Hypercolor, extended hypercolor, and the generation problem

Abstract

We analyze some of the detailed consequences of the recently proposed grand unified theory based on $\mathrm{SO}{(10)}_{V}\ifmmode\times\else\texttimes\fi{}\mathrm{SO}{(10)}_{H}$ subject to a discrete $V\ensuremath{\leftrightarrow}H$ symmetry. The model attempts to unify flavor, color, and hypercolor, and provide a multigenerational grand unified theory. It predicts SU(4) as the unique unitary group for hypercolor. With the fundamental fermions belonging to the (16, 10) \ensuremath{\bigoplus} (10, 16) irreducible representation of $\mathrm{SO}{(10)}_{V}\ifmmode\times\else\texttimes\fi{}\mathrm{SO}{(10)}_{H}$, there are exactly four generations of ordinary fermions (hypercolor singlets). The dynamical symmetry breaking which gives masses to the vector bosons of the standard electroweak theory is accomplished through the condensates of a single generation of hyperfermions belonging to the sextet of SU(4). We show that the Weinberg relation ${M}_{W}={M}_{Z}cos\ensuremath{\theta}$ will be satisfied provided the hypercolor dynamics satisfies certain constraints. Present in the model are the much desired extended-hypercolor gauge bosons whose radiative transitions between the ordinary fermions and the hyperfermions give rise to both masses and mixing of the ordinary fermions; hence the generalized Cabibbo angles are in principle calculable. We also analyze the pseudo-Goldstone bosons and the rare decay modes of the $K$ and $D$ mesons. With the hyperfermions in the TeV range and the extended gauge bosons in the 1000-TeV range, we show that there is no conflict in the model with any known experimental bounds on such decays. We establish a hypercolor---Pati-Salam-color symmetry at medium energies.