Large Top Quark Yukawa Coupling and Horizontal Symmetries

Abstract

We consider the maximal U(3) horizontal scheme as a handle on fermion masses and mixings. In particular, we attempt to explain the large top Yukawa coupling and the masses and mixing in the two heaviest generations. A simple model is constructed by enlarging the matter content of the Standard Model with that of a $10+\bar{10}$ pair of SU(5). The third generation particles get their masses when U(3) is broken to U(2). Top quark mass is naturally of order one. Bottom and tau masses are suppressed because of a hierarchy in the effective Yukawa couplings and not from the hierarchy in the Higgs doublet vacuum expectation values. The hierarchy is a consequence of the fact that the particle spectrum contains an incomplete vector-like generation and can come from hierarchies between scales of breaking of different grand unified groups. Hierarchies and mixings between the second and third generation are obtained by introducing a single parameter epsilon' representing the breaking U(2) -> U(1). As a consequence, we show that the successful (and previosuly obtained) relations V_{cb} \approx (m_s / m_b) \approx \sqrt (m_c / m_t) easily follow from our scheme.