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 lauched the last Revolution in particle physics continued all the way up to Kabayashi-Maskawa work which completed the Standard Model today. Inspired by the 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 $\gamma_m \simeq 1$, the $\bar t t$ composite ("top-Higgs") in the top-quark condensate model with $\gamma_m \simeq 2$, and their variants in the models with $1<\gamma_m <2$ (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 $\gamma_m =1$. 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 $500-600 {\rm GeV}$ and can be discovered at LHC. We shall also touch upon the endeavor to discover WTC on the lattice.Comment: To appear in the Proceedings of "Shoichi Sakata Centennial Symposium" October 27-28, 2011, held at Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, Japan: 16 pages; Progress of Theoretical Physics, Supplement (2012

Top Quark Condensate Revisited

In the light of recent discovery of a very heavy top quark, we reexamine the top quark condensate model proposed by Miransky, Tanabashi and Yamawaki (MTY) and by Nambu. We first review the original MTY formulation based on the ladder Schwinger-Dyson equation and the Pagels-Stokar formula. It is particularly emphasized that the critical phenomenon gives a simple reason why the top quark can have an extremely large mass compared with other quarks and leptons. Then we discuss the Bardeen-Hill-Lindner (BHL) formulation based on the renormalization-group equation and the compositeness condition, which successfully picks up 1/N_c-sub-leading effects disregarded by MTY. In fact BHL is equivalent to MTY at the 1/N_c-leading order. Such a simplest version of the model predicts the top quark mass, m_t \simeq 250 GeV (MTY) and m_t \simeq 220 GeV (BHL), for the cutoff on the Planck scale. In this version we cannot take the cutoff beyond the Landau pole of U(1)_Y gauge coupling, which yields a minimum value of the top mass prediction m_t \simeq 200 GeV. We then propose a ``top mode walking GUT'' : The standard gauge groups are unified into a (``walking'') GUT so that the cutoff can be taken to infinity thanks to the renormalizability of the four-fermion theory coupled to ``walking'' gauge theory. The top and Higgs mass prediction is then controlled by the Pendleton-Ross infrared fixed point at GUT scale and can naturally lead to m_t \simeq m_H \simeq 180 GeV.Comment: 21 pages, To appear in Proc. YKIS'95, ``From the Standard model to Grand Unified Theories'', YITP, Kyoto University, Kyoto, August 21-25, 1995 (Supplement of Prog. Theor. Phys., 1996), ed. T. Kugo, Abstract reformatte

Quest for the Dynamical Origin of Mass - An LHC perspective from Sakata, Nambu and Maskawa

I review the dynamical symmetry breaking (DSB) approach to the Origin of Mass, which is traced back to the original (2008 Nobel prize) work of Nambu based on the BCS analogue of superconductor where mass of nucleon (then elementary particle) arises due to Cooper paring and pions are provided as massless Nambu-Goldstone (NG) bosons, being composite as in Fermi-Yang/Sakata model. In this talk I will focus on the modern version of DSB or composite Higgs models: Walking/Conformal Technicolor, Hidden Local Symmetry (HLS) or Moose, and Top Quark Condensate, with the their extra dimension versions closely related with HLS. Particular emphasis will be placed on the large anomalous dimension and conformal symmetry at the conformal fixed points, developed along the line of the pioneering work of Maskawa and Nakajima. Due to (approximate) conformal symmetry these models do have composite Higgs particle ("Techni-dilaton", "Top-sigma" etc.). Weakly coupled composite gauge boson is realized at "Vector Manifestation" formulated at conformal fixed point, which may be applied to the composite W/Z boson models. They will be tested in the upcoming LHC experiments.Comment: 18 pages, 5 figures, Talk presented on Jan. 26, 2009 at Yukawa International Seminar (YKIS) "Particle Physics beyond the Standard Model" Yukawa Institute for Theoretical Physics (YITP),Kyoto University, Japan, January 26 - March 25, 200