Systematic SO(10) operator analysis for fermion masses

A new approach for deducing the theory of fermion masses at the scale of grand unification is proposed. Combining SO(10) grand unification, family symmetries and supersymmetry with a systematic operator analysis, the minimal set of fermion mass operators consistent with low-energy data is determined. Exploiting the full power of SO(10) to relate up, down, and charged lepton mass matrices, we obtain predictions for seven of the mass and mixing parameters. The assumptions upon which the operator search and resulting predictions are based are stressed, together with a discussion of how the predictions are affected by a relaxation of some of the assumptions. The masses of the heaviest generation, $m_t$, $m_b$, and $m_{\tau }$, are generated from a single renormalizable Yukawa interaction, while the lighter masses and the mixing angles are generated by nonrenormalizable operators of the grand unified theory. The hierarchy of masses and mixing angles is thereby related to the ratio of grand to Planck scales, $\frac{M_G}{M_P}$. An explicit realization of the origin of such an economical pattern of operators is given in terms of a set of spontaneously broken family symmetries. In the preferred models the top quark is found to be heavy, $M_t=180\mathrm{}\pm 15$ GeV, and $tan\beta$ is predicted to be very large. Predictions are also given for $m_s$, $\frac{m_s}{m_d}$, $\frac{m_u}{m_d}$, $V_{\mathrm{cb}}$, $\frac{V_{\mathrm{ub}}}{V_{\mathrm{cb}}}$ and the amount of $\mathrm{CP}$ violation. Stringent tests of these theories will be achieved by more precise measurements of $M_t$, $V_{\mathrm{cb}}$, ${\alpha }_s$, and $\frac{V_{\mathrm{ub}}}{V_{\mathrm{cb}}}$ and by measurements of $\mathrm{CP}$ violation in neutral $B$ meson decays.