The littlest Higgs is a cruiserweight

We study the exact (one-loop) effective potential of the littlest Higgs model and determine the dependence of physical quantities, such as the vacuum expectation value v_W and mass m_h of the Higgs boson, on the fundamental parameters of the Lagrangian--masses, couplings of new states, the fundamental scale f of the sigma model, and the coefficients of operators quadratically sensitive to the cutoff of the theory. On the one hand, we show that it is possible to have the electroweak ground state and a relatively large cutoff \Lambda = 4\pi f with f in the 2 TeV range without requiring unnaturally small coefficients for quadratically divergent quantities, and with only moderate cancellations between the contribution of different sectors to the effective potential of the Higgs. On the other hand, this cannot be achieved while at the same time keeping m_h close to its (bantamweight) current lower bound of 114.4 GeV. The natural expectation for m_h is O(f), mainly because of large logarithmically divergent contributions to the effective potential of the top-quark sector. Even a fine-tuning at the level of O(10^{-2}) in the coefficients of the quadratic divergences is not enough to produce small physical Higgs masses, and the natural expectation is in the 800 GeV range (cruiserweight) for f \sim 2 TeV. We conclude that the littlest Higgs model is a solution of the little hierarchy problem, in the sense that it stabilizes the electroweak symmetry breaking scale to be a factor of 100 less than the cutoff of the theory, but this requires a quite large physical mass for the Higgs, and hence precision electroweak studies should be redone accordingly. We also study finite temperature corrections.Comment: 18 pages, 9 figures, RevTex4. Final version accepted for publication in Phys. Rev.

The S-parameter in Holographic Technicolor Models

We study the S parameter, considering especially its sign, in models of electroweak symmetry breaking (EWSB) in extra dimensions, with fermions localized near the UV brane. Such models are conjectured to be dual to 4D strong dynamics triggering EWSB. The motivation for such a study is that a negative value of S can significantly ameliorate the constraints from electroweak precision data on these models, allowing lower mass scales (TeV or below) for the new particles and leading to easier discovery at the LHC. We first extend an earlier proof of S>0 for EWSB by boundary conditions in arbitrary metric to the case of general kinetic functions for the gauge fields or arbitrary kinetic mixing. We then consider EWSB in the bulk by a Higgs VEV showing that S is positive for arbitrary metric and Higgs profile, assuming that the effects from higher-dimensional operators in the 5D theory are sub-leading and can therefore be neglected. For the specific case of AdS_5 with a power law Higgs profile, we also show that S ~ + O(1), including effects of possible kinetic mixing from higher-dimensional operator (of NDA size) in the $5D$ theory. Therefore, our work strongly suggests that S is positive in calculable models in extra dimensions.Comment: 21 pages, 2 figures. v2: references adde

Wilson Loops in string duals of Walking and Flavored Systems

We consider the VEV of Wilson loop operators by studying the behavior of string probes in solutions of Type IIB string theory generated by Nc D5 branes wrapped on an internal manifold. In particular, we focus on solutions to the background equations that are dual to field theories with a walking gauge coupling as well as for flavored systems. We present in detail our walking solution and emphasize various general aspects of the procedure to study Wilson loops using string duals. We discuss the special features that the strings show when probing the region associated with the walking of the field theory coupling.Comment: 28 pages. Various figures. Version to be published