Mooses, Topology and Higgs

New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking.Comment: 16 pages, 11 figure

Supersymmetry-Breaking Loops from Analytic Continuation into Superspace

We extend to all orders in perturbation theory a method to calculate supersymmetry-breaking effects by analytic continuation of the renormalization group into superspace. A central observation is that the renormalized gauge coupling can be extended to a real vector superfield, thereby including soft breaking effects in the gauge sector. We explain the relation between this vector superfield coupling and the "holomorphic" gauge coupling, which is a chiral superfield running only at 1 loop. We consider these issues for a number of regulators, including dimensional reduction. With this method, the renormalization group equations for soft supersymmetry breaking terms are directly related to supersymmetric beta functions and anomalous dimensions to all orders in perturbation theory. However, the real power of the formalism lies in computing finite soft breaking effects corresponding to high-loop component calculations. We prove that the gaugino mass in gauge-mediated supersymmetry breaking is ``screened'' from strong interactions in the messenger sector. We present the complete next-to-leading calculation of gaugino masses (2 loops) and sfermion masses (3 loops) in minimal gauge mediation, and several other calculations of phenomenological relevance.Comment: 50 pages, 1 ps and 1 eps figure, LaTe

The Littlest Higgs

We present an economical theory of natural electroweak symmetry breaking, generalizing an approach based on deconstruction. This theory is the smallest extension of the Standard Model to date that stabilizes the electroweak scale with a naturally light Higgs and weakly coupled new physics at TeV energies. The Higgs is one of a set of pseudo Goldstone bosons in an $SU(5)/SO(5)$ nonlinear sigma model. The symmetry breaking scale $f$ is around a TeV, with the cutoff \Lambda \lsim 4\pi f \sim 10 TeV. A single electroweak doublet, the ``little Higgs'', is automatically much lighter than the other pseudo Goldstone bosons. The quartic self-coupling for the little Higgs is generated by the gauge and Yukawa interactions with a natural size $O(g^2,\lambda_t^2)$, while the top Yukawa coupling generates a negative mass squared triggering electroweak symmetry breaking. Beneath the TeV scale the effective theory is simply the minimal Standard Model. The new particle content at TeV energies consists of one set of spin one bosons with the same quantum numbers as the electroweak gauge bosons, an electroweak singlet quark with charge 2/3, and an electroweak triplet scalar. One loop quadratically divergent corrections to the Higgs mass are cancelled by interactions with these additional particles.Comment: 15 pages. References added. Corrected typos in the discussion of the top Yukawa couplin

Worldlines on Orbifolds and the Fayet-Iliopoulos Term

We adapt ``string-inspired'' worldline techniques to one-loop calculations on orbifolds, in particular on the $S^1/Z_2$ orbifold. Our method also allows for the treatment of brane-localized terms, or bulk-brane couplings. For demonstration, we reproduce the well-known result for the one-loop induced Fayet-Iliopoulos term in rigidly supersymmetric Abelian gauge theory, and generalize it to the case where soft supersymmetry breaking mass terms for the bulk scalar fields are present on the branes.Comment: Typos corrected, clarifying remarks adde

The Little Hierarchy in Universal Extra Dimensions

In the standard model in universal extra dimensions (UED) the mass of the Higgs field is driven to the cutoff of the higher-dimensional theory. This re-introduces a small hierarchy since the compactification scale 1/R should not be smaller than the weak scale. In this paper we study possible solutions to this problem by considering five-dimensional theories where the Higgs field potential vanishes at tree level due to a global symmetry. We consider two avenues: a Little Higgs model and a Twin Higgs model. An obstacle for the embedding of these four-dimensional models in five dimensions is that their logarithmic sensitivity to the cutoff will result in linear divergences in the higher dimensional theory. We show that, despite the increased cutoff sensitivity of higher dimensional theories, it is possible to control the Higgs mass in these two scenarios. For the Little Higgs model studied, the phenomenology will be significantly different from the case of the standard model in UED. This is due to the fact that the compactification scale approximately coincides with the scale where the masses of the new states appear. For the case of the Twin Higgs model, the compactification scale may be considerably lower than the scale where the new states appear. If it is as low as allowed by current limits, it would be possible to experimentally observe the standard model Kaluza-Klein states as well as a new heavy quark. On the other hand, if the compactification scale is higher, then the phenomenology at colliders would coincide with the one for the standard model in UED.Comment: 25 pages, 2 figure

Oblique Parameter Constraints on Large Extra Dimensions

We consider the Kaluza-Klein scenario in which gravity propagates in the $4+n$ dimensional bulk of spacetime and the Standard Model particles are confined to a 3-brane. We calculate the gauge boson self-energy corrections arising from the exchange of virtual gravitons and present our results in the $STU$-formalism. We find that the new physics contributions to $S$, $T$ and $U$ decouple in the limit that the string scale $M_S$ goes to infinity. The oblique parameters constrain the lower limit on $M_S$. Taking the quantum gravity cutoff to be $M_S$, $S$-parameter constraints impose $M_S>1.55$ TeV for $n=2$ at the 1$\sigma$ level. $T$-parameter constraints impose $M_S>1.25 (0.75)$ TeV for $n=3 (6)$.Comment: Version to appear in PR

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules

The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased, and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel's widely-used time-dependent density functional theory benchmark set [M. Schreiber et al. J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step, and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory

Little Technicolor

Inspired by the AdS/CFT correspondence, we show that any G/H symmetry breaking pattern can be described by a simple two-site moose diagram. This construction trivially reproduces the CCWZ prescription in the context of Hidden Local Symmetry. We interpret this moose in a novel way to show that many little Higgs theories can emerge from ordinary chiral symmetry breaking in scaled-up QCD. We apply this reasoning to the simple group little Higgs to see that the same low energy degrees of freedom can arise from a variety of UV complete theories. We also show how models of holographic composite Higgs bosons can turn into brane-localized little technicolor theories by "integrating in" the IR brane.Comment: 26 pages, 2 figures; v2: references added; v3: added section on vacuum alignment to match JHEP versio