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Neutrinoless double beta decay and Lepton Flavor Violation

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 nbb decay if it is ever observed. Petr Vogel, Caltech Erice, 9/20/2005. Based on

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Neutrinoless double beta decay and Lepton Flavor Violation

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  1. Neutrinoless double beta decay andLepton Flavor Violation Or, in other words, how the study of LFV can help us to decide what mechanism is responsible for the 0nbb decay if it is ever observed Petr Vogel, Caltech Erice, 9/20/2005

  2. Based on “Lepton number violation without supersymmetry” Phys.Rev.D 70 (2004) 075007 V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V. And on “Neutrinoless double beta decay and lepton flavor violation” Phys. Rev. Lett. 93 (2004) 231802 V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V.

  3. Observation of the 0 decay means that neutrinos are massive Majorana particles Theorem due to Schechter and Valle, (1982). Existence of the vertex causes, by the multiloop graph shown, existence of the Majorana mass term.

  4. Light or heavy Majorana neutrino. Model extended to include right-handed WR. Mixing extended between the left and right-handed neutrinos. Light Majorana neutrino, only Standard Model weak interactions Supersymmetry with R-parity violation. Many new particles invoked. Light Majorana neutrinos exist also. Heavy Majorana neutrino interacting with WR. Model extended to include right-handed current interactions.

  5. It is well known that the amplitude for the light neutrino exchange scales as <m>. On the other hand, if heavy particles of scale are involved the amplitude scales as 1/5. The relative size of the heavy (AH) vs. light particle (AL) exchange to the decay amplitude is(a crude estimate) AL ~ GF2 mbb/<k2>, AH ~ GF2 MW4/L5 , where L is the heavy scale and k ~ 50 MeV is the virtual neutrino momentum. For L ~ 1 TeV and mbb ~ 0.1 – 0.5 eV AL/AH ~ 1, hence both mechanisms contribute equally.

  6. AL/AH ~ m5/ <k2> MW4 • Thus for m= 0.2 eV, <k2> = 502 MeV2, and AL/AH~ 1 • 5 ~ 502x1012x804x1036/0.2 eV ~ 5x1059 eV • ~ 1012 eV = 1 TeV Clearly, the heavy particle mechanism could compete with the light Majorana neutrino exchange only if the heavy scale  is between about 1 - 5 TeV. Smaller  are already excluded and larger ones will be unobservable due to the fast 5 scale dependence.

  7. APS Joint Study on the Future ofNeutrino Physics (2004) (physics/0411216) We recommend, as a high priority, a phased program of sensitive searches for neutrinoless double beta decay (first on the list of recommendations) The answer to the question whether neutrinos are their own antiparticles is of central importance, not only to our understanding of neutrinos, but also to our understanding of the origin of mass.

  8. It is well known that for the light neutrino exchange mechanism knowing <m> helps to fix the absolute mass scale. This is based on the parameters of the solar + KamLAND solution. The cross-hatched region is for 1s errors. Arrows indicate that by determining <mbb> , even crudely we can constrain the neutrino mass pattern.

  9. The relation between <m> and the mass hierarchy requires a comment: As one can see e.g. in the plot of <m> vs. the sum of neutrino masses the sign of m2atm (i.e. normal or inverted hierarchy) cannot be determined at all for even if <m> is accurately known in the case of the degenerate pattern, and even in the case commonly known as the `inverted hierarchy’ region.

  10. Alternatively, plot <m> versus <m> =[|Uei|2mi2]1/2,the quantity that can be determined in ordinary  decay. Note that these two quantities are propor- tional to each other, except in the unreachable low mass region. The gap in shading shows where inverted hierarchy begins.

  11. 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 <m> from the rate since only then  ~ <m> 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.

  12. There is one known exception to this statement, the `classical’ case of right-handed currents, characterized by the phenomenological parameters  and . In that case, indeed, single electron spectra are different when compared to the light Majorana exchange. However, the corresponding decay rate is expected to be smaller than the rate where the distinction cannot be made (see e.g. G. Prezeau, M. Ramsey-Musolf & P.V., Phys. Rev. D68, 034016 (2003)).

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

  14. In the standard model lepton flavor conservation is 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 - + (Z,A) -> e- + (Z,A), or + -> e+ + e+ + e- . Impressive limits for the branching ratios have been established: < 1.2x10-11 < 8x10-13

  15. There are ambitious new proposals with much better sensitivities: MECO: Bm ->e < 5x10-17 on Al MEG: Bm -> e+g < 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 (Dmn2/MW2)2 ~ 10-50 hence unobservable.  W e  

  16. So, why are people even looking for LFV? Because most particle physics models of `physics beyond the Standard Model’ contain LFV originating at some high mass scale. Most of them also contain LNV and, naturally, all realistic models should include light and mixed neutrinos, known to exist. If the scales of both LFV and LNV are well above the weak scale, then ~ <m>2 and <m> can be derived from the 0 decay rate. However, the `dangerous’ case is when both LFV and LNV scales are low (~ TeV). In that case there might be an ambiguity in interpreting the results of 0 decay experiments.

  17. 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) m -> e + g is enhanced by a factor ~1/a compared to m -> e conversion. The feature b) is generic for theories with high scale LNV

  18. 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!

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

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

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

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

  23. Clearly, the way to avoid the connection between LFV and LNV is if l’111 >> l’211 , etc. That is if l’ is nearly flavor diagonal. Note that empirically both lijk and l’ijk are small << 1. For the discussion of neutrino masses in the R-parity violating supersymmetric models see Y. Grossman and S. Rakshit, hep-ph/0311310 Generally, hierarchical neutrino spectrum is predicted, but small neutrino masses require some fine tuning.

  24. 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 

  25. Matter fields: Higgs sector

  26. hij are coupling constants of leptons and the doubly charged Higgs They are related to the mixing matrix KR of the heavy neutrinos Note that glfv vanishesfor degenerate heavy neutrinos, but hij need not.

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

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

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

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