1. Neutrino mixing angle θ 13 In a SUSY SO(10) GUT Xiangdong Ji Peking University University of Maryland

2. Outline 1. Neutrino (lepton) mixing 2. Why SUSY SO(10)? 3. A new SUSY SO(10) model 4. Looking ahead X. Ji, Y. Li, R. Mohapatra, Phys. Lett. B633, 755 (2006) hep-ph/0510353

3. Neutrino (lepton) mixing Neutrinos, like quarks, have both masses and weak charges (flavor), and the mass eigenstates are not the same as the flavor eigenstates. One can write the neutrino of a definite flavor as Where U is the neutrino (or lepton) mixing matrix.

4. Three flavors From the standard model, we know there are at least 3 neutrino flavor (e,μ,τ), therefore, there are at least three mass eigenstates. In the minimal case, we have 3-mixing angle (θ 12 θ 23 θ 13 ) and 1(Dirac)+2(Majorana) CP- violating phases PNMS matrix

5. What do we know? From past experiments, we know θ 12 & θ 23 quite well Solar-ν mixing angle θ 12 Super-K, SNO, KamLand sin 2 θ 12 = 0.30 ±0.07 Atmosphetic-ν mixing angle θ 23 Super-K, K2K, sin 2 θ 23 = 0.52 ±0.20 There is an upper bound on θ 13 sin 2 θ 23 < 0.054 or sin 2 2θ 23 < 0.1 from Chooz exp.

6. Solar mixing angle

7. Current limit on θ 13 Chooz

8. Why do we care about precision on θ 13 Three important questions in neutrino physics What is the neutrino mass hierarchy? Are neutrinos Dirac or Majorana particles? What is the CP violation in lepton sector? CP violation Important for understanding baryon genesis in the universe One of the major goals for neutrino superbeam expts. Is related to the size of θ 13 (Jarlskog invariant)

9. Upcoming experiments Reactor neutrinos Double Chooz, <0.03 approved Daya Bay <0.01? US-China collaboration? Braidwood <0.01 $100M Neutrino superbeams Much more expensives hundreds of Million $ nuclear reactor detector 1 detector 2 Distance (km) P ee PeePee

11. Theories on neutrino mixing angles Top-down approach Assume a fundamental theory which accommodates the neutrino mixing and derive the mixing parameters from the constraints of the model. Bottom-up approach From experimental data, look for symmetry patterns and derive neutrino texture.

12. Why a GUT theory? Unifies the quarks and leptons, and treat the neutrinos in the same way as for the other elementary particles. A SO(10) GUT naturally contains a GUT scale mass for right-handed neutrinos and allows the sea-saw mechanism Which explains why neutrino mass is so much smaller than other fermions!

13. SUSY SO(10) GUT There are two popular ways to break SUSY SO(10) to SU(5) to SM Low-dimensional Higgs 16, 16-bar, 45, 10 16 s (break B-L symmetry) can be easily obtained from string theory High-dimensional Higgs 126, 126-bar, 120, 10 does not break R-parity (Z 2 ), hence allows SUSY dark matter candidates. R = (-1) 3(B-L)+2S

14. What can SUSY SO(10) GUTs achieve? SUSY GUT Stabilize weak scale & dark matter Coupling constant unification Delay proton decay Mass pattern for quarks and leptons Flavor mixing & CP violation Neutrino masses and mixing Mixing θ 13 126 H large θ 13 sin 2 2θ 13 ~ 0.16 (Mohapatra etal) 16 H small θ 13 sin 2 2θ 13 < 0.01 (Albright, Barr)

15. Albright-Barr Model Fermions in 16-spinor rep. 16 = 3 (up) + 3 (up-bar) + 3 (down) + 3 (down-bar) + 1 (e) + 1 (e-bar) + 1(nu-L) + 1(nu-R) Assume 3-generations 16 i (i=1,2,3) Mass term For example, eta contribute the mass to the first family, up quark, down quark, electrons and electron neutrino

16. Mass matrices Dirac masses Majorana Masses Lopsidedness

17. Diagonalization An arbitrary complex matrix can be diagonalized by two unitary matrices M D = L (m 1, m 2 m 3 )R + Majorana neutrino mass matrix is complex and symmetric, and can be diagonalized by a unitary matrix M M = U (m 1, m 2 m 3 )U *

18. CKM & lepton mixing The quark-mixing CKM matrix is almost diagonal The lepton mixing matrix (large mixing)

19. Large solar mixing angle It can either be generated from lepton or neutrino or a combination of both. From lepton matrix, Babu and Barr, PLB525, 289 (2002) again very small sin 2 2θ 13 < 0.01 If it is generated from neutrino mass matrix, it can come from either Dirac or Majorana mass or a mixture of both. In the Albright-Barr model, the large solar mixing comes from the Majorana mass. Fine tuning….

20. Lopsided mass matrix Generate the large atmospheric mixing angle from lepton mass matrix. Georgi-Jarlskog relation Why

21. A model ( Ji,Li,Mohapatra ) Assume the large solar mixing is generated from the neutrino Dirac mass and the Majorana mass term is simple The above mass terms can be generated from 16, 16-bar & 45

22. What can the model predict ? In the non-neutrino sector, there are 10 parameters, which can be determined by 3 up-type, and 3-lepton masses, and 4 CKM parameters. 3 down quark masses come out as predictions In the neutrino sector, we use solar mixing angle and mass ratios as input Prediction: right-handed neutrino spectrum Atmospheric mixing and θ 13

23. Predictions

24. Looking ahead Leptogenesis Baryon number asymmetry cannot be generated at just the EW scale (CP violation too small) CP-violating decay of heavy majorana neutrino generates net lepton number L. The lepton number can be converted into B- number through sphaleron effects (B-L conserved.) Does model generates enough lepton number asymmetry?

25. Looking ahead Proton Decay Is the proton decay too fast? Dimension-5 operator from the exchange of charged Higgsino.