Neutrino mixing angle θ 13 In a SUSY SO(10) GUT

1. Neutrino mixing angle θ13 In a SUSY SO(10) GUT Xiangdong Ji Peking University University of Maryland

2. Outline • Neutrino (lepton) mixing • Why SUSY SO(10)? • A new SUSY SO(10) model • 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 (θ12 θ23 θ13) and 1(Dirac)+2(Majorana) CP-violating phases PNMS matrix

5. What do we know? • From past experiments, we know θ12 & θ23 quite well • Solar-ν mixing angle θ12 Super-K, SNO, KamLand sin2 θ12 = 0.30 ±0.07 • Atmosphetic-ν mixing angle θ23 Super-K, K2K, sin2 θ23 = 0.52 ±0.20 • There is an upper bound on θ13 sin2 θ23 < 0.054 or sin2 2θ23 < 0.1 from Chooz exp.

6. Solar mixing angle

7. Current limit on θ13 Chooz

8. Why do we care about precision on θ13 • 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 θ13 (Jarlskog invariant)

9. Pee detector 1 Pee detector 2 nuclear reactor Distance (km) 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 $

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 16s (break B-L symmetry) can be easily obtained from string theory • High-dimensional Higgs 126, 126-bar, 120, 10 does not break R-parity (Z2), 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 θ13 • 126H large θ13 sin2 2θ13 ~ 0.16 (Mohapatra etal) • 16H small θ13 sin2 2θ13 < 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 16i (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 MD = L (m1, m2 m3)R+ • Majorana neutrino mass matrix is complex and symmetric, and can be diagonalized by a unitary matrix MM = U (m1, m2 m3)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 sin2 2θ13 < 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 θ13

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.