What can we learn about the See-Saw mechanism from experimental data?

1. International Meeting in Lepton Physics Colombia 07 Alberto Casas (IFT-UAM/CSIC, Madrid) What can we learn about the See-Saw mechanism from experimental data? Collab. with Alejandro Ibarra, Fernando Jiménez

2. The see-saw is a beautiful mechanism to produce (small) -masses ...but it has (too) many parameters “Freedom is nice, but too much freedom is not so nice” Pasquale di Bari 2007

3. with Recall

4. Any can be accommodated Many give the “observed”

5. ...maybe just looking at the experimental data we can hardly say anything about the (high-energy) parameters of the see-saw

6. Still we can ask: How the present data restrict the (high-energy) see-saw parameters Which choices, among the allowed ones, produce more naturally the experimental data

7. Take the example of the MSSM The theory beyond the SM has several parameters: Many combinations of them give the right , BUT not all of them are equally natural

8. To obtain with no fine-tuningswe need That’s why we expect SUSY within the LHC reach

9. Note: The problem is more involved than in the MSSM The information about is incomplete Maybe we can use experimental datato restrict the most natural patterns of the see-saw parameters which may be good!

10. suggests unknown Experimental information about the neutrino sector Note: All -features are opposite to other fermions’

11. This is an opportunity for the see-saw mechanism: Maybe the peculiar pattern of -masses and mixings is a consequence of the peculiar way they are generated (through the see-saw).(as it happens with the smallness of )

12. More precisely

13. Consider first This ratio contrasts with other fermions: For neutrinos Hierarchy in ms Same hierarchy inys

14. Additional question: Is it possible (and natural) to get starting with hierarchical similar to otherfermions? yi

15. top-down & basis-independent parametrization of the see-saw For this kind of analysis it is convenient to have a

16. A botton-up parametrization, like (High-energy)R-Yukawa matrix Low-energy-masses and mixings (High-energy)R-masses (Complex)orthogonal matrix does not allow e.g.to guess easily the values of yior to play with them to see how change

17. So we parametrize the see-saw by the following 18 basis-independent (high-energy) parameters: (Convention: )

20. quite transparent meaning

21. Moreover,mi do not depend on VL :

22. VL is related to UMNS : Defining WLas: then (uniquely determined)

23. Summary of the top-down parametrization

24. Comment on the relation to the orthogonal (R) parametrization The R-matrix is related to Mi, yi and the VRmatrix as:

25. The top-down problem for the -masses in the see-saw can be written as 3 par. 3 par. 6 par. 3 par. VL becomes decoupled

26. We come back to the questions: How the present data restrict the (high-energy) see-saw parameters Which choices, among the allowed ones, produce more naturally the experimental data Is it possible (and natural) to get starting with hierarchical similar to otherfermions? yi

27. Example: If VR =1 Normally (far) too large, unless What about VR 1 ??

28. It is convenient to write with &

29. For random VR entries: M1≈M2≈M3 Mi/Mj ~ yi/yj Normally huge huge!!

30. VR entries are far from random

31. If M1≈M2≈M3 requires a delicate cancellation in the numerator Should be « 1 ≤ 1 Normally huge unnatural

32. The numerator can be small with no cancellations if In addition sizeable maximizes the denominator Should be « 1 ≤ 1 Normally huge If M1«M2«M3

33. sizeable If M1«M2«M3 a clear pattern emerges: just as VCKM!

34. The numerical results fit nicely the analytical expectations

35. Suppose suppr.factor An intuitive to understand these results:

36. can be made soft, but only with a strong fine-tuning In consequence: is softened, and is typically huge

37. If yihierarchical M1≈M2≈M3 disfavoured M1<<M2<<M3 favoured, with , large typically huge VR~ VCKM structure, Some conclusions and from

38. If yinon-hierarchical More possibilities are allowed.M1<<M2<<M3 is not consistent with random VR(e.g. is still required)

39. A suggestive ansatz Try VR~ VCKM More precisely Try also

40. The identification must be made at large energy (~ M). At that scale This represents a very regular hierarchy of O(300) In addition we have taken

41. In summary, we have made the assumption

42. Recall that VR = 1 would produce VR random would produce It is highly non-trivial for VR~ VCKM to produce the correct ratio

43. To see this more clearly, recall the previous plot Only a tiny part of the plane is consistent with

46. For the SUSY case works similar (and even better)

47. Recall with we expect to constrain and also Consider now (work in progress with A. Ibarra)

48. How do these relations constrain ? and From Consider the case

49. case 6 possibilities for consistent with unitarity

50. completely general case for Note that