We measure the evolution of the coupling constant using the Schrödinger functional method in the lattice formulation of SU(2) gauge theory with two massless Dirac fermions in the adjoint representation. We observe strong evidence for an infrared fixed point, where the theory becomes conformal. We measure the β-function and the coupling constant as a function of the energy scale.

An SU(2) gauge theory with two fermions transforming under the adjoint representation of the gauge group may appear conformal or almost conformal in the infrared. We use lattice simulations to study the spectrum of this theory and present results on the masses of several gauge singlet states as a function of the physical quark mass determined through the axial Ward identity and find indications of a change from chiral symmetry breaking to a phase consistent with conformal behaviour at β L ∼ 2. However, the measurement of the spectrum is not alone sufficient to decisively confirm the existence of conformal fixed point in this theory as we show by comparing to similar measurements with fundamental fermions. Based on the results we sketch a possible phase diagram of this lattice theory and discuss the applicability and importance of these results for the future measurement of the evolution of the coupling constant.

We investigate the continuum spectrum of the SU (2) gauge theory with N f = 2 flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the w 0 parameter, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are m V /F PS ∼ 13.1(2.2) and m A /F PS ∼ 14.5(3.6) (combining statistical and systematic errors).In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are m V > 3.2(5) TeV and m A > 3.6(9) TeV, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.

We study, via lattice simulations, the nonperturbative dynamics of SU(2) gauge theory with two fundamental Dirac flavors. The model can be used simultaneously as a template for composite Goldstone boson dark matter and for breaking the electroweak symmetry dynamically. We compute the form factor, allowing us to estimate the associated electromagnetic charge radius. Interestingly we observe that the form factor obeys vector meson dominance even for the two color theory. We finally compare the model predictions with dark matter direct detection experiments. We find that the composite Goldstone boson dark matter cross section is constrained by the most stringent direct-detection experiments. Our results are a foundation for quantitative new composite dynamics relevant for model building, and are of interest to current experiments.

We update Monte Carlo simulations of the three-dimensional SU(3) + adjoint Higgs theory, by extrapolating carefully to the infinite volume and continuum limits, in order to estimate the contribution of the infrared modes to the pressure of hot QCD. The sum of infrared contributions beyond the known 4-loop order turns out to be a smooth function, of a reasonable magnitude and specific sign. Unfortunately, adding this function to the known 4-loop terms does not improve the match to four-dimensional lattice data, in spite of the fact that other quantities, such as correlation lengths, spatial string tension, or quark number susceptibilities, work well within the same setup. We outline possible ways to reduce the mismatch.Comment: 14 page