Conformal Higgs, or techni-dilaton- composite Higgs near conformality

Abstract: In contrast to the folklore that Technicolor (TC) is a "Higgsless theory", we shall discuss existence of a composite Higgs boson, Techni-Dilaton (TD), a pseudo-Nambu-Goldstone boson of the scale invariance in the Scale-invariant/Walking/Conformal TC (SWC TC) which generates a large anomalous dimension $\gamma_m \simeq 1$ in a wide region from the dynamical mass $m$ $= {\cal O}$ (TeV) of the techni-fermion all the way up to the intrinsic scale $\Lambda_{\rm TC}$ of the SWC TC (analogue of $\Lambda_{\rm QCD}$), where $\Lambda_{\rm TC}$ is taken typically as the scale of the Extended TC scale $\Lambda_{\rm ETC}$: $$\Lambda_{\rm TC} \simeq \Lambda_{\rm ETC}\sim10<sup>3$$ TeV $(\gg m)$. All the techni-hadrons have mass on the same order ${\cal O} (m)$, which in SWC TC is extremely smaller than the intrinsic scale $\Lambda_{\rm TC} \simeq \Lambda_{\rm ETC}$, in sharp contrast to QCD where both are of the same order. The mass of TD arises from the {\it non-perturbative scale anomaly} associated with the techni-fermion mass generation and is typically 500-600 GeV, even {\it smaller than other techni-hadrons} of the same order of ${\cal O} (m)$, in another contrast to QCD which is believed to have no scalar $\bar q q$ bound state lighter than other hadrons. We discuss the TD mass in various methods, Gauged NJL model via ladder Schwinger-Dyson (SD) equation, straightforward calculations in the ladder SD/ Bethe-Salpeter equation, and the holographic approach including techni-gluon condensate. The TD may be discovered in LHC.