Working in a two-representation lattice gauge theory that is close to a composite Higgs model, we calculate the low-energy constantCwhich controls the contribution of the electroweak gauge bosons to the Higgs potential. In QCD, the corresponding low-energy constant governs the mass splitting of the pion multiplet. Taking the continuum and chiral limits, we find that_{LR}C, in units of the pseudoscalar decay constant, is roughly of the same size as its QCD counterpart._{LR}

V. Ayyar, T. DeGrand, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an SU(4) gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the scenario of obtaining a realistic top mass in this model.

V. Ayyar, T. DeGrand, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

We investigate the phase structure of SU(4) gauge theory with the gauge field simultaneously coupled to two flavors of fermion in the fundamental representation and two flavors of fermion in the two-index antisymmetric representation. We find that the theory has only two phases, a low-temperature phase with both species of fermion confined and chirally broken, and a high-temperature phase with both species of fermion deconfined and chirally restored. The single phase transition in the theory appears to be first order, in agreement with theoretical predictions.

V. Ayyar, T. DeGrand, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

We use lattice simulations to compute the baryon spectrum of SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. This model is closely related to a composite Higgs model in which the chimera baryon made up of fermions from both representations plays the role of a composite top-quark partner. The dependence of the baryon masses on each underlying fermion mass is found to be generally consistent with a quark-model description and large-Nscaling. We combine our numerical results with experimental bounds on the scale of the new strong sector to derive a lower bound on the mass of the top partner._{c}

V. Ayyar, T. DeGrand, M. Golterman, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the non-anomalous U(1) symmetry of the model. Our results are broadly consistent with large-Nscaling and vector-meson dominance._{c}

B. Svetitsky,

Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to address fundamental dynamical questions. I survey recent work in this area.

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