Dark sectors, consisting of new, light, weakly-coupled particles that do not interact with the known strong, weak, or electromagnetic forces, are a particularly compelling possibility for new physics. Nature may contain numerous dark sectors, each with their own beautiful structure, distinct particles, and forces. This review summarizes the physics motivation for dark sectors and the exciting opportunities for experimental exploration. It is the summary of the Intensity Frontier subgroup "New, Light, Weakly-coupled Particles" of the Community Summer Study 2013 (Snowmass). We discuss axions, which solve the strong CP problem and are an excellent dark matter candidate, and their generalization to axion-like particles. We also review dark photons and other dark-sector particles, including sub-GeV dark matter, which are theoretically natural, provide for dark matter candidates or new dark matter interactions, and could resolve outstanding puzzles in particle and astro-particle physics. In many cases, the exploration of dark sectors can proceed with existing facilities and comparatively modest experiments. A rich, diverse, and lowcost experimental program has been identified that has the potential for one or more game-changing discoveries. These physics opportunities should be vigorously pursued in the US and elsewhere.

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W W scattering is dominated at high energies by their longitudinal components, which are the most sensitive to the nature of the electroweak symmetry breaking. Prior to the discovery at the LHC of a Higgs-like particle, unitarization tools were extensively used to show that, in the absence of a light Higgs boson, new resonances resulting from the would-be strongly interacting electroweak sector would appear, and furthermore these techniques would approximately predict their masses, widths, and signal strengths. With the discovery of a Higgs-like particle now firmly established, we reinvestigate these techniques assuming this particle couples exactly as in the SM, but still being open to the possibility of an extended symmetry breaking sector. While the SM itself is free from problems with perturbative unitarity in the electroweak sector, "anomalous" self-couplings of the vector bosons -low-energy remnants of such higher-energy symmetry breaking sectors -are easily shown to reintroduce them. We demonstrate how new resonances should still appear in the scattering of electroweak vector bosons after imposing constraints from unitarity, and we discuss their ability to be probed with current and future LHC data.

We clarify some aspects of the LSZ formalism and wave-function renormalization for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyze the renormalization of the Cabibbo-Kobayashi-Maskawa ͑CKM͒ mixing matrix which is closely related to wavefunction renormalization. We critically review earlier attempts to define a set of ''on-shell'' wave-function renormalization constants. With the aid of extensive use of the Nielsen identities complemented by explicit calculations we corroborate that the counterterm for the CKM mixing matrix must be explicitly gauge independent and demonstrate that the commonly used prescription for the wave-function renormalization constants leads to gauge parameter dependent amplitudes, even if the CKM counterterm is gauge invariant as required. We show that a proper LSZ-compliant prescription leads to gauge independent amplitudes. The resulting wave-function renormalization constants necessarily possess absorptive parts, but we verify that they comply with the expected requirements concerning CP and CPT. The results obtained using this prescription are different ͑even at the level of the modulus squared of the amplitude͒ from the ones neglecting the absorptive parts in the case of top decay. The difference is numerically relevant.

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