Composite avenue beyond the standard model. Legacy of Sakata in LHC era

Higgs boson may be a composite particle as Sakata vigorously looked for never-ending substructures of Nature. He proposed the Sakata model for hadrons, which was the prototype of the quark model and thus launched the last Revolution in particle physics continued all the way up to Kabayashi-Maskawa work which completed the Standard Model today. Inspired by Sakata's spirit we shall discuss composite Higgs boson in various models of our own for the dynamical symmetry breaking with large anomalous dimension: The techni-dilaton in the walking technicolor (WTC) with γm ≅ 1, the t-bar t composite ('top-Higgs') in the top-quark condensate model with γm ≅ 2, and their variants in the models with 1 < γm < 2 (strong ETC Technicolor, etc.). Among others we will focus on WTC which has an approximate scale symmetry in the region relevant to the dynamical mass generation. Such a conformal gauge dynamics is characterized by the essential singularity scaling, breakdown of the Ginzburg-Landau/Gell-Mann-Levy effective theory, and also by a large anomalous dimension γm=1. In contrast to the folklore that Technicolor is a 'Higgsless theory', there exists a composite Higgs, techni-dilaton, in the WTC as a composite pseudo Nambu-Goldstone boson associated with the spontaneously broken (approximate) scale symmetry, with its mass only arising from the (nonperturbative) scale anomaly and hence being much smaller than those of other techni-hadrons. The techni-dilaton has a mass typically of order 500 - 600 GeV and can be discovered at LHC. We shall also touch upon the endeavor to discover WTC on the lattice. (author)