1. Probing Majorana Neutrinos in Rare Meson Decays Claudio Dib UTFSM I.S. & B.K. Fest, UTFSM, May 2010 G. Cvetic, C.D., S.K. Kang, C.S. Kim, PRD 82, 053010, 2010

2. Outline  1. Recent history  2. Issues on neutrino masses  3. Probing Majorana neutrinos via (a) 0nbb (b) K, D, Ds, B, Bc Rare Meson decays  4. Concluding remarks

3.  Before: Neutrinos are massless in the SM 1. History No right-handed ’s  Dirac mass term is not allowed. SU(2)_L symmetry, and Higgs doublet only: (B - L) conservation  Majorana mass term is forbidden.  The Neutrino Era Atmospheric  ’s disappearance (SK) (1998) …converted most likely to  (2000) Solar e is converted to either  or  (SNO) (2002) Only LMA solution for solar neutrinos (Homestake+Gallium+SK+SNO) (2002) Reactor anti- e oscillate (KamLAND) (2004)

4. 4 What we have learned Lepton Flavor is not conserved Neutrinos have tiny mass (a hierarchy issue) Neutrinos have large mixing Very different from quark sectors the first evidence for incompleteness of Minimal Standard Model 1. History

5. What we don’t know  absolute mass scale of neutrinos remains an open question.  m 1, 2 m 3 ?  normal or inverted hierarchy?  What is the value of  13 ? Is it zero or not? how small?  Reactor & accelerator -oscillation experiments can answer, but possibly estimated from a global fit  Why  23 and  12 are large and close to special values?  Very strong hints at a certain (underlying) flavor symmetry.  Is CP violated in leptonic sector?  Neutrinos are Dirac or Majorana? 1. History

6. 6  Window to high energy physics beyond the SM  Why is the neutrino mass interesting?  The problem of mass in the SM  The problem of Baryon Asymmetry in Cosmology  Candidate for Dark Matter 2. Issues on Neutrino masses

7. Experimental ways to learn about neutrinos:  Experimental ways to learn about neutrinos:  Neutrino oscillation exp. (solar, atm, reactors, accel.)  Nuclear decays (beta and double-beta)  Nu-Nuclei scattering (accel.)  Rare decays (high intensity accel.)  etc. 2. Issues on Neutrino masses

8.  The issue of Dirac vs Majorana character: -> Majorana particle: nu(right) = anti-nu(left) -> Possible mass terms: invariant  Dirac mass terms are invariant under global symmetry not invariant Majorana mass terms are not invariant. Dirac mass  conserved quantum number ( L ) but Majorana mass  L not conserved 2. Issues on Neutrino masses

9.  Majorana Masses must have a different origin than masses of charged leptons and quarks.  A natural theoretical way to understand why 3 -masses are very small : Seesaw mechanism Type-I : Right-handed Majorana neutrinos. Type-II : Higgs triplet. Type-III : Triplet fermions. ν : 2. Issues on Neutrino masses

10. If Neutrinos are Majorana  Majorana character is observable in processes with ΔL=2 : Mass term connects neutrinos with antineutrinos: A Z  A (Z+2) + 2e -, μ - + A Z  e + + A (Z-2), etc. (0- 2Beta) (  -e conversion in nuclei) some rare decays 2. Issues on Neutrino masses

11.  Lepton number violation by 2 units,, plays a crucial role to probe the Majorana nature of ’s,  Provides a promising lab. method for determining the absolute neutrino mass scale complementary to other measurement techniques 3.a. Neutrinoless double-beta nuclear decay: 3.a. Neutrinoless double-beta nuclear decay: 0  3. Probing Majorana Neutrinos

12. The half-life time of the 0  decay,, can be factorized as: phase space factor Nuclear matrix element (large uncertainties) (depends on neutrino mass hierarchy) 3.a …in neutrinoless double-Beta decay in the limit of small neutrino masses : Effective neutrino mass (model independent) 3. Probing Majorana Neutrinos

13. Estimate by using the best fit values of parameters including uncertainties in Majorana phases Long Baseline

14.  Large uncertainties in NME About factor of 100 in NME  affect order 2-3 in | | Uncertainties (O.Cremonesi, 05)

15. …taking mesons in the initial and final state to be pseudoscalars (M : K , D , D s, B , B c M’ =  , K , D ,…) (G.Cvetic, C.D., S.Kang, C.S.Kim) (S. Kovalenko, I. Schmidt, A. Gribanov, C.D.) 3. Probing Majorana Neutrinos 3.b. …via Rare Meson Decays

16. Effective Hamiltonian: Decay Amplitude: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

17. The leptonic tensor: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

18.  transition rates are proportional to 3.a. Probing Majorana Neutrinos …via Rare Meson Decays

19. (i) Light neutrino case: (i) Light neutrino case:  Dominant contribution comes from the “t-type” diagram when the light neutrino and intermediate hadron state goes on its mass shell. - Analogous to nuclear 0 2  decay 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

20. (i) Light neutrino case: e.g. in (i) Light neutrino case: e.g. in 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

21.  Dominant contribution comes from the “s-type” diagram because the neutrino alone can be on its mass shell. (ii) Intermediate neutrino mass case: (ii) Intermediate neutrino mass case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

22. Effective amplitude at meson level: (neglecting charged lepton masses) (ii) Intermediate neutrino mass case: (ii) Intermediate neutrino mass case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

23. Branching ratio for as function of m, with mixing factor divided out (ii) Intermediate neutrino mass case: (ii) Intermediate neutrino mass case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

24. (ii) Intermediate neutrino mass case: (ii) Intermediate neutrino mass case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

25. (E. Nardi, E. Roulet, D. Tommasini (2005) ) (ii) Intermediate neutrino mass case: (ii) Intermediate neutrino mass case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

26.  Now both amplitudes, “s-type” and “t-type”, are comparable  neutrino propagators reduce to -1/(m N ) 2 (iii) Heavy neutrino case: (iii) Heavy neutrino case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

27. The effective amplitude and rate: (iii) Heavy neutrino case: (iii) Heavy neutrino case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

28. (iii) Heavy neutrino case: (iii) Heavy neutrino case: 3.a. Probing Majorana Neutrinos..via Rare Meson Decays

29. 4. Concluding Remarks Much to be discovered about neutrinos: For light (standard) neutrinos: Mass hierarchy, absolute masses, mixings (especially 1-3) Dirac vs Majorana? Are there more neutrinos? Majorana? (Seesaw says yes…) Look for Majorana neutrinos in  L=2 processes: Neutrinoless double beta decays Rare meson Decays Intermediate masses may lead to signals… Let us build the next meson factory…