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This statement from the American Linear Collider Committee to the P5 subpanel has three purposes. It presents a brief summary of the case for an $e^+e^-$ Higgs factory that has emerged from Snowmass 2021. It highlights the special virtues of the ILC that are shared with other linear colliders but not with circular colliders. Finally, it calls attention to the resources available in the ILC White Paper for Snowmass (arXiv:2203.07622). The ALCC urges P5 to move the Higgs factory forward as a global project by assigning the idea of an $e^+e^-$ Higgs factory high priority, initiating a global discussion of the technology choice and cost sharing, and offering the option of siting the Higgs factory in the U.S., Comment: 6 pages

We discuss considerations that can be used to formulate recommendations for initiating a lepton collider project that would provide precision studies of the Higgs boson and related electroweak phenomena., Comment: contribution to Snowmass 2021

A comprehensive review of physics at an e+e- Linear Collider in the energy range of sqrt{s}=92 GeV--3 TeV is presented in view of recent and expected LHC results, experiments from low energy as well as astroparticle physics.The report focuses in particular on Higgs boson, Top quark and electroweak precision physics, but also discusses several models of beyond the Standard Model physics such as Supersymmetry, little Higgs models and extra gauge bosons. The connection to cosmology has been analyzed as well., Comment: 179 pages, plots and references updated, version to be published at EPJC

High-precision analyses of supersymmetry parameters aim at reconstructing the fundamental supersymmetric theory and its breaking mechanism. A well defined theoretical framework is needed when higher-order corrections are included. We propose such a scheme, Supersymmetry Parameter Analysis SPA, based on a consistent set of conventions and input parameters. A repository for computer programs is provided which connect parameters in different schemes and relate the Lagrangian parameters to physical observables at LHC and high energy e+e- linear collider experiments, i.e., masses, mixings, decay widths and production cross sections for supersymmetric particles. In addition, programs for calculating high-precision low energy observables, the density of cold dark matter (CDM) in the universe as well as the cross sections for CDM search experiments are included. The SPA scheme still requires extended efforts on both the theoretical and experimental side before data can be evaluated in the future at the level of the desired precision. We take here an initial step of testing the SPA scheme by applying the techniques involved to a specific supersymmetry reference point., Comment: 17pp; references corrected

Several proposals are being developed around the world for an e+e- linear collider with an initial center of mass energy of 500 GeV. In this paper, we will discuss why a project of this type deserves priority as the next major initiative in high energy physics., Comment: 65 pages, 17 figures, LaTeX, minor erratum corrections

The partial breaking of supersymmetry in flat space can be accomplished using any one of three dual representations for the massive N=1 spin-3/2 multiplet. Each of the representations can be ``unHiggsed'', which gives rise to a set of dual N=2 supergravities and supersymmetry algebras., Comment: 12 pages, 1 figure, cosmetic changes

We provide a mini-guide to some of the possible manifestations of weak scale supersymmetry. For each of six scenarios we provide a brief description of the theoretical underpinnings, the adjustable parameters, a qualitative description of the associated phenomenology at future colliders, comments on how to simulate each scenario with existing event generators., Comment: Report of Snowmass Supersymmetry Theory Working Group; 14 pages plus 3 figures using latex2e and snow2e.cls; this version has corrected a number of typos from the first version

We study the gold-plated purely leptonic signal and background rates at the LHC for the $ZZ,$ $W^{+}W^-,$ $W^\pm Z$ and $W^\pm W^\pm$ final states associated with strongly interacting electroweak symmetry breaking. We work at an energy of $\sqrt s = 14$ TeV, and develop a combination of back-to-back leptonic, central-jet-vetoing and forwaring cuts that suppresses the Standard-Model backgrounds. We find that the LHC with an annual luminosity of 100 fb$^{-1}$ will achieve a reasonably good sensitivity to the physics of strongly interacting electroweak symmetry breaking., Comment: 14 pages, LaTeX, final version (with minor changes) to appear in Phys. Rev. D; postscript file available via anonymous ftp at ftp://ucdhep.ucdavis.edu/han/sews/paper_ww.ps and figure files separated as figs.uu or *.ps

We compute the full set of weak-scale gauge and Yukawa threshold corrections in the minimal supersymmetric standard model, and use them to study the effects of the supersymmetric particle spectrum on gauge and Yukawa coupling unification., Comment: Talk given at SUSY94, Warsaw, Poland.

We use nonlinear realizations to describe the spontaneous breaking of $N=2$ supersymmetry to $N=1$ in four dimensions. We identify the Goldstone multiplet with an $N=1$ chiral superfield, and show that chiral $N=1$ matter is consistent with the partially broken $N=2$ supersymmetry. We find that the chiral matter can be in any representation of the gauge group; no mirror particles are required. We present the Goldstone action and the general couplings to $N=1$ matter to the first nontrivial order in the scale of symmetry breaking., Comment: JHU-TIPAC-94011, 9 pages. References added

In this paper we survey the signals and backgrounds for a strongly-interacting electroweak symmetry breaking sector at hadron supercolliders in the TeV region. We study the process pp->WWX, and compute the rates for the ``gold-plated'' channels, where W^{+/-}->l^{+/-}\nu and Z -> l^+l^- (l = e,\mu), for a wide variety of models. Using a forward jet-tag, a central jet-veto and a back-to-back lepton cut to suppress the Standard Model backgrounds, we demonstrate that the SSC and LHC have substantial sensitivity to strong interactions in the electroweak symmetry breaking sector., Comment: 39 pages, FERMILAB-Pub-93/040-T, JHU-TIPAC-930008, MAD/PH/747, MSUHEP 93/05, NUB 3060-93 TH, NUHEP-TH-93-13, UCD-93-5 (uses PHYZZX with the tables.tex macro; nine pages of PostScript figures in uuencoded format)

We use chiral perturbation theory to show that pseudo-Goldstone boson scattering and gluon fusion probe different aspects of electroweak symmetry breaking at hadron colliders. In particular, the physics responsible for unitarizing the lowest-order pseudo-Goldstone boson scattering amplitudes need not significantly affect the gluon fusion process. We first show this within the context of strict chiral perturbation theory, and then discuss it using the language of resonances., Comment: 14 pp, uses phyzzx 3 figures appended as postscript files. FERMILAB-PUB-92/177-T

We compute the effects of anomalous gauge-boson couplings at high-energy hadron colliders using next-to-leading order $SU(2) \times SU(2)$ chiral perturbation theory. By comparing the yields from the universal $p^2$ terms with those arising from new physics at order $p^4$, we estimate the sensitivity of the SSC and LHC to the indirect effects of electroweak symmetry breaking., Comment: FERMILAB-PUB-92/75-T; Figures not included