We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models.

We propose leveraging our proficiency for detecting Higgs resonances by using the Higgs as a tagging object for new heavy physics. In particular, we argue that searches for exotic Higgs production from decays of color-singlet fields with electroweak charges could beat current searches at the LHC which look for their decays to vectors. As an example, we study the production and decay of vector-like leptons which admit Yukawa couplings with SM leptons. We find that bounds from Run 2 searches are consistent with anywhere from hundreds to many thousands of Higgses having been produced in their decays over the same period, depending on the representation. Dedicated searches for these signatures may thus be able to significantly improve our reach at the electroweak energy frontier.

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In this paper we study on-shell diagrams in 𝒩 < 4 supersymmetric Yang-Mills (SYM) theory. These are on-shell gauge invariant objects which appear as cuts of loop integrands in the context of generalized unitarity and serve as building blocks for amplitudes in recursion relations. In the dual formulation, they are associated with cells of the positive Grassmannian G+(k, n) and the on-shell functions can be reproduced as canonical differential forms. While for the case of the 𝒩 = 4 maximally supersymmetric Yang-Mills theory all poles in on-shell diagrams correspond to IR poles when the momentum flows in edges are zero, for 𝒩 < 4 SYM theories there are new UV poles when the loop momenta go to infinity. These poles originate from the prefactor of the canonical dlog form and do not correspond to erasing edges in on-shell diagrams. We show that they can be interpreted as a diagrammatic operation which involves pinching a loop and performing a “non-planar twist” on external legs, which gives rise to a non-planar on-shell diagram. Our result provides an important clue on the role of poles at infinite momenta in on-shell scattering amplitudes, and the relation to non-planar on-shell functions.