Lepton flavour and neutrino mass aspects of the Ma-model

1. Lepton flavour and neutrino mass aspects of the Ma-model Based on: Adulpravitchai, Lindner, AM: Confronting Flavour Symmetries and extended Scalar Sectors with Lepton Flavour Violation Bounds, Phys. Rev. D80 (2009) 055031 Adulpravitchai, Lindner, AM, Mohapatra: Radiative Trans-mission of Lepton Flavor Hierarchies, Phys. Lett. B680 (2009) 476 - 479 Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg, Germany Southampton, Friday Seminar, October 30, 2009

2. Contents: • Introduction • The Ma-model • Flavour and the Ma-model • The LR-extension of the Ma-model • Conclusions

3. 1. Introduction: Particle masses

4. the masses of the Standard Model particles seem to increase with the generation number • HOWEVER: neutrinos have masses that are (at least) a factor of 106 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses • there are different possibilities to generate small neutrino masses

5. the masses of the Standard Model particles seem to increase with the generation number • HOWEVER: neutrinos have masses that are (at least) a factor of 106 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses • there are different possibilities to generate small neutrino masses

6. the masses of the Standard Model particles seem to increase with the generation number • HOWEVER: neutrinos have masses that are (at least) a factor of 106 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses • there are different possibilities to generate small neutrino masses

7. Tree-level diagrams: e.g. seesaw type I

8. Tree-level diagrams: e.g. seesaw type I

9. Tree-level diagrams: e.g. seesaw type I good: “natural” value for the Yukawa coupling “natural” explanation for large MR bad: scale for MR is arbitrary

10. Radiative masses: e.g. Zee/Wolfenstein model

11. Radiative masses: e.g. Zee/Wolfenstein model

12. Radiative masses: e.g. Zee/Wolfenstein model good: neutrino mass loop suppressed bad: this model is ruled out…

13. 2. Ma’s scotogenic model (Ma-model)

14. 2. Ma’s scotogenic model (Ma-model) • Ingredients apart from the SM: • 3 heavy right-handed Majorana neutrinos Nk (SM singlets) • second Higgs doublet η without VEV (with SM-like quantum numbers) • additional Z2-parity, under which all particles are even except for Nk and η

15. 2. Ma’s scotogenic model (Ma-model) • Ingredients apart from the SM: • 3 heavy right-handed Majorana neutrinos Nk (SM singlets) • second Higgs doublet η without VEV (with SM-like quantum numbers) • additional Z2-parity, under which all particles are even except for Nk and η

16. 2. Ma’s scotogenic model (Ma-model) • Ingredients apart from the SM: • 3 heavy right-handed Majorana neutrinos Nk (SM singlets) • second Higgs doublet η without VEV (with SM-like quantum numbers) • additional Z2-parity, under which all particles are even except for Nk and η

17. 2. Ma’s scotogenic model (Ma-model) • Ingredients apart from the SM: • 3 heavy right-handed Majorana neutrinos Nk (SM singlets) • second Higgs doublet η without VEV (with SM-like quantum numbers) • additional Z2-parity, under which all particles are even except for Nk and η

18. Features of the Ma-model: • relatively minimal extension of the SM (essentially a 2HDM) • Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1 • tree-level neutrino mass vanishes → generated at 1 loop

19. Features of the Ma-model: • relatively minimal extension of the SM (essentially a 2HDM) • Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1 • tree-level neutrino mass vanishes → generated at 1 loop

20. Features of the Ma-model: • relatively minimal extension of the SM (essentially a 2HDM) • Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1 • tree-level neutrino mass vanishes → generated at 1 loop

21. Features of the Ma-model: • relatively minimal extension of the SM (essentially a 2HDM) • Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1 • tree-level neutrino mass vanishes → generated at 1 loop

22. The Ma-model neutrino mass:

23. The Ma-model neutrino mass: Yukawa coupling:

24. The Ma-model neutrino mass: Yukawa coupling: This part would lead to a neutrino mass. BUT: ‹η0›=0 → tree-level contribution vanishes

25. The Ma-model neutrino mass: Yukawa coupling: This part would lead to a neutrino mass. BUT: ‹η0›=0 → tree-level contribution vanishes

26. Leading order: 1-loop diagram

27. Leading order: 1-loop diagram

28. Leading order: 1-loop diagram

29. Leading order: 1-loop diagram

30. Leading order: 1-loop diagram

31. Light neutrino mass matrix:

32. Light neutrino mass matrix:

33. Light neutrino mass matrix:

34. Light neutrino mass matrix: Higgs masses:

35. Light neutrino mass matrix: • Features: • “natural” Yukawa couplings • loop suppression 1/(16π2) • radiative seesaw → TeV-scale heavy neutrinos

36. Light neutrino mass matrix: • Features: • “natural” Yukawa couplings • loop suppression 1/(16π2) • radiative seesaw → TeV-scale heavy neutrinos

37. Light neutrino mass matrix: • Features: • “natural” Yukawa couplings • loop suppression 1/(16π2) • radiative seesaw → TeV-scale heavy neutrinos

38. Light neutrino mass matrix: • Features: • “natural” Yukawa couplings • loop suppression 1/(16π2) • radiative seesaw → TeV-scale heavy neutrinos

39. 3. Flavour and the Ma-model:

40. 3. Flavour and the Ma-model: The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

41. 3. Flavour and the Ma-model: The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

42. 3. Flavour and the Ma-model: The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

43. LFV-processes are strongly constrained (MEGA experiment):

44. LFV-processes are strongly constrained (MEGA experiment): BUT: these bounds only constrain combinations of Yukawa coupling elements → cancellations possible → no problem for the Ma-model

45. LFV-processes are strongly constrained (MEGA experiment): BUT: these bounds only constrain combinations of Yukawa coupling elements → cancellations possible → no problem for the Ma-model

46. What will happen if a (discrete) flavour symmetry is imposed?

47. What will happen if a (discrete) flavour symmetry is imposed? • without symmetry, the combination of Yukawa coupling matrix elements can be zero • a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

48. What will happen if a (discrete) flavour symmetry is imposed? • without symmetry, the combination of Yukawa coupling matrix elements can be zero • a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

49. What will happen if a (discrete) flavour symmetry is imposed? • without symmetry, the combination of Yukawa coupling matrix elements can be zero • a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

50. What will happen if a (discrete) flavour symmetry is imposed? • without symmetry, the combination of Yukawa coupling matrix elements can be zero • a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints