Theoretical Particle Physics Yonsei Univ.

Transcription

1 Yang-Hwan Ahn (KIAS) Appear to arxiv : 1409.xxxxx sooooon Theoretical Particle Physics Yonsei Univ.

2 Introduction Now that the Higgs boson has been discovered at 126 GeV, assuming that it is indeed exactly the one predicted by the SM, there are several theoretical arguments (inclusion of gravity, instability of the Higgs potential, neutrino masses and mixing angles with the CP violating phases, strong CP problem, ) and cosmological evidence (dark matter, inflation, cosmological constant, ) point toward the existence of physics beyond the SM.

3 Why flavor physics?

4 Standard Model Puzzles

5 Standard Model Puzzles

6 Goal and Motivations The goal of this talk is to construct a minimalistic supersymmetric model for quarks and leptons based on A4 U(1) X symmetry Naturalness problem Flavor puzzle Anomalous global U(1) X symmetry Spontaneous breaking of U(1) X ( Z N discrete symmetry) Ex) N=2

7 What determines the observed pattern of masses and mixings of quarks and leptons? Our Idea No clear direction for future searches large number of independent (1) parameters In a complete model, the mass scale suppression can be identified as the masses of the messenger fields

8 (arxiv: 1405, 7540 Forero, Tortola and Valle) Where Do we Stand? Large mixings (solar & Atm) New flavor symmetry Relatively large 13 can give constraint CP (LBL experiments T2K and No A)

9 (arxiv: 1405, 7540 Forero, Tortola and Valle) Where Do we Stand?

10 Where Do we Stand? Non- oscillation experiments

11 Where Do we Stand?

12 Model independent approach : - symmetry - symmetry But, such a symmetry can not be realized in nature

13 Model independent approach : - power law We propose a power law called - power law where certain elements associated with flavors and in the mass matrices are distinguished by each and flavor x 2 x 3 and y 2 y 3 : - symmetry!!

14 Model independent approach : - power law We propose a power law called - power law where certain elements associated with flavors and in the mass matrices are distinguished by each and flavor We consider the renormalizable UV complete theory above a new physics scale

15 Model independent approach : - power law We propose a power law called - power law where certain elements associated with flavors and in the mass matrices are distinguished by each and flavor considering a mass matrix giving an TBM-like based on - power law and UV complete texture

16 A4 Symmetry (Smallest group for three-families) Even permutations of 4 objects : S 2 =T 3 =(ST) 3 =I S 2 =I Z2 symmetry T 3 =I Z3 symmetry Finite group of S, TST 2, T 2 ST 12 elements in 4 T, TS, ST, STS conjugacy classes T 2, ST 2, T 2 S, TST 1 There are 4 irreducible representation : 1, 1, 1, 3 Why A4 (Discrete & non-abelian)? 3 2 A4 is the smallest discrete group that has 3-dimensional irreducible representation A4 flavor symmetry can give a µ- symmetric pattern for experimental data subgroup itself large mixings mismatch between Z2 and Z3 symmetry 4

17 Tetrahedral A 4 & Flavored-PQ U(1) X Symmetry According to both the - power law and the UV-completion textures under A4 X U(1) X symmetry The U(1) X invariance forbids renormalizable Yukawa couplings for the light families, but would allow them through effective non-renormalizable couplings suppressed by ( / ) n The global U(1) X symmetry which is anomalous can provide a solution for strong CP invariance PQ mechanism = spontaneous breaking of global U(1) PQ

18 Tetrahedral A 4 & Flavored-PQ U(1) X Symmetry According to both the - power law and the UV-completion textures under A4 X U(1) X symmetry

19 Tetrahedral A 4 & Flavored-PQ U(1) X Symmetry to break the flavor group along required VEV directions and to allow the flavons to get VEVs, which couple only to the flavons ( Driving field method, first, by Altarelli and Feruglio 2006 ) spontaneous breaking of the flavor symmetry Superpotential H u H d is not allowed, while next leading term is allowed which promote the -term

20 Tetrahedral A 4 & Flavored-PQ U(1) X Symmetry Hierarchy of the SM fermions Vacuum configuration Axion as a solution to strong CP and N DW = 1

21 Tetrahedral A 4 & Flavored-PQ U(1) X Symmetry The most general superpotential depending on the driving fields

22 Fermionic tetrahedral Symmetry A 4 Comparison with Ma, Rajasekaran (2001), Babu, Ma, Valle (2003) Ahn See also, Ahn, Paolo-Gondolo (2014) Ma, Rajasekaran (2001) Babu, Ma, Valle (2003)

23 U(1) X Hierarchy : Strong & Mild neutrino masses and down-type quark masses A successful Leptogenesis

24 Leptonic tetrahedral A 4 & flavored-pq U(1) x Symmetry y e,, y e,, ( )

25 Leptonic tetrahedral A 4 & flavored-pq U(1) x Symmetry y e,, y e,, ( )

26 Leptonic tetrahedral A 4 & flavored-pq U(1) x Symmetry y e,, y e,, ( )

27 Leptonic tetrahedral A 4 & flavored-pq U(1) x Symmetry y e,, y e,, ( )

28 Quark tetrahedral A 4 & flavored-pq U(1) x Symmetry A4 triplet : Non-diagonal entries CKM

29 Quark tetrahedral A 4 & flavored-pq U(1) x Symmetry A4 triplet : Non-diagonal entries CKM

30 Quark tetrahedral A 4 & flavored-pq U(1) x Symmetry A4 triplet : Non-diagonal entries CKM

31 Quark tetrahedral A 4 & flavored-pq U(1) x Symmetry A4 triplet : Non-diagonal entries CKM

32 flavored-pq symmetry U(1) X

33 Axion and Strong CP Three U(1) symmetries : U(1) PQ, U(1) L, U(1) Y (except for U(1) R X U(1) B ) EW symmetry breaking = -1 J A

34 Axion and Strong CP invariance Under the U(1) X transformation, the axion field A translates with the decay constant F A

35 Axion and Strong CP invariance

36 Axion and Strong CP invariance

37 Axion and Strong CP invariance

38 Axion

39 Spontaneously-broken Leptonic A 4 U(1) x Symmetry

40 Spontaneously-broken Leptonic A 4 U(1) x Symmetry In a basis where the charged leptons are real, positive and diagonal basis By the fields L, l L,R redefinition y 2 and y 3 real and positive

41 After seesawing In the limit y 2 y 3 - symmetry 13 =0 and 23 =45 In the limit y 2 =y 3 1 TBM 13 =0, 23 =45 and 12 =sin -1 (1/ 3) Small deviations of y 2 and y 3 from unity are guaranteed by the measured non-zero but small 13 For y 2,3 = 1, there is a neutrino mass sum-rule

42 After seesawing In the limit y 2 y 3 - symmetry 13 =0 and 23 =45 In the limit y 2 =y 3 1 TBM 13 =0, 23 =45 and 12 =sin -1 (1/ 3) Non-zero 13 requires deviations of y 2, y 3 from unit Overall scale m 0 is closely related with a successful leptogenesis, constraint of LFV and 0 decay rate through the seesaw formula as well as the down-type quark masses

43 After seesawing In the limit y 2 y 3 - symmetry 13 =0 and 23 =45 In the limit y 2 =y 3 1 TBM 13 =0, 23 =45 and 12 =sin -1 (1/ 3)

44 Phenomenology of light neutrino Model prediction: CP-violating phases and 0 -decay

45 Neutrinoless double beta decay NMO : IMO :

46 Leptonic Dirac CP-phase vs Atm. angle NMO : + IMO : NMO favors 23 >45 and 23 <45 (but small deviations from the maximality), while IMO favors 23 <45 and 23 >45 with large deviations from maximality.

47 Leptonic Dirac CP-phase vs Atm. angle NMO : + IMO :

48 Leptonic Dirac CP-phase vs Atm. angle NMO : + IMO :

49 0 -decay m ee vs Atm. mixing 23 NMO : + IMO : Our model can be tested in the very near future neutrino oscillation experiments and/or 0 -decay experiments

50 0 -decay m ee vs Atm. mixing 23 NMO : + IMO : Our model can be tested in the very near future neutrino oscillation experiments and/or 0 -decay experiments

51 0 -decay m ee vs Atm. mixing 23 NMO : + IMO :

52 0 -decay m ee vs Atm. mixing 23 NMO : + IMO :

53 Conclusion

54 Conclusion

55 Conclusion