Unparticle and Higgs boson as composites

We propose a generic framework in which the Higgs and the unparticle are both composite. The underlying theories are four-dimensional, asymptotically-free, nonsupersymmetric gauge theories with fermionic matter. We sketch a possible unification of these two sectors at a much higher scale resembling extended technicolor models. By construction our extensions are natural, meaning that there is no hierarchy problem. The coupling of the unparticle sector to the composite Higgs emerges as a four-Fermi operator. The bilinear unparticle operator near the electroweak scale has scaling dimension in the range 1 < d(U) < 3. We investigate, in various ways, the breaking of scale invariance induced by the electroweak scale resulting in an unparticle condensate. The latter acts as a natural infrared cutoff or hadronic scale. We give the low-energy effective theory valid near the electroweak scale. The unparticle-Higgs mixing is found to be suppressed within our framework.