Narrow Results

We study the bridge between the phenomenological mass matrix model and SO(10) GUT. Namely, we consider the four-zero texture model in the framework of the renormalizable SO(10) GUT model. This unification gives more stringent constraints than the case where only either model is considered. However, we can obtain good fitting by expanding the minimal SO(10) GUT to include 120 in addition to 10 and in Yukawa coupling and by considering both type I and type II seesaw mechanisms.

The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.

The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.

We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun’s equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher-order singularity which requests higher regularity condition demanding that parameters of the theory should be related to one another. As a result, the Hadron spectrum is consistent with the Regge trajectory only when quark mass vanishes. Therefore, in this model, the chiral symmetry is a consequence of the confinement.

Our model (Refs. 1–7) with a complex action in a functional integral formulation with path integrals extending over all times, both past and future, is reviewed. Several numerical relations between coupling constants are presented as supporting evidence. The new evidence is that several more hitherto unexplained coincidences are explained by our model:

(1) The "scale problem" is solved because the Higgs field expectation value is predicted to be very small compared to say some fundamental scale, that might be the Planck scale.

(2) The Higgs VEV need not be just zero, but rather is predicted to be so that the running top-quark Yukawa coupling just is about to be unity at this scale; in this way the (weak) scale easily becomes "exponentially small." Instead of the top-Yukawa we should rather say the highest flavor Yukawa coupling here.

These predictions are only achieved by allowing the principle of minimization of the imaginary part of the action S_I(history) to a certain extent adjust some coupling constants in addition to the initial conditions.

If supersymmetric partners are not found at LHC it would strengthen the need for a "solution" to the hierarchy problem in our direction of an explanation via a fine-tuning scheme inside the Standard Model, from say minimizing "the imaginary part of the action" in our complex action model.