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.

This is one of the six reports submitted to Snowmass by the International Muon Collider Collaboration. The Indico subscription page: https://indico.cern.ch/event/1130036/ contains the link to the reports and gives the possibility to subscribe to the papers.The policy for signatures is that, for each individual report, you can subscribe as "Author" or as "Signatory", defined as follows:-"Author" indicates that you did contribute to the results documented in the report in any form, including e.g. by participating to the discussions of the community meeting, sending comments on the drafts, etc, or that you plan to contribute to the future work. The "Authors" will appear as such in on arXiv. -"Signatory" means that you express support to the Collaboration effort and endorse the Collaboration plans. The "Signatories" list will be reported in the text only.

Muon colliders are an exciting possibility for reaching the highest energies possible on the shortest timescale. They potentially combine the greatest strengths of e+e− and pp colliders by bridging the energy versus precision dichotomy. In this paper we study the sensitivity of Higgs properties that can be achieved with a future 3 or 10 TeV muon collider from single Higgs production. The results presented here represent the first comprehensive picture for the precision achievable including backgrounds and using fast detector simulation with Delphes. Additionally, we compare the results of fast detector simulation with available full simulation studies that include the muon collider specific Beam Induced Background, and show the results are largely unchanged. We comment on some of the strengths and weaknesses of a high energy muon collider for Higgs physics alone, and demonstrate the complementarity of such a collider with the LHC and e+e− Higgs factories. Furthermore, we discuss some of the exciting avenues for improving future results from both theoretical and detector R&D that could be undertaken.

We present a formalism and detailed analytical results for soft-gluon resummation for 2 → n processes in single-particle-inclusive (1PI) kinematics. This generalizes previous work on resummation for 2 → 2 processes in 1PI kinematics. We also present soft anomalous dimensions at one and two loops for certain 2 → 3 processes involving top quarks and Higgs or Z bosons, and we provide some brief numerical results.

We discuss the associated production of a top quark with a photon via anomalous t-q-γ couplings, and present higher-order corrections from soft-gluon emission for the processes gq → tγ at LHC energies. We perform soft-gluon resummation at next-to-leadinglogarithm accuracy and derive approximate next-to-next-to-leading order (aNNLO) doubledifferential cross sections. We calculate at aNNLO the total tγ production cross sections and the top-quark transverse-momentum and rapidity distributions for various LHC energies, and show that the soft-gluon corrections are large and dominant in these processes.