Complex Spinors and Unified Theories

Global three-parameter model for neutrino oscillations using Lorentz violation

“…The standard three-neutrino massive model (1) has a solid foundation in renormalizable quantum field theory, and it is consistent with all data other than LSND using only four parameters. Moreover, its mass scales & 0:1 eV are compatible with a seesaw origin [38,39]. Therefore, if Lorentz violation is to be invoked, it is desirable to consider models that (i) are based on quantum field theory, (ii) involve only renormalizable terms, (iii) offer an acceptable description of the basic features of neutrino-oscillation data, (iv) have any mass scales & 0:1 eV for seesaw compatibility, (v) involve fewer parameters than the four used in the standard picture, (vi) have coefficients for Lorentz violation consistent with a Planck-scale suppression & 10 ÿ17 , and (vii) can accommodate the LSND signal.…”

Broken S 3L × S 3R flavor symmetry and leptonic CP violation

“…Since the source of CP violation comes in with a factor of (m e /m µ ) 1/2 , both the Dirac CP -violating phase in Eq. (17) and CP asymmetries in Eq. (28) are suppressed.…”

The Case for a Standard Model with Anomalous U(1)

“…The second anomaly equation simplifies to 10) stating that the relative suppression of the down to the charged lepton sector is proportional to the difference of two anomaly coefficients. The data, extrapolated to near unification scales indicates that there is no relative suppression between the two sectors, suggesting that difference should vanish.…”

“…Neutrino masses are naturally generated by the seesaw mechanism [10] if the three right-handed neutrinos N i acquire a Majorana mass in the DSW vacuum. The flat direction analysis indicates that their X-charges must be negative half-odd integers, with X N = −3/2 preferred by the vacuum analysis.…”

“…A simple model [4] with one family-dependent anomalous U (1) beyond the standard model was the first to exploit these features to produce Yukawa hierarchies and fix the Weinberg angle. It was soon realized that some features could be abstracted from the presence of the anomalous U (1): expressing the ratio of down-like quarks to charged lepton masses in terms of the Weinberg angle [5,6,7], the suppression of the bottom to the top quark masses [8], relating [9] the uniqueness of the vacuum to Yukawa hierarchies and the presence of MSSM invariants in the superpotential, and finally relating the see-saw mechanism [10] to R-parity conservation.…”