Nonperturbative Infrared Finiteness in a Superrenormalizable Scalar Quantum Field Theory.

We present a study of the IR behavior of a three-dimensional superrenormalizable quantum field theory consisting of a scalar field in the adjoint of SU(N) with a φ^{4} interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory, the critical mass is ambiguous due to IR divergences, and we indeed find that at two loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [R. Jackiw et al., Phys. Rev. D 23, 2291 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2291, T. Appelquist et al., Phys. Rev. D 23, 2305 (1981)PRVDAQ0556-282110.1103/PhysRevD.23.2305] that superrenormalizable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov Chain Monte Carlo simulations of the lattice-regularized theory, frequentist and Bayesian data analysis, and considerations of a corresponding effective theory, we gather evidence that this is indeed the case.

Novel |V_{us}| Determination Using Inclusive Strange τ Decay and Lattice Hadronic Vacuum Polarization Functions.

We propose and apply a new approach to determining |V_{us}| using dispersion relations with weight functions having poles at Euclidean (spacelike) momentum which relate strange hadronic τ decay distributions to hadronic vacuum polarization (HVP) functions obtained from lattice quantum chromodynamics. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting |V_{us}| agrees well with determinations from K physics and three-family Cabibbo-Kobayashi-Maskawa unitarity. Advantages of this new approach over the conventional hadronic τ decay determination employing flavor-breaking sum rules are also discussed.

Exploratory Lattice QCD Study of the Rare Kaon Decay K

We report a first, complete lattice QCD calculation of the long-distance contribution to the K^{+}→π^{+}νν[over ¯] decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics, there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.