is generic for theories with high scale LNV

10. Linking LNV to LFV Summary: - SM extensions with low (  TeV) scale LNV  ** - SM extensions with high (GUT) scale LNV [ ]  ** In absence of fine-tuning or hierarchies in flavor couplings. Important caveat!

11. Linking LNV to LFV I Simple criteria** based on ratio 1.  2.  3. Non observation  (Need more input to discriminate)

12. Effective theory description I - arises at loop level -, may arise at tree level - Leading pieces in c i are nominally of order (Yukawa) 2 Operators (omitting L  R)

13. Effective theory description II Phase space + overlap integrals:  n are coefficients of O(1) Origin of large logs: one loop operator mixing for light nuclei [Raidal-Santamaria ’97]

14. Effective theory description III (i) No tree level,  (ii) Tree level, *  log enhancement and (iii) Tree level **  Need to show that in models with low scale LNV O l and/or O lq are generated at tree level. No general proof, but two illustrations

15. Illustration I: RPV SUSY [R = (-1) 3(B-L) + 2s ]

16. Clearly, the way to avoid the connection between LFV and LNV is if ’ 111 >> ’ 211, etc. That is if ’ is nearly flavor diagonal. Note that empirically both ijk and ’ ijk are small << 1.

17. Illustration II: Left-Right Symmetric Model SU(2) L  SU(2) R  U(1) B-L  SU(2) L  U(1) Y  U(1) EM 

18. h ij are coupling constants of leptons and the doubly charged Higgs They are related to the mixing matrix K R of the heavy neutrinos Note that g lfv vanishes for degenerate heavy neutrinos, but h ij need not.

19. Within LRSM the LFV branching ratios depend only on g lfv. Thus the present limits suggest that either the scale is >> 1 TeV, or that g lfv is very small, i.e. that he heavy neutrino spectrum is degenerate or has very little mixing.

20. Conclusions The ratio provides insight into the 0  mechanism and possibility to access LNV mass scale Low scale LNV  * Simple criteria : - if  - if, TeV scale LNV is possible and thus more expt./th. input needed to decide  mechanism