Calculability of the Flavor-Mixing Parameters

Abstract

Despite the impressive success of the standard model, the repetition of the family-generation of leptons and quarks persists as one of the most challenging unresolved problems in particle physics. The fermion family problem is to understand the fermion mass hierarchy of the leptons and quarks as observed in family-generations. Any consistent solution to this problem should also describe the flavor mixings in the charged-current sector including the CP-invariance violation as well as the empirical flavor-conservation up to the αGf order in the neutral weak interaction sector. In the standard model the fermion masses are generated by spontaneous breaking of the electroweak symmetry via the Higgs mechanism, but they are arbitrary free parameters. In other words, the standard model can be adjusted to accommodate the fermion family-generations but lacks calculability for the fermion mass spectrum. Because there are several fermion generations, the weak interaction eigenstates are not necessarily the mass eigenstates and therefore there will inevitably be mixings between different flavor states in the charged current sector thus introducing further arbitrary parameters to the standard model. However, the neutral-current sector is flavor diagonal up to αGf order in the standard model because the fermions in each generation are assigned in the same dimensional representations.