Probing Majorana Neutrinos in Rare Meson Decays

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 Majorananeutrinos via • (a) 0nbb • (b) K, D, Ds, B, BcRare Meson decays • 4. Concluding remarks

3. 1. History • Before: Neutrinos aremasslessin the SM • 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 nm’s disappearance (SK) (1998) • …converted most likely to nt(2000) • Solar neis converted to either nm or nt(SNO) (2002) • Only LMA solution for solar neutrinos • (Homestake+Gallium+SK+SNO) (2002) • Reactor anti-neoscillate (KamLAND) (2004)

4. 1. History 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

5. Why q23 andq12 are large and close to special values?  Very strong hints at a certain (underlying) flavor symmetry. 1. History What we don’t know • absolute mass scale of neutrinos remains an open question. • m1, 2 < or > m3 ?  normal or inverted hierarchy? • What is the value of q13? Is it zero or not? how small?  Reactor & accelerator -oscillation experiments can answer, but possibly estimated from a global fit • Is CP violated in leptonicsector? • Neutrinos are Dirac or Majorana?

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

7. 2. Issues on Neutrino masses • 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.

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

9. 2. Issues on Neutrino masses • 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 :

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

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

12. 3. Probing Majorana Neutrinos 3.a …in neutrinoless double-Beta decay inthe limit of small neutrino masses : The half-life time of the0nbbdecay, , can be factorized as: Effective neutrino mass (model independent) (depends on neutrino mass hierarchy) Nuclear matrix element(large uncertainties) phase space factor

13. 3. Probing Majorana Neutrinos 3.b. …via Rare Meson Decays (G.Cvetic, C.D., S.Kang, C.S.Kim) …taking mesons in the initial and final state to be pseudoscalars (M : K+, D+, Ds , B+, BcM’ = p-, K-, D-,…) (S. Kovalenko, I. Schmidt, A. Gribanov, C.D.)

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

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

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

17. 3.a. Probing Majorana Neutrinos ..via Rare Meson Decays (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 0n2b decay

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

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

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

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

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

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

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

25. 3.a. Probing Majorana Neutrinos ..via Rare Meson Decays (iii) Heavy neutrino case: Theeffectiveamplitude and rate:

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

27. 4. Concluding Remarks • Muchtobediscoveredabout neutrinos: • For light (standard) neutrinos: • Masshierarchy, absolutemasses, mixings (especially 1-3) • Dirac vs Majorana? • Are there more neutrinos? Majorana? (Seesawsays yes…) • Look forMajorana neutrinos in DL=2 processes: • Neutrinolessdouble beta decays • RaremesonDecays • Intermediatemassesmay lead tosignals… • Letusbuildthenextmesonfactory…