Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2 Muons vs. Protons 2.1 Muon annihilation 2.1 Muon annihilation 2.2 Vector boson fusion 2.2 Vector boson fusion 2.3 Annihilation vs. VBF 2.3 Annihilation vs. VBF 2.4 Signal vs. background 2.4 Signal vs. background 3 Muon Colliders Are Gauge Boson Colliders 3 Muon Colliders Are Gauge Boson Colliders 3.1 From the effective vector approximation to PDFs 3.1 From the effective vector approximation to PDFs 3.2 PDFs with broken electroweak symmetry 3.2 PDFs with broken electroweak symmetry 3.3 Impact of subleading logs 3.3 Impact of subleading logs 3.4 Finite mass effects 3.4 Finite mass effects 4 Physics 4.1 Electroweak symmetry breaking 4.1 Electroweak symmetry breaking 4.2 Dark matter 4.2 Dark matter 4.3 Naturalness 4.3 Naturalness 5 Complementarity 5.1 EDMs 5.1 EDMs 5.2 Flavor 5.2 Flavor 5.3 Gravitational waves 5.3 Gravitational waves 6 Summary and Future Directions 6 Summary and Future Directions Acknowledgments Acknowledgments A. Simplified Models A. Simplified Models A.1 Standard Model A.1 Standard Model A.2 Supersymmetry A.2 Supersymmetry A.3 Vector-like quarks A.3 Vector-like quarks A.4 Higgs portal A.4 Higgs portal A.5 Hidden valleys A.5 Hidden valleys A.6 Axion-like particles A.6 Axion-like particles References References 5.3 Gravitational waves The central importance and capabilities of a future collider must be seen within the context of the broader experimental efforts in particle physics. We have already discussed the connections between possible discoveries in precision flavor and CP violation experiments, direct and indirect dark matter detection, as well as searches for new light fields and dark forces. On the cosmological front, we are entering an era in which dramatic new forms of “fossil” evidence for BSM physics may be found, within stochastic gravitational wave backgrounds (SGWB) [201, 202] and within primordial non-Gaussianities in Large Scale Structure (LSS) and high-redshift 21-cm 3D “maps” [203]. While discoveries in any of these non-collider experiments would be spectacular, powerful new colliders would provide the “gold standard” laboratory conditions to corroborate, connect, extend, and analyze their full significance. First order cosmological phase transitions that could occur due to extensions of the SM or within dark sectors could be powerful sources of SGWB, while possibly providing the non-equilibrium conditions needed for generating matter asymmetries. The peak SGWB frequency, after redshifting from the time of production in the very early universe, is given by where TPT is the temperature immediately after the phase transition, 1/β is essentially its duration, and HPT is the Hubble expansion rate during this era [204, 205]. Typically, one expects β ∼ O(10 - 100)HPT. Fortuitously then, for TPT in the BSM-motivated range, TeV - 100 TeV, we can expect SGWB in roughly the mHz - Hz range accessible to proposed gravitational wave detectors such as LISA, BBO, and DECIGO. If a SGWB from a phase transition is detected, it would be critical to piece together the information in its frequency spectrum with the complementary microphysics accessible within collider experiments to whatever extent possible. Quite plausibly, these elements relate to extensions of the SM Higgs sector. A high energy muon collider provides a balance of potential to probe the Higgs sector, to create very massive BSM states related to the phase transition, and given its clean environment to possibly produce and diagnose a small number of events resulting from the presence of a dark sector in case the SGWB originated there. Upcoming precision LSS and 21-cm surveys offer the potential to detect heavy particle production and propagation during inflation, imprinted on the non-Gaussian bispectrum in distinctive non-local effects (non-analytic in co-moving momenta). This field of “cosmological collider physics” is sensitive to particle masses of order the inflationary Hubble scale or even somewhat higher [215, 216]. (For very recent work and references, see [217]). We do not as yet know the scales of inflation. If new particles are discovered in cosmological nonGaussianities, they may lie far above the reach of terrestrial colliders, in which case they would give complementary information to what we learn from even a powerful muon collider. But there are two scenarios in which they could give us a (pre)view of collider-accessible physics: (i) if the inflationary Hubble scale is of order 100 TeV or less, then obviously “cosmological collider physics” may directly be within reach of future terrestrial colliders; (ii) even if the inflationary Hubble scale is orders of magnitude above the TeV scale, there is a “heavy-lifting” mechanism [218] whereby the particles seen in non-Gaussianities were given inflationary scale masses through strong curvature effects, but such effects are negligible today so that the particles may now be within terrestrial collider reach. Authors:
(1) Hind Al Ali, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(2) Nima Arkani-Hamed, School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA;
(3) Ian Banta, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(4) Sean Benevedes, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(5) Dario Buttazzo, INFN, Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy;
(6) Tianji Cai, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(7) Junyi Cheng, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(8) Timothy Cohen, Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;
(9) Nathaniel Craig, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(10) Majid Ekhterachian, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA;
(11) JiJi Fan, Department of Physics, Brown University, Providence, RI 02912, USA;
(12) Matthew Forslund, C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794, USA;
(13) Isabel Garcia Garcia, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA;
(14) Samuel Homiller, Department of Physics, Harvard University, Cambridge, MA 02138, USA;
(15) Seth Koren, Department of Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA;
(16) Giacomo Koszegi, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(17) Zhen Liu, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA and School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA;
(18) Qianshu Lu, Department of Physics, Harvard University, Cambridge, MA 02138, USA;
(19) Kun-Feng Lyu, Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., P.R.C;
(20) Alberto Mariotti, Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel, and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels, Belgium;
(21) Amara McCune, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(22) Patrick Meade, C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794, USA;
(23) Isobel Ojalvo, Princeton University, Princeton, NJ 08540, USA;
(24) Umut Oktem, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(25) Diego Redigolo, CERN, Theoretical Physics Department, Geneva, Switzerland and INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy;
(26) Matthew Reece, Department of Physics, Harvard University, Cambridge, MA 02138, USA;
(27) Filippo Sala, LPTHE, CNRS & Sorbonne Universite, 4 Place Jussieu, F-75252 Paris, France
(28) Raman Sundrum, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA;
(29) Dave Sutherland, INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy;
(30) Andrea Tesi, INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Department of Physics and Astronomy, University of Florence, Italy;
(31) Timothy Trott, Department of Physics, University of California, Santa Barbara, CA 93106, USA;
(32) Chris Tully, Princeton University, Princeton, NJ 08540, USA;
(33) Lian-Tao Wang, Department of Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA;
(34) Menghang Wang, Department of Physics, University of California, Santa Barbara, CA 93106, USA. Authors: Authors: (1) Hind Al Ali, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (2) Nima Arkani-Hamed, School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA; (3) Ian Banta, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (4) Sean Benevedes, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (5) Dario Buttazzo, INFN, Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy; (6) Tianji Cai, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (7) Junyi Cheng, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (8) Timothy Cohen, Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA; (9) Nathaniel Craig, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (10) Majid Ekhterachian, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA; (11) JiJi Fan, Department of Physics, Brown University, Providence, RI 02912, USA; (12) Matthew Forslund, C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794, USA; (13) Isabel Garcia Garcia, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA; (14) Samuel Homiller, Department of Physics, Harvard University, Cambridge, MA 02138, USA; (15) Seth Koren, Department of Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA; (16) Giacomo Koszegi, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (17) Zhen Liu, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA and School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA; (18) Qianshu Lu, Department of Physics, Harvard University, Cambridge, MA 02138, USA; (19) Kun-Feng Lyu, Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., P.R.C; (20) Alberto Mariotti, Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel, and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels, Belgium; (21) Amara McCune, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (22) Patrick Meade, C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794, USA; (23) Isobel Ojalvo, Princeton University, Princeton, NJ 08540, USA; (24) Umut Oktem, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (25) Diego Redigolo, CERN, Theoretical Physics Department, Geneva, Switzerland and INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy; (26) Matthew Reece, Department of Physics, Harvard University, Cambridge, MA 02138, USA; (27) Filippo Sala, LPTHE, CNRS & Sorbonne Universite, 4 Place Jussieu, F-75252 Paris, France (28) Raman Sundrum, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA; (29) Dave Sutherland, INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy; (30) Andrea Tesi, INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Department of Physics and Astronomy, University of Florence, Italy; (31) Timothy Trott, Department of Physics, University of California, Santa Barbara, CA 93106, USA; (32) Chris Tully, Princeton University, Princeton, NJ 08540, USA; (33) Lian-Tao Wang, Department of Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA; (34) Menghang Wang, Department of Physics, University of California, Santa Barbara, CA 93106, USA. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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