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 5.2 Flavor One of the biggest puzzles in the SM is the pattern of fermion masses and mixings. Both the quark and lepton sectors have significant mass hierarchies, whereas the mixing matrices take a very different form in the two sectors. We expect that at high energies, where the flavor pattern of the SM is established, there may be much larger rates of flavor-changing processes than the SM predicts. This is a strong motivation for searching for flavor-violating processes at high-energy colliders. 5.2.1 Lepton-flavor violating contact interactions 5.2.1 Lepton-flavor violating contact interactions In Fig. 22, these results are compared to the constraints on the analogous 4-fermion operator in the µ → 3e decay with various ansatz regarding flavor violation. The diagonal lines show the expected relationship between the two Wilson coefficients assuming (i) flavor anarchy (all coefficients ∼ 1), (ii) Minimal Leptonic Flavor Violation (MLFV) [192], (iii) the Wilson coefficients scale like the square root of the Yukawa couplings of the leptons involved in the flavor violation, and (iv) the Wilson coefficients scale like the product of the same Yukawa couplings.[15] While the muon decay sets the strongest limits assuming anarchical coefficients, we see that a 14 TeV muon collider could set a bound comparable to the current SINDRUM limit in the case of MLFV, and would be comparable to the Stage-I Mu3e sensitivity if the coefficients scale like the square root of the Yukawa couplings. In the extreme case, where the Wilson coefficients behave like the product of the two Yukawas, even a 3 TeV muon collider would provide a bound complementary to the final Mu3e sensitivity, with higher energy machines improving this bound by orders of magnitude. In addition to the τ3µ operators considered here, we expect roughly similar sensitivity to the µ +µ − → µ ±e ∓ process, as well as to the processes such as µ +µ − → τ ±e ∓ that violate lepton flavor by two units. Overall, we see that a muon collider would be capable of directly probing flavor-violating interactions that are quite complementary to future precision constraints. 5.2.2 Direct probes of lepton-flavor violation in the MSSM 5.2.2 Direct probes of lepton-flavor violation in the MSSM Charged lepton flavor violation in the MSSM arises as a result of the soft-breaking terms in the slepton mass matrix having non-diagonal entries in the basis where the SM lepton Yukawas are diagonal. In this case, the physical sleptons will be mixtures of different flavors, and their interactions with leptons and neutralinos/charginos will be flavor-violating. These flavor violating interactions lead to processes such as rare muon decays or muon-to-electron conversion at loop level, and thus, low energy experiments can indirectly probe these interactions with sensitivities extending beyond the TeV scale, depending on the flavor structure of the theory [179,193]. A high-energy muon collider, on the other hand, would not only be capable of producing superpartners at high masses, but would also provide direct measurements of the lepton-flavor violating processes that would complement these lowenergy probes and provide detailed insight into the mechanism of supersymmetry breaking. 5.2.2.1 Nearly-degenerate sleptons: As a first benchmark scenario we consider the situation where the selectron and smuon are nearly degenerate in mass. This situation is well-motivated from gauge-mediated supersymmetry breaking scenarios, and also leads to a strong suppression of the lepton-flavor violation via a “super-GIM” mechanism, allowing the superpartners to be relatively light. Such a scenario was previously studied in the context of e +e − collisions in Ref. [194], but for relatively light superpartners. A high-energy muon collider would allow similar tests with a substantially more impressive mass reach. 5.2.2.1 Nearly-degenerate sleptons: In the limit of a small mass splitting, the parameter governing the amount of flavor violation is given by The primary background for these flavor-violating processes at a lepton collider is production of the different flavor final states and missing energy via intermediate W bosons. The total cross section for this background, including branching ratios, is 52 fb at a 6 TeV collider (15/0.6 fb at a 14/100 TeV machine), but the kinematics of this process are quite different from the slepton-pair production signal of interest. Moreover, for the flavor-violating scenarios at hand, it is likely that the relevant slepton and neutralino masses will have already been measured from the corresponding flavor-conserving processes (for details on how this can be done, see e.g., Refs. [199, 200]). With the slepton masses known, it is then possible to fully reconstruct the two final state neutralino momenta by requiring that the neutralino and lepton momenta satisfy the slepton mass-shell constraint, along with conservation of energy and momentum. In general, these conditions will be impossible to satisfy for the background events, and indeed, we find in simulation that only ∼ 1/500 background events can reconstruct the neutralino momenta while satisfying conservation of energy, while ∼ 98% of the signal events reconstruct the momenta successfully. 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 [15] One should be cautious that if a flavorful ansatz is used, the inferred scale from the 100 TeV bounds may be low enough that an effective field theory description is no longer valid.

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