Very light dilaton and naturally light Higgs boson

We study very light dilaton, arising from a scale-invariant ultraviolet theory of the Higgs sector in the standard model of particle physics. Imposing the scale symmetry below the ultraviolet scale of the Higgs sector, we alleviate the fine-tuning problem associated with the Higgs mass. When the electroweak symmetry is spontaneously broken radiatively \`a la Coleman-Weinberg, the dilaton develops a vacuum expectation value away from the origin to give an extra contribution to the Higgs potential so that the Higgs mass becomes naturally around the electroweak scale. The ultraviolet scale of the Higgs sector can be therefore much higher than the electroweak scale, as the dilaton drives the Higgs mass to the electroweak scale. We also show that the light dilaton in this scenario is a good candidate for dark matter of mass $m_D\sim 1~{\rm eV}-10~{\rm keV}$, if the ultraviolet scale is about $10-100~{\rm TeV}$. Finally we propose a dilaton-assisted composite Higgs model to realize our scenario. In addition to the light dilaton the model predicts a heavy ${\rm U}(1)$ axial vector boson and two massive, oppositely charged, pseudo Nambu-Goldstone bosons, which might be accessible at LHC.Comment: 20 pages, 5 figures; v4. an appendix added, to appear in JHE

Effective theory of color superconductivity

We briefly review an effective theory of QCD at high baryon density, describing the relevant modes near the Fermi surface. The high density effective theory has properties of reparametrization invariance and gauge invariance, maintained in a subtle way. It also has a positive measure, allowing lattice simulations at high baryon density. We then apply it to gapless superconductors and discuss recent proposals to resolve the magnetic instability of gapless superconductivity.Comment: 8 pages, 3 figures; To appear in the proceedings of YKIS Seminar on New Frontiers in QCD, Kyoto, Japan, 20 Nov - 8 Dec 200