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Neutrino mixing angle θ13 In a SUSY SO(10) GUT Xiangdong Ji Peking University University of Maryland 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 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. 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) CPviolating phases PNMS matrix U e1 U e 2 U e 3 U U 1 U 2 U 3 U 1 U 2 U 3 1 0 0 cos 23 0 sin 23 0 cos13 sin 23 0 i CP cos 23 e sin 13 0 ei CP sin 13 cos12 1 0 sin 12 0 cos13 0 sin 12 cos12 0 0 1 0 0 0 0 e i / 2 0 1 0 0 e i / 2i 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. Solar mixing angle Current limit on θ13 Chooz 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) Upcoming experiments Reactor neutrinos approved US-China collaboration? $100M PP eeee Double Chooz, <0.03 Daya Bay <0.01? Braidwood <0.01 detector 1 detector 2 nuclear reactor Neutrino superbeams Much more expensives hundreds of Million $ Distance (km) 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. 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 m ~ mD 2 / mR Which explains why neutrino mass is so much smaller than other fermions! 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 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 16H small θ13 sin2 2θ13 ~ 0.16 sin2 2θ13 < 0.01 (Mohapatra etal) (Albright, Barr) 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 L 16 116110H 16216310H 45H 16116216H16H ' '16116316H16H ' 16216H16316H ' For example, eta contribute the mass to the first family, up quark, down quark, electrons and electron neutrino Mass matrices Dirac masses Majorana Masses Lopsidedness 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* CKM & lepton mixing The quark-mixing CKM matrix is almost diagonal VCKM L†U LD The lepton mixing matrix (large mixing) VPMNS L†L L 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…. Lopsided mass matrix Generate the large atmospheric mixing angle from lepton mass matrix. Georgi-Jarlskog relation Why 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 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 Predictions 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 Bnumber through sphaleron effects (B-L conserved.) Does model generates enough lepton number asymmetry? Looking ahead Proton Decay Is the proton decay too fast? Dimension-5 operator from the exchange of charged Higgsino.