Within recent years, the lattice community has seen a surge in efforts attempting to understand strongly coupled theories other than QCD. In addition to mapping out the largely unknown, but intriguing landscape of theories, these studies also could prove to be necessary to understanding physics at the TeV scale that will be probed at the Large Hadron Collider (LHC). In general, strongly coupled field theories beyond the Standard model (often referred to as "technicolor" theories) are the least understood of the possible extensions of the Standard Model (due to demanding numerical calculations) and need to be understood to have a complete picture of possible mechanisms for spontaneous breaking of electroweak symmetry. The lattice group at LLNL, in conjunction with the Lattice Strong Dynamics collaboration, has made a dedicated computational effort to address this problem employing over 500 million BG/L hours, which stands as the largest numerical beyond the Standard Model effort to date. The primary motivation for specific projects are both theoretical and phenomenological in nature.

Theory:

While technicolor has the potential to solve the outstanding puzzle of electroweak symmetry breaking without introducing any deep theoretical problems, it is desirable for such a BSM model to provide insight into other outstanding theoretical questions as well. One such question is the "flavor problem", the unexplained hierarchy of quark masses in the Standard Model. By extending the basic technicolor framework in the direction of a more fundamental theory, the dynamically-generated condensate does have the potential to explain the quark mass hierarchy. Naive technicolor, also known as scaled-up QCD, does not provide a large enough techni-quark condensate to both generate the SM quark masses AND avoid stringent flavor-changing-neutral-current constraints from phenomenology; but there are many possibilities beyond the simplest one, which are worth exploring. To that end, our group at LLNL has made a large effort to explore the theories with two, six, and ten techni-quark flavors, with qualitative and quantitative differences from the simplest idea growing with the number of flavors. Early evidence indeed indicates that the tension which rules out naive technicolor is reduced when the number of flavors is increased from two to six (Phys.Rev.Lett. 104 (2010) 071601). Work is underway to understand the evolution of the model from six to ten flavors and to control formidable systematic uncertainties which stem from the fact that these studies are very computationally demanding. In addition, we have begun exploring the model with eight flavors, too, in order to explore this evolution from one model to the next at higher resolution.

Phenomenology:

One benefit that lattice calculations afford us is that once the first and most demanding phase of the computational work has been performed (generating gauge configurations), many interesting investigations can be carried out using the results. This information includes phenomenologically interesting quantities, such as the S-parameter or WW scattering. The S-parameter is a phenomenological quantity that depends on weak measurements (W and Z masses, weak couplings, etc.). In the naive scaled-up QCD technicolor scenario, the S parameter is far too large, one of a few reasons this scenario is "dead." One line of thinking is that changing the number of techni-quark flavors can result in different dynamics and a compatible S-parameter. Early evidence shows this is the case when comparing two and six flavor theories (Phys. Rev. Lett. 106, 231601 (2011)). Another direction we can take is to predict what will be found at the LHC in certain processes, such as WW scattering. To that end, a theoretical formalism has been developed, and early predictions have been made (http://arxiv.org/abs/1201.3977). Ongoing efforts include reducing systematic effects in these calculations and also incorporating additional quantities of phenomenological relevance to the LHC and other high-energy experiments into our explorations.