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 3.2 PDFs with broken electroweak symmetry where Nγ counts the number of ways the photon can annihilate to quark and lepton pairs, and the plus function is defined in the standard way: The boundary conditions are where θW is the weak mixing angle, and the mixed Zγ PDF accounts for possible interference effects among diagrams involving a Z + γ initial state. For reference, the parton luminosity for Z and γ initial states is derived using the combination The full DGLAP evolution equations are given in [53]. To provide an example, the DGLAP evolution equation for fB_ is where the splitting functions are given by[4] 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 [3] We do note that there are some subtle questions about how to treat the longitudinal components, such that the Goldstone equivalence theorem is respected. However, this issue only appears at subleading order so we do not have to treat it carefully here; see [53] for a discussion.

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