# Interim report for the International Muon Collider Collaboration

###### Abstract

This document summarises the International Muon Collider Collaboration (IMCC)
progress and status of the Muon Collider R&D programme.

###### keywords:

Accelerator physics, Muon colliders, Accelerator and Detector Technology,
Higgs Physics, Physics beyond the Standard Model (BSM).

Interim report for the
International Muon Collider Collaboration (IMCC)

C. Accettura1, S. Adrian2, R. Agarwal3, C. Ahdida1, C. Aimé4, A. Aksoy1,5, G.
L. Alberghi6, S. Alden7, N. Amapane8,9, D. Amorim1, P. Andreetto10, F.
Anulli11, R. Appleby12, A. Apresyan13, P. Asadi14, M. Attia Mahmoud15, B.
Auchmann16,1, J. Back17, A. Badea18, K. J. Bae19, E. J. Bahng20, L.
Balconi21,22, F. Balli23, L. Bandiera24, C. Barbagallo1, R. Barlow25, C.
Bartoli26, N. Bartosik9, E. Barzi13, F. Batsch1, M. Bauce11, M. Begel27, J. S.
Berg27, A. Bersani28, A. Bertarelli1, F. Bertinelli1, A. Bertolin10, P.
Bhat13, C. Bianchi26, M. Bianco1, W. Bishop17,29, K. Black30, F. Boattini1, A.
Bogacz31, M. Bonesini32, B. Bordini1, P. Borges de Sousa1, S. Bottaro33, L.
Bottura1, S. Boyd17, M. Breschi26,6, F. Broggi22, M. Brunoldi34,4, X. Buffat1,
L. Buonincontri35,10, P. N. Burrows36, G. C. Burt37,38, D. Buttazzo39, B.
Caiffi28, S. Calatroni1, M. Calviani1, S. Calzaferri34, D. Calzolari1, C.
Cantone40, R. Capdevilla13, C. Carli1, C. Carrelli41, F. Casaburo11,42, M.
Casarsa43, L. Castelli42,11, M. G. Catanesi44, L. Cavallucci26,6, G.
Cavoto42,11, F. G. Celiberto45, L. Celona46, A. Cemmi41, S. Ceravolo40, A.
Cerri47,48,39, F. Cerutti1, G. Cesarini40, C. Cesarotti49, A. Chancé23, N.
Charitonidis1, M. Chiesa4, P. Chiggiato1, V. L. Ciccarella40,42, P. Cioli
Puviani50, A. Colaleo51,44, F. Colao41, F. Collamati11, M. Costa52, N.
Craig53, D. Curtin54, L. D’Angelo55, G. Da Molin56, H. Damerau1, S. Dasu30, J.
de Blas57, S. De Curtis58, H. De Gersem55, T. Del Moro42,41, J.-P. Delahaye1,
D. Denisov27, H. Denizli59, R. Dermisek60, P. Desiré Valdor1, C. Desponds1, L.
Di Luzio10, E. Di Meco40, K. F. Di Petrillo18, I. Di Sarcina41, E.
Diociaiuti40, T. Dorigo10,61, K. Dreimanis62, T. du Pree63,64, T. Edgecock25,
S. Fabbri1, M. Fabbrichesi43, S. Farinon28, G. Ferrand23, J. A. Ferreira
Somoza1, M. Fieg65, F. Filthaut66,63, P. Fox13, R. Franceschini67,68, R.
Franqueira Ximenes1, M. Gallinaro56, M. Garcia-Sciveres3, L. Garcia-Tabares69,
R. Gargiulo42, C. Garion1, M. V. Garzelli70, M. Gast71, C. E. Gerber72, L.
Giambastiani35,10, A. Gianelle10, E. Gianfelice-Wendt13, S. Gibson7, S.
Gilardoni1, D. A. Giove22, V. Giovinco1,C. Giraldin35,10, A. Glioti23, A.
Gorzawski73,1, M. Greco68, C. Grojean74, A. Grudiev1, E. Gschwendtner1, E.
Gueli11,11, N. Guilhaudin1, C. Han75, T. Han76, J. M. Hauptman20, M.
Herndon30, A. D. Hillier29, M. Hillman77, T. R. Holmes77, S. Homiller78, S.
Jana79, S. Jindariani13, S. Johannesson73, B. Johnson77, O. R. Jones1, P.-B.
Jurj80, Y. Kahn13, R. Kamath80, A. Kario64, I. Karpov1, D. Kelliher29, W.
Kilian81, R. Kitano82, F. Kling74, A. Kolehmainen1, K. C. Kong83, J. Kosse16,
G. Krintiras83, K. Krizka84, N. Kumar85, E. Kvikne1, R. Kyle86, E. Laface73,
K. Lane87, A. Latina1, A. Lechner1, J. Lee19, L. Lee77, S. W. Lee19, T.
Lefevre1, E. Leonardi11, G. Lerner1, P. Li88, Q. Li89, T. Li90, W. Li91, R. Li
Voti42,40, M. Lindroos73, R. Lipton13, D. Liu76, M. Liu1, Z. Liu88, A.
Lombardi1, S. Lomte30, K. Long80,29, L. Longo44, J. Lorenzo92, R. Losito1, I.
Low93,94, X. Lu17, D. Lucchesi35,10, T. Luo3, A. Lupato35,10, E. Métral1, K.
Mękała95,74, Y. Ma6, J. M. Mańczak1, S. Machida29, T. Madlener74, L.
Magaletti96,44, M. Maggi44, H. Mainaud Durand1, F. Maltoni97,26,6, M.
Mandurrino9, C. Marchand23, F. Mariani22,42, S. Marin1, S. Mariotto21,22, S.
Martin-Haugh29, M. R. Masullo98, G. S. Mauro46, A. Mazzolari24,99, B. Mele11,
F. Meloni74, X. Meng100, M. Mentink1, R. Miceli26, N. Milas73, A. Mohammadi30,
D. Moll55, A. Montella101, M. Morandin10, M. Morrone1, T. Mulder1, R.
Musenich28, M. Nardecchia42,43, F. Nardi35, D. Neuffer13, D. Newbold29, D.
Novelli28,42, M. Olvegård102, Y. Onel103, D. Orestano67,68, J. Osborne1, S.
Otten64, Y. M. Oviedo Torres104, D. Paesani40,1, S. Pagan Griso3, D. Pagani6,
K. Pal1, M. Palmer27, A. Pampaloni28, P. Panci39,105, P. Pani74, Y.
Papaphilippou1, R. Paparella22, P. Paradisi35,10, A. Passeri68, N. Pastrone9,
A. Pellecchia44, F. Piccinini4, H. Piekarz13, T. Pieloni106, J. Plouin23, A.
Portone92, K. Potamianos17, J. Potdevin106,1, S. Prestemon3, T. Puig107, J.
Qiang3, L. Quettier23, T. R. Rabemananjara108,63, E. Radicioni44, R.
Radogna51,44, I. C. Rago11, A. Ratkus62, E. Resseguie3, J. Reuter74, P. L.
Ribani26, C. Riccardi34,4, S. Ricciardi29, T. Robens109, Y. Robert1, C.
Rogers29, J. Rojo63,108, M. Romagnoni99,24, K. Ronald86,38, B. Rosser18, C.
Rossi1, L. Rossi21,22, L. Rozanov18, M. Ruhdorfer110, R. Ruiz111, F. S.
Queiroz104,111, S. Saini47,1, F. Sala26,6, C. Salierno26, T. Salmi112, P.
Salvini4,34, E. Salvioni47, N. Sammut113, C. Santini22, A. Saputi24, I.
Sarra40, G. Scarantino22,42, H. Schneider-Muntau114, D. Schulte1, J. Scifo41,
T. Sen13, C. Senatore115, A. Senol59, D. Sertore22, L. Sestini10, R. C. Silva
Rêgo104,111, F. M. Simone96,44, K. Skoufaris1, G. Sorbello116,46, M.
Sorbi21,22, S. Sorti21,22, L. Soubirou23, D. Spataro74, A. Stamerra51,44, S.
Stapnes1, G. Stark117, M. Statera22, B. M. Stechauner118,1, S. Su119, W. Su75,
X. Sun89, A. Sytov24, J. Tang75, J. Tang120,100, R. Taylor1, H. Ten Kate64,1,
P. Testoni92, L. S. Thiele2,1, R. Tomas Garcia1, M. Topp-Mugglestone1,36, T.
Torims62,1, R. Torre28, L. T. Tortora68,67, S. Trifinopoulos49, S.-A.
Udongwo2,1, I. Vai34,4, R. U. Valente22, U. van Rienen2, R. van Weelderen1, M.
Vanwelde1, G. Velev13, R. Venditti51,44, A. Vendrasco77, A. Verna41, A.
Verweij1, P. Verwilligen44, Y. Villamzar104, L. Vittorio121, P. Vitulo34,4, I.
Vojskovic73, D. Wang89, L.-T. Wang18, X. Wang122, M. Wendt1, M. Widorski1, M.
Wozniak1, Y. Wu123, A. Wulzer124,125, K. Xie76, Y. Yang126, Y. C. Yap74, K.
Yonehara13, H. D. Yoo127, Z. You75, M. Zanetti35, A. Zaza51,44, L. Zhang86, R.
Zhu128,129, A. Zlobin13, D. Zuliani35,10, J. F. Zurita130

1 European Organization for Nuclear Research, Geneva, Switzerland,
2 University of Rostock, Rostock, Germany,
3 Lawrence Berkeley National Laboratory, Berkeley, CA, United States,
4 INFN Sezione di Pavia, Pavia, Italy,
5 Ankara University, Ankara, Türkiye,
6 INFN Sezione di Bologna, Bologna, Italy,
7 Royal Holloway University of London, Egham, United Kingdom,
8 University of Turin, Turin, Italy,
9 INFN Sezione di Torino, Turin, Italy,
10 INFN Sezione di Padova, Padua, Italy,
11 INFN Sezione di Roma I, Rome, Italy,
12 University of Manchester, Manchester, United Kingdom,
13 Fermi National Accelerator Laboratory, Batavia, IL, United States,
14 University of Oregon, Eugene, OR, United States,
15 Fayoum University, Al Fayyūm,, Egypt,
16 Paul Scherrer Institute, Villigen, Switzerland,
17 University of Warwick, Coventry, United Kingdom,
18 University of Chicago, Chicago IL, United States America,
19 Kyungpook National University, Daegu, South Korea,
20 Iowa State University, Ames, IA, United States,
21 University of Milan, Milan, Italy,
22 INFN Laboratorio LASA, Segrate, Italy,
23 Institut de recherche sur les lois fondamentales de l’Univers, Gif-sur-
Yvette, France,
24 INFN Sezione di Ferrara, Ferrara ,Italy,
25 University of Huddersfield, Huddersfield, United Kingdom,
26 University of Bologna, Bologna, Italy,
27 Brookhaven National Laboratory, Upton, NY, United States,
28 INFN sezione di Genova, Genova, Italy,
29 ISIS Neutron and Muon Source, Didcot, United Kingdom,
30 University of Wisconsin-Madison, Madison, WI, United States,
31 Thomas Jefferson National Accelerator Facility, Newport News, VA, United
States,
32 INFN Sezione di Milano, Milan,Italy,
33 Tel Aviv University, Tel Aviv, Israel,
34 University of Pavia, Pavia, Italy,
35 University of Padua, Padua, Italy,
36 John Adams Institute for Accelerator Science, Oxford, United Kingdom,
37 Lancaster University, Lancaster, United Kingdom,
38 Cockcroft Institute, Daresbury, United Kingdom,
39 INFN Sezione di Pisa, Pisa, Italy,
40 INFN National Laboratory of Frascati, Frascati, Italy,
41 National Agency for New Technologies, Energy and Sustainable Economic
Development, Rome, Italy,
42 Sapienza University of Rome, Rome,Italy,
43 INFN Sezione di Trieste, Trieste, Italy,
44 INFN Sezione di Bari, Bari, Italy,
45 Universidad de Alcalá, Alcalá de Henares, Spain,
46 INFN Laboratori Nazionali del Sud, Catania, Italy,
47 University of Sussex, Brighton, United Kingdom,
48 University of Siena, Siena, Italy,
49 Massachusetts Institute of Technology, Cambridge, MA, United States,
50 Polytechnic University of Turin, Turin, Italy,
51 University of Bari, Bari, Italy,
52 Perimeter Institute, Waterloo, ON, Canada,
53 University of California, Santa Barbara, Santa Barbara, CA, United States,
54 University of Toronto, Toronto, ON, Canada,
55 Technical University of Darmstadt, Darmstadt, Germany,
56 LIP—Laboratory of Instrumentation and Experimental Particle Physics,
Lisbon, Portugal,
57 Universidad de Granada, Granada, Spain,
58 INFN Sezione di Firenze, Sesto Fiorentino, Italy,
59 Bolu Abant Izzet Baysal University, Bolu, Türkiye,
60 Indiana University, Bloomington, IN, United States,
61 Luleȧ University of Technology, Luleȧ, Sweden,
62 Riga Technical University, Riga, Latvia,
63 National Institute for Subatomic Physics, Amsterdam, Netherlands,
64 University of Twente, Enschede, Netherlands,
65 University of California, Irvine, Irvine, CA, United States,
66 Radboud University Nijmegen, Nijmegen, Netherlands,
67 Roma Tre University, Rome, Italy,
68 INFN Sezione di Roma III, Rome, Italy,
69 Centro de Investigaciones Energéticas, Medioambientales y Tecnologicas,
Madrid, Spain,
70 Universität Hamburg, Hamburg, Germany,
71 Karlsruhe Institute of Technology, Karlsruhe, Germany,
72 University of Illinois at Chicago, Chicago, IL, United States,
73 European Spallation Source, Lund, Sweden,
74 Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany,
75 Sun Yat-sen University, Guangzhou, China,
76 University of Pittsburgh, Pittsburgh, PA, United States,
77 University of Tennessee at Knoxville, Knoxville, TN, United States,
78 Harvard University, Cambridge, MA, United States,
79 Max Planck Institute for Nuclear Physics, Heidelberg, Germany,
80 Imperial College London, London, United Kingdom,
81 University of Siegen, Siegen, Germany,
82 High Energy Accelerator Research Organization, Tsukuba, Japan,
83 University of Kansas, Lawrence, KS, United States,
84 University of Birmingham, Birmingham, United Kingdom,
85 Shree Guru Gobind Singh Shree Guru Gobind Singh Tricentenary University,
Gurgaon, India,
86 University of Strathclyde, Glasgow, United Kingdom,
87 Boston University, Boston, MA, United States,
88 University of Minnesota, Minneapolis, MN, United States,
89 Peking University, Beijing, China,
90 Nankai University, Tianjin, China,
91 Rice University, Houston, TX, United States,
92 Fusion for Energy, Barcelona, Spain,
93 Northwestern University, Evanston, IL, United States,
94 Argonne National Laboratory, Lemont, IL, United States,
95 University of Warsaw, Warsaw, Poland,
96 Polytechnic University of Bari, Bari, Italy,
97 UCLouvain, Louvain-la-Neuve, Belgium,
98 INFN Sezione di Napoli, Naples, Italy,
99 University of Ferrara, Ferrara, Italy,
100 Institute of High Energy Physics, Beijing, China,
101 Stockholm University,Stockholm, Sweden,
102 Uppsala University, Uppsala, Sweden,
103 University of Iowa, Iowa City, IA, United States,
104 Universidade Federal do Rio Grande do Norte, Campus Universitário, Natal,
Brazil,
105 University of Pisa, Pisa, Italy,
106 École polytechnique fédérale de Lausanne, Lausanne, Switzerland,
107 Institut de Ciencia de Materials de Barcelona, Cerdanyola del Vallès,
Spain,
108 Vrije Universiteit Amsterdam, Amsterdam, Netherlands,
109 Rudjer Boskovic Institute, Zagreb, Croatia,
110 Cornell University, Ithaca, NY, United States,
111 Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland,
112 Tampere University, Tampere, Finland,
113 University of Malta, Msida, Malta,
114 CS&T, France,
115 University of Geneva, Geneva, Switzerland,
116 University of Catania, Catania, Italy,
117 University of California, Santa Cruz, Santa Cruz, CA, United States,
118 TU Wien, Vienna, Austria,
119 University of Arizona, Tucson, AZ, United States,
120 University of Science and Technology of China, Hefei, China,
121 Laboratoire d’Annecy de Physique des Particules LAPP, Annecy, France,
122 University of California, San Diego, La Jolla, CA, United States,
123 Nanjing Normal University, Nanjing, China,
124 Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain,
125 Institut de Física d’Altes Energies (IFAE), Barcelona, Spain,
126 University of Southampton, Southampton, United Kingdom,
127 Yonsei University, Seoul, South Korea,
128 Institute of Modern Physics, Lanzhou, China,
129 University of Chinese Academy of Sciences, Beijing, China,
130 Instituto de Física Corpuscular, Paterna, Spain

###### Contents

  1. Executive summary
  2. 0.1 Overview of collaboration goals, challenges and R&D programme
    1. 0.1.1 Motivation
    2. 0.1.2 The accelerator concept
    3. 0.1.3 Muon collider challenges
    4. 0.1.4 Developing the muon collider study
    5. 0.1.5 R&D programme
    6. 0.1.6 Timeline and staging
    7. 0.1.7 Site considerations
    8. 0.1.8 Synergies and outreach
  3. 0.2 Physics opportunities
    1. 0.2.1 Exploring the energy frontier
    2. 0.2.2 Synergies and staging
  4. 0.3 Physics, detector and accelerator interface
    1. 0.3.1 Physics and detector needs
    2. 0.3.2 Machine-detector interface
    3. 0.3.3 Neutrino beams
  5. 0.4 Detector
    1. 0.4.1 Concepts
    2. 0.4.2 Performance
    3. 0.4.3 Technologies
    4. 0.4.4 Software and computing: Concepts
  6. 0.5 Accelerator design
    1. 0.5.1 Proton complex
    2. 0.5.2 Muon production and cooling
    3. 0.5.3 Acceleration
    4. 0.5.4 Collider ring
    5. 0.5.5 Collective effects
  7. 0.6 Accelerator technologies
    1. 0.6.1 Magnets
    2. 0.6.2 Power converters for the muon acceleration to TeV energies
    3. 0.6.3 RF
    4. 0.6.4 Target
    5. 0.6.5 Radiation shielding
    6. 0.6.6 Muon cooling cell
    7. 0.6.7 Cryogenics
    8. 0.6.8 Vacuum system
    9. 0.6.9 Instrumentation
    10. 0.6.10 Radiation protection
    11. 0.6.11 Civil engineering
    12. 0.6.12 Movers
    13. 0.6.13 Infrastructure
    14. 0.6.14 General safety considerations
  8. 0.7 Synergies
    1. 0.7.1 Technologies
    2. 0.7.2 Technology applications
    3. 0.7.3 Facilities
    4. 0.7.4 Synergies—summary
  9. 0.8 Development of the R&D programme
    1. 0.8.1 Demonstrator
    2. 0.8.2 RF test stand
    3. 0.8.3 Magnet test facility
    4. 0.8.4 Other test infrastructure required (HiRadMat, …)
  10. 0.9 Implementation considerations
    1. 0.9.1 Timeline considerations
    2. 0.9.2 Site considerations
    3. 0.9.3 Costing and power consumption considerations

## Executive summary

The recent European Strategy for Particle Physics Update (ESPPU) and the
Snowmass processes have firmly established the need to get to the 10 TeV
partonic center-of-mass (pCOM) energy collisions in order to make a major step
forward in our understanding of particle physics. The International Muon
Collider Collaboration (IMCC) was formed in 2020 to secure a novel,
sustainable path toward this goal by developing the muon collider concept and
addressing the related challenges. The collaboration obtained strong support
by many partner institutes and funding agencies across the globe, the European
Union and recently the Particle Physics Project Prioritization Panel (P5) in
the US. It is currently hosted at CERN and has 50 full and several associated
members. IMCC aims to develop a staged approach to a 10 TeV, high-luminosity
muon collider.

The report summarizes progress made since the inception of IMCC and describes
what is expected to be achieved by 2026 with currently secured resources. It
also outlines important additional accelerator and detector studies that could
be addressed and completed by 2026, if additional resources were made
available. In 2025, IMCC will provide the ESPPU with an evaluation report that
assesses the muon collider potential and an R&D path plan. Later it will
submit the updated information to strategy process in the U.S. and potentially
other regions and countries.

### Motivation

A muon collider with 10 TeV energy would enable an exceptionally broad physics
programme. It could discover new particles with presently inaccessible mass,
including weakly interacting massive particles (WIMP) dark matter candidates.
It could discover cracks in the Standard Model by the precise study of the
Higgs boson, including the direct observation of double-Higgs production and
the precise measurement of triple Higgs coupling. It will uniquely pursue the
quantum imprint of new phenomena in novel observables by combining precision
with energy. It gives unique access to new physics coupled to muons and
delivers beams of neutrinos with unprecedented properties from the muons’
decay.

This unmatched physics program can be realised because the muon collider
offers major advantages in terms of the footprint, cost, and power consumption
when compared to the next generation of high-energy lepton and hadron
machines. In order to directly probe the existence of new heavy states, the
luminosity of colliders has to increase with the square of the collision
energy to compensate for the reduction in $s$-channel cross sections. The
potential of muon colliders to improve the luminosity to beam power ratio at
high energies is therefore a major benefit. Based on a combination of physics
and technical considerations, the integrated luminosity target was set to 10
ab-1 at 10 TeV.

### Work programme and resources

The IMCC, the muon beam panel of the European Large National Laboratories
Directors Group (LDG) and the Snowmass process in the U.S. have all assessed
the muon collider concept. They concluded that the concept is less mature than
linear colliders but that there are no insurmountable obstacles. The concept
promises a unique path toward high energy and high luminosity with limited
cost and power consumption; this makes it important to address the challenges
of the concept and open this path to the future.

A vigorous R&D program is needed to develop an end-to-end design and to
unequivocally demonstrate feasibility of the machine and the detector
performance. With involvement of the global community, a concise set of work-
packages has been developed for the European Strategy for Particle
Physics—Accelerator R&D Roadmap by the Laboratory Directors Group, hereinafter
referred to as the European LDG roadmap. This process provided an excellent
basis for the global collaboration and planning of future work. The short-term
goal is to assess initial technical feasibility of a 10 TeV collider, identify
key R&D items, develop an implementation timeline, and provide an initial cost
estimate in time for the next ESPPU process. Further studies will address
strategic needs in the U.S. and other regions.

IMCC is actively pursuing resources to complement the resources already
foreseen by CERN and from other collaboration partners. In 2023 European
Commission support was obtained for a design study of a muon collider. This
project started in March 2023 and its work-packages are well aligned with the
overall IMCC studies. The secured resources are used following the priorities
established in the European LDG roadmap and will be able to cover about 40% of
the programme by the end of 2026.

The project continues to make important progress and the collaboration
steadily grows as detailed in this report. Examples of the ongoing efforts
include studies and prototyping plans of the magnet and RF systems and their
integration into a muon cooling cell. Progress is being made in designs of the
muon production target, the muon cooling section, the fast-ramping
accelerators, and the collider ring. Detailed studies of the machine-detector
interface and the beam-induced background in the detector are also advancing.

A further increase in the design effort for the accelerator complex and the
detector as well as the associated technologies is required to achieve the
goals presented in the European LDG roadmap. In addition, the start of an
experimental program is essential to develop the technologies, in particular
the muon cooling cell magnets, RF systems and absorbers as well as their
integration. Other key items are the muon production target and its solenoid,
which is similar to what is required for fusion reactors. The fast-ramping
magnets and power converter of the acceleration system. Several test
infrastructures are instrumental to achieve progress, including one to test RF
cavities in high magnetic field and one to test a muon cooling module
prototype.

In December 2023, the U.S. Particle Physics Projects Prioritization Panel (P5)
recommended that the U.S. should develop a collider with 10 TeV parton
collision energies, such as a muon collider, a proton collider, or possibly an
electron-positron collider. The report states: “In particular, a muon collider
presents an attractive option both for technological innovation and bringing
the energy frontier back to the U.S. The U.S. should participate to the IMCC
and have the ambition to host a future collider.” Several U.S. institutes have
already officially joined the IMCC and members of the U.S. community are
actively engaged in the collaboration’s work. The amount of dedicated
resources in the U.S. is not finalized and a considerable amount of time will
be needed to ramp up the effort. IMCC plans to revise both the organization
and the work plan together with colleagues from the U.S. and other regions.
The ambition of the U.S. to host a muon collider facility further strengthens
motivation for the R&D and facilitates the demonstrator planning at a faster
pace. Besides the U.S., collaborative ties are being established with other
regions of the world.

### Site and timeline

The study is currently focusing on a site-agnostic design. The benefits of
reusing the existing infrastructure, such as the existing proton complexes and
collider tunnels, will be considered but detailed studies will only follow at
a later time. Potential sites in Europe near CERN and in the United States at
Fermilab are being explored and other regions may propose alternative sites as
the study progresses. Close to CERN, a potential location and orientation of
the collider ring have been identified that can mitigate effects of the
neutrino flux. Muon collider implementation at Fermilab requires that the
accelerator rings all fit within the laboratory’s boundaries and first
considerations indicate that this is possible.

There are many global uncertainties in planning of the next generation of
collider facilities. These include budgetary and geopolitical considerations
that are often outside of control for our field. The muon collider is an
important concept in the long run since it allows highest lepton collision
energies; it could operate after or in parallel to a Higgs factory. In the
U.S., the muon collider can be the next high-energy frontier project for
particle physics. If no Higgs factory is being built Europe, the muon collider
could be the next project after the High-Luminosity Large Hadron Collider (HL-
LHC). In light of these uncertainties, we focus on development of the fastest
implementation timeline, while maintaining as much flexibility as possible.
This timeline is based on technical considerations, such as the typical amount
of time needed to make one iteration on the magnet technology, and hence we
refer to it as “technically limited”. We assume that no show-stoppers will
occour during the course of the R&D programme and that the required funding
and resources will be made available.

We consider a staged implementation of the collider, based on the anticipated
maturity of the relevant technologies in about 15 years, in particular the
most critical ones: the muon cooling technology, the detector technologies and
the high temperature superconductor (HTS) solenoid technology. Only HTS-based
collider ring magnet technology may not be mature at this timescale and is not
planned for the first stage. Depending on the physics needs and the funding
situation, energy staging or luminosity staging can be considered. One can
start with a cheaper, lower energy stage (e.g. 3 TeV) at full luminosity
performance that is later extended to 10 TeV or higher with improved
technology. Alternatively, one can implement a 10 TeV collider directly,
albeit with reduced luminosity, which can later be upgraded to the nominal
luminosity, similarly to HL-LHC. Both approaches do not require HTS dipoles
and allow a fast implementation of a muon collider with a start of operation
before 2050, provided the decision-making process is well prepared and
development resources are made available. A muon collider can thus be the next
high-energy frontier flagship project in all regions, e.g. in Europe it could
follow directly after the HL-LHC.

### Synergies and outreach

Many young scientists have developed their scientific and technical skills in
the field of particle physics and the associated accelerators; they also
learned to work in large international collaborations. The muon collider is a
novel concept and opens opportunities for junior researches to make innovative
contributions that are much harder to make in long-established design
approaches.

The muon collider has synergies with other particle and nuclear physics
projects, e.g. in the detector technologies and concepts, the magnet
technology for hadron colliders, the high-efficiency RF technology and high-
power targets for neutron spallation sources. It also needs several
technologies that differ from other colliders. High-field solenoids based on
high-temperature superconductor are a prime example and are also of interest
for fusion reactors and power generators for off-shore windmills as well as
life and material sciences, e.g. nuclear magnetic resonance and magnetic
reasonance imaging.

The test facility and the collider itself require a high power proton source.
This allows to share technology and potentially even facilities with neutrino
facilities (e.g. NuSTORM, neutrino factory, DUNE), lepton flavour violation
experiments (e.g. Mu2e, Mu2e-II, COMET, AMF) and the next generation of low-
energy, highly polarized muon beams.

### Conclusion

The unparalleled physics case coupled with sustainability arguments created a
very strong recent interest in the muon collider concept. This interest led to
formation of the International Muon Collider Collaboration. The near term goal
for the collaboration is to assess initial technical feasibility of the
machine, identify key R&D items, develop an implementation timeline, and
provide an initial cost estimate in time for the next ESPPU process. There has
been a significant R&D progress made by the collaboration and its partner
institutions, including those from the U.S. during the Snowmass process. The
recent P5 recommendations further stressed the importance of the R&D program.
Realization of a staged muon collider appears promising but the effort is in
strong need for additional resources, in particular to strengthen the hardware
developments.

##  0.1 Overview of collaboration goals, challenges and R&D programme

The International Muon Collider Collaboration (IMCC) [1] was established in
2020 following the recommendations of the European Strategy for Particle
Physics (ESPP) and the implementation of the European Strategy for Particle
Physics—Accelerator R&D Roadmap by the Laboratory Directors Group [2],
hereinafter referred to as the the European LDG roadmap. The Muon Collider
Study (MuC) covers the accelerator complex, detectors and physics for a future
muon collider. In 2023, European Commission support was obtained for a design
study of a muon collider (MuCol) [3]. This project started on 1st March 2023,
with work-packages aligned with the overall muon collider studies. In
preparation of and during the 2021–22 U.S. Snowmass process, the muon collider
project parameters, technical studies and physics performance studies were
performed and presented in great detail. Recently, the P5 panel [4] in the
U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages
that the U.S. should prepare to host a muon collider, calling this their “muon
shot”. In the past the U.S. Muon Accelerator Programme (MAP) [5] has been
instrumental in studies of concepts and technologies for a muon collider.

###  0.1.1 Motivation

High-energy lepton colliders combine cutting edge discovery potential with
precision measurements. Because leptons are point-like particles in contrast
to protons, they can achieve comparable physics at lower centre-of-mass
energies [6, 7, 8, 9]. However, to efficiently reach the 10+ TeV scale
recognized by ESPP and P5 as a necessary target requires a muon collider. A
muon collider with 10 TeV energy or more could discover new particles with
presently inaccessible mass, including WIMP dark matter candidates. It could
discover cracks in the Standard Model (SM) by the precise study of the Higgs
boson, including the direct observation of double-Higgs production and the
precise measurement of triple Higgs coupling. It will uniquely pursue the
quantum imprint of new phenomena in novel observables by combining precision
with energy. It gives unique access to new physics coupled to muons and
delivers beams of neutrinos with unprecedented properties from the muons’
decay. Based on physics considerations, an integrated luminosity target of 10
ab-1 at 10 TeV was chosen. However, various staging options are possible that
allow fast implementation of a muon collider with a reduced collision energy
or the luminosity in the first stage and reaches the full performance in the
second stage.

In terms of footprint, costs and power consumption a muon collider has
potentially very favourable properties.

Figure 0.1.1: Left: Conceptual scheme of the muon collider. Right: Comparison
of CLIC and a muon collider luminosities normalised to the beam power and as a
function of the centre-of-mass energy.

The luminosity of lepton colliders has to increase with the square of the
collision energy to compensate for the reduction in $s$-channel cross
sections. Figure 0.1.1 (right panel) compares the luminosities of the Compact
Linear Collider (CLIC) and a muon collider, based on the U.S. Muon Accelerator
Programme (MAP) parameters [7], as a function of centre-of-mass energy. The
luminosities are normalised to the beam power. The potential of muon colliders
to improve the luminosity to beam power ratio at high energies is one of the
main advantages of the concept.

###  0.1.2 The accelerator concept

IMCC studies a muon collider concept that has initially developed by MAP; a
schematic view is shown in Fig. 0.1.1 (left panel).

The proton complex produces a short, high-intensity proton pulse that hits the
target and produces pions. The decay channel guides the pions and collects the
produced muons into a buncher and phase rotator system to form a muon beam.
Several cooling stages then reduce the longitudinal and transverse emittance
of the beam using a sequence of absorbers and RF cavities in a high magnetic
field. A system of a linac and two recirculating linacs accelerate the beams
to 63 GeV followed by a sequence of high-energy accelerator rings; the optimum
sequence needs to be determined based on the ongoing studies. Finally the
beams are injected at full energy into the collider ring. Here, they will
circulate to produce luminosity until they are decayed; alternatively they can
be extracted once the beam current is strongly reduced.

A set of parameters has been defined for 10 TeV and also 3 TeV. These are
target parameters to explore the limits of each technology and design. If they
can be fully met, the integrated luminosity goal could be reached within five
years (or $2.5$ years, with two detectors) of full luminosity operation. This
provides margin for further design and technology studies and a realistic
ramp-up of the luminosity. It also enables to consider initial stages that can
be implemented faster but often with reduced luminosity performance in this
stage.

Table 0.1.1: Tentative target parameters for a muon collider at different energies. These values are only to give a first indication and correspond to the two stagin scenarios discussed in Section 0.1.6. The estimated luminosity refers to the value that can be reached if all target specifications can be reached; it also includes the beam-beam effect. Parameter | Symbol | unit | Scenario 1 | Scenario 2
---|---|---|---|---
|  |  | Stage 1 | Stage 2 | Stage 1 | Stage 2
Centre-of-mass energy | $E_{\mathrm{cm}}$ | TeV | 3 | 10 | 10 | 10
Target integrated luminosity | $\int{\cal L}_{\mathrm{target}}$ | $\rm ab^{-1}$ | 1 | 10 | 10
Estimated luminosity | ${\cal L}_{\mathrm{estimated}}$ | $10^{34}\rm cm^{-2}s^{-1}$ | 2.1 | 21 | tbc | 14
Collider circumference | $C_{\mathrm{coll}}$ | $\rm km$ | 4.5 | 10 | 15 | 15
Collider arc peak field | $B_{\mathrm{arc}}$ | $\rm T$ | 11 | 16 | 11 | 11
Luminosity lifetime | $N_{\mathrm{turn}}$ | turns | 1039 | 1558 | 1040 | 1040
Muons/bunch | $N$ | $10^{12}$ | 2.2 | 1.8 | 1.8 | 1.8
Repetition rate | $f_{\mathrm{r}}$ | $\rm Hz$ | 5 | 5 | 5 | 5
Beam power | $P_{\mathrm{coll}}$ | $\rm MW$ | 5.3 | 14.4 | 14.4 | 14.4
RMS longitudinal emittance | $\varepsilon_{\parallel}$ | $\rm eVs$ | 0.025 | 0.025 | 0.025 | 0.025
Norm. RMS transverse emittance | $\varepsilon_{\perp}$ | µm | 25 | 25 | 25 | 25
IP bunch length | $\sigma_{z}$ | $\rm mm$ | 5 | 1.5 | tbc | 1.5
IP betafunction | $\beta$ | $\rm mm$ | 5 | 1.5 | tbc | 1.5
IP beam size | $\sigma$ | µm | 3 | 0.9 | tbc | 0.9
Protons on target/bunch | $N_{\mathrm{p}}$ | $10^{14}$ | 5 | 5 | 5 | 5
Protons energy on target | $E_{\mathrm{p}}$ | $\rm GeV$ | 5 | 5 | 5 | 5
BS photons | $N_{\mathrm{BS},0}$ | per muon | 0.075 | 0.2 | tbc | 0.2
BS photon energy | $E_{\mathrm{BS,0}}$ | MeV | 0.016 | 1.6 | tbc | 1.6
BS loss/lifetime (2 IP) | $E_{\mathrm{BS,tot}}$ | GeV | 0.002 | 1.0 | tbc | 0.67
Table 0.1.2: Tentative target beam parameters along the acceleration chain. A 10 % emittance growth budget has been foreseen in the transverse and longitudinal planes, both for 3 and 10 TeV. This assumes that the technology and tuning procedures will have been improved between the two stages. The very first acceleration is assumed to be part of the final cooling. This choice allows to optimise the energy in the last absorber with no strong impact on the acceleration chain. Parameter | Symbol | Unit | Final cooling | at 3 TeV | at 10 TeV
---|---|---|---|---|---
Beam total energy | $E_{\mathrm{beam}}$ | GeV | 0.255 | 1500 | 5000
Muons/bunch | $N_{\mathrm{b}}$ | $10^{12}$ | 4 | 2.2 | 1.8
Longitudinal emittance | $\varepsilon_{\parallel}$ | $\rm eVs$ | 0.0225 | 0.025 | 0.025
RMS bunch length | $\sigma_{z}$ | $\rm mm$ | 375 | 5 | 1.5
RMS rel. momentum spread | $\sigma_{P}/P$ | $\rm\%$ | 9 | 0.1 | 0.1
Transverse norm. emittance | $\varepsilon_{\perp}$ | µm | 22.5 | 25 | 25
Aver. grad. $0.2$–$1500\rm\,GeV$ | $G_{\mathrm{avg}}$ | $\rm MV/m$ | — | 2.4 |
Aver. grad. $1.5$–$5\rm\,TeV$ | $G_{\mathrm{avg}}$ | $\rm MV/m$ | — |  | 1.1

###  0.1.3 Muon collider challenges

The Muon Collider Collaboration, the muon beam panel of the Laboratory
Directors Group (LDG) and the Snowmass process in the U.S. have all assessed
the muon collider challenges with the support of the global community. Key
conclusions are that although the muon collider concept is less mature than
several linear collider concepts no insurmountable obstacles have been
identified, and that important design and technical challenges have to be
addressed with a coherent international effort. Furthermore, past work, in
particular within the U.S. Muon Accelerator Programme (MAP) [5], has
demonstrated several key MuC technologies and concepts, and gives confidence
that the overall concept is viable. Since then further component designs and
technologies have been developed that provide increased confidence that one
can cool the initially diffuse beam and accelerate it to multi-TeV energy on a
time scale compatible with the muon lifetime. However, a fully integrated
design has yet to be developed and further development and demonstrations of
technology are required.

The current IMCC programme prepares the way towards a full conceptual design
report (CDR) and a demonstration programme for a muon collider. The IMCC
efforts cover physics potential as well as detector and accelerator design and
performance studies. The programme will provide the necessary information and
input for the next European Strategy for Particle Physics Update and other
international strategy processes, allowing stakeholders to make informed
decisions about these next steps.

Considering the facility design and technical challenges key performance
drivers and goals have been identified, providing guidance for prioritising
studies and efforts. They include the challenges that have previously
identified by the MAP study but represent a wider set. Particularly important
are:

  * •

Environmental impact. The compact footprint, limited cost and power
consumption are intrinsic features that motivate the muon collider study in
the first place. Radiation protection measures will ensure a negligible impact
of the facility on the environment, similar to the LHC. Based on the
experience of LHC and other accelerators, one can expect to mitigate the
impact of losses in different parts of the accelerator complex. Particular
attention will be paid to the neutrino flux that is produced by the decays of
the muons in the collider ring and that exits the ground far from the
collider. A mover system has been proposed that will avoid significant
localised neutrino flux from the arcs by vertically changing the beam angle
between $-1$ mradian to $1$ mradian and indeed can achieve a negligible level.
The mover system is currently under study and the impact it has one the beam
will be studied soon. The orientation of the The straight experimental
insertions of the collider ring will lead to a localised higher neutrino flux.
Civil engineering studies identified a position and an orientation of the
collider ring in which the neutrinos will exit into the mediteranian sea and
on the uninhabited side of a mountain, which could be fenced.

  * •

Machine-detector interface and detector. The muons of the beams that circulate
in the collider ring decay, each producing two neutrinos and one electron or
positron. The latter will hit the aperture and create showers. Tungsten masks
protect the detector from this beam induced background. The detector will
reduce the impact of the residual background by using components with high
time and space resolution. Also the potential background from beam-beam
effects is being explored but should be less severe. The studies indicate that
the radiation in the detector is roughly similar to HL-LHC. A part of the
physics measurements is not affected by the background, some part shows some
residual impact. Further optimisation is ongoing to also remove this impact.

  * •

Proton complex. In the baseline, a proton beam power of around 2 MW at 5 Hz is
used for muon production. Designs for proton facilities with similar or larger
power exist. The main proton complex challenge arises from the combination of
the protons into short, high-charge bunches. The corresponding workpackage of
the collaboration is addressing this.

  * •

Muon production. The key challenge for the high-power target is the survival
of the target itself under the shock waves of the incoming beam pulses and the
temperature gradients to remove the deposited heat. Three technologies are
under consideration, a solid graphite target, a liquid metal target or an
fluidised tungsten target. The target is immersed into a 20 T solenoid field
to efficiently collect the muons. This solenoid requires a large aperture to
allow for sufficient shielding against the transverse showers from the target.
Currently the studies indicate that a graphite target and its solenoid are
feasible and can provide a sufficient number of muons.

A liquid metal or fludised tungsten target would allow to sustain a higher
proton beam power and produce a larger number of muons. This can lead to
improved performance and provides margin with the muon bunch charge that could
be used to reduce the cost of the downstream systems. The FCC-ee also plans to
use a liquid metal target to dump the beamstrahlung photons from the
interaction region.

  * •

Muon cooling design. Muon ionisation cooling increases the muon beam
brightness by repeatedly slowing it in absorbers and re-accelerating it in RF
cavities; both inside of strong solenoid fields to keep the beam focused. This
principle has been demonstrated in MICE [10]. The target parameters anticipate
some improvement of the cooling complex performance, e.g. a factor two
reduction of the transverse emittance in the final cooling. Studies of the
physical limitations of the cooling indicate that the target can be reached in
principle. The current effort focuses on improving the lattice with the aim to
reach this principle limit.

  * •

Muon cooling technology. The muon cooling system requires close integration of
absorbers and RF cavities in a strong magnetic field. The operation of RF
cavities in a magnetic field can strongly limit the gradient that can be
achieved with no breakdown. This has been addressed by the MAP study, which
showed that gradients in excess of the design target can be achieved by using
cavities with beryllium endplates or by filling the cavities with hydrogen [].
Unfortunately, the RF test stands in which these experiments were carried out
has been dismanteled. The collaboration is developing a design for a new
facility to test the RF in high magnetic field. IMCC is actively searching for
the resources to implement such a facility and considers this a prime goals of
the collaboration.

The collaboration started to develop and engineering design of a cooling cell.
This will address the challenges of its components and their integration into
one unit. The findings may have important impact on the lattice design.

The final cooling uses highest-field small aperture solenoids. Currently,
fields of more than 30 T can be achieved using HTS in the whole solenoid. The
goal for the next generation is 40 T and we use this value in the current
design effort for the final cooling.

  * •

Muon acceleration. The lion share of the muon beam acceleration will be
performed by a sequence of pulsed synchrotrons (RCS); an alternative use of
fixed field accelerators (FFAs) is also considered. In each RCS the magnet
field is ramped up in proportion to the energy gain of the beam. Some
synchrotrons are based on a hybrid design where the fast-ramping magnets are
interleaved with static superconducting ones. The pulsed synchrotrons face
challenges in terms of optics design, the fast-ramping magnet systems and the
RF systems. Field ramp rates between a few hundred T/s in the largest final
and several kT/s in the smallest first ring are currently foreseen. The latter
requires normal-conducting magnets while for the former superferric or HTS
magnets can also be considered. Studies indicate that the ramp speeads can be
obtained. A specific challenge is the large stored energy in the magnets (in
total in the range of O(100 MJ)), which requires demanding power converters
with very efficient recovery of the energy of each pulse for the subsequent
one.

Ongoing studies of the RCS considering lattice design, pulsed magnets and RF
are promising. An integrated cost model is being developed that allows to
identify the ramp shape with the best trade-off between RF and magnet demands.

  * •

Collider ring. The collider ring requires a small beta-function at the
collision point, resulting in significant chromaticity that needs to be
compensated. It also needs to maintain a short bunch.

High-energy electrons and positrons that arise from muon decay and strike the
collider ring magnets can cause radiation damage and unwanted heat load.
Studies show that this can be mitigated with sufficient tungsten shielding and
concepts of efficient cooling of these shields have been made. The shielding
requires a larger magnet aperture in the range which is taken into account in
their concept.

A solution for 3 TeV collider ring lattice has been developed by the MAP study
and successfully addresses the challenges. The design is based on Nb3Sn
magnets with performances similar to the ones for HL-LHC. The magnet experts
expect that this technology is fully mature in 15 years.

A design of 10 TeV is more challenging because it requires an even smaller
beta-function. The current studies with higher field HTS and hybrid magnets
currently achieves the beta-function but does not yet achieve the target
energy acceptance. Further efforts aim to improve this. Otherwise one would
need to reduce the beam energy spread by about a factor two, potentially
leading to a 30% luminosity reduction.

  * •

Collective effects. A very high muon bunch charge is required to achieve the
luminosity goal. This can lead to important collective effects—such as space
charge, beam loading, wakefields—that might limit the collider performance.

  * •

Cost and power consumption. The cost and power consumtion of the faciliy is an
important challenge since sustainability must be prime concern for future
scientific projects.

###  0.1.4 Developing the muon collider study

During and after the development of the European LDG roadmap, several steps
were important to generate the framework for the muon collider studies:

  * •

The muon collider has been reviewed by the global community. Both, the muon
beam panel of the European LDG roadmap as well as the Energy Frontier and
Accelerator Frontier working groups of the U.S. Snowmass process used the
world-wide expertise in assessing the challenges of the concept. This has been
instrumental in identifying the required R&D programme.

  * •

The International Muon Collider Collaboration has been established. The
collaboration provides the organisational framework for all the efforts to
develop the collider concept.

  * •

The inclusion of the muon collider in the medium term plan of CERN in 2021,
providing an important part of the resources.

  * •

The decision of the European Union to fund the proposal for a co-financed
design study (MuCol) that started in 2023. This also served to initiate the
additional contributions from many of the collaboration partners.

  * •

At the end of 2023, the U.S. P5 process recommended that the U.S. join the
IMCC and to consider hosting such a facility. The collaboration organisation
will adapt to fully include the U.S. as efforts will ramp up. The goals set
out for the muon collider studies during the Snowmass process and in the P5
recommendations are being integrated into the IMCC future programme.

The European LDG roadmap identifies a prioritised R&D programme to make fully
informed decisions at the next strategy process. It estimated the required
resources to complete this programme to be a total of 446 FTE-years and 11.9
MEUR. With the currently secured funding the collaboration can provide
slightly less than 200 FTE-years until and including 2025\. Almost no material
budget is available at this moment. However, the collaboration is activley
seeking to increase the funding.

#### IMCC short-term goals

The International Muon Collider Collaboration has formed with the short term
goal to address the European LDG roadmap in time for the next European
Strategy for Particle Physics Update. More than 60 partner institutions are
currently involved in the muon collider studies. Three main deliverables are
foreseen:

  * •

a project evaluation report that assesses the muon collider potential;

  * •

a R&D plan that describes a path towards the collider;

  * •

an interim report early in 2024 (the present document) that documents progress
and allows the wider community to be updated on the concept and to give
feedback to the collaboration.

IMCC envisages to study the 10 TeV option, and also explore lower and higher
energy options, e.g., a 3 TeV option as a step toward 10 TeV. The details of
the required work and the required resources are documented in the European
LDG roadmap [2].

Overall facility parameters as cost, power/energy consumption and carbon
footprint will be estimated as the design matures, but are in many cases
driving technical choices and optimisation.

#### IMCC organisation

A memorandum of cooperation (MoC) for the IMCC has been drawn up and the
collaboration is rapidly growing. The formal structure of the collaboration,
as shown in Fig. 0.1.2 consists of the following main bodies:

  * •

International collaboration board (ICB): The ICB role is to provide a forum
for participants to examine ongoing activities, assure appropriate, well
directed use of contributions and ensure a balanced portfolio of engagements.
The chair of the ICB is elected by its members (simple majority). The ICB
consists of one representative of each participating institute that has signed
the MoC. The ICB has been active since October 2022.

  * •

Steering board (SB): The SB oversees the execution of the muon collider study
by assessing the progress, resource usage and providing guidance. The SB
reports to the LDG in Europe and to similar regional supervising organisations
in other regions as required. The SG is active and operational since Spring
2023.

  * •

International advisory committee (IAC): The mandate of the IAC is to review
the scientific and technical progress of the study. This body is active since
Spring 2024.

  * •

Coordination committee (CC): The CC performs the overall coordination and
execution of the muon collider study. It is chaired by the study leader. This
body consists of the workpackage leaders and some additional experts of the
collaboration and is very active. It provides the daily guidance of the study.

The workpackages of the collaboration are shown in Fig. 0.1.2.

Figure 0.1.2: Organigram of the muon collider study governance structure

The study leader is proposed by the host organization, and endorsed by the
ICB. The study leader was appointed in 2022 and has led the work to build up
the collaboration and activities since then.

#### The EU co-funded design study MuCol

IMCC successfully applied for an EU cofunded design study (named MuCol) [3].
The project started on $1^{\mathrm{st}}$ March 2023. The total co-funding of
MuCol amounts to 3 MEUR, provided by the European Commission, the U.K. and
Switzerland. In the design study, CERN only receives limited contributions for
administrative support and travel, but has, in support of the successful
design study bid, increased its contribution to the muon collider study.

The design study is fully integrated in the overall muon collaboration. The
technical meetings and leaders are in common and governance and management are
also synchronised. The organisation is shown in Fig. 0.1.3. Important
activities in the collaboration are directly supported by the MuCol work-
packages. In particular MuCol contains the workpackges Physics and Detector
Requirements, Proton Complex, Muon Production and Cooling, High-energy
Complex, Radio Frequency Systems, Magnet Systems and Cooling Cell Integration.

Figure 0.1.3: The MuCol work-packages and their interactions.

#### Extending the collaboration—US plans after P5

In the US, the Particle Physics Projects Prioritization Panel (P5) recommended
in December 2023 that the U.S. should develop a collider with 10 TeV parton
collision energies, such as a muon collider, a proton collider, or maybe an
electron-positron collider. The report states: “In particular, a muon collider
presents an attractive option both for technological innovation and bringing
the energy frontier back to the US. The U.S. should participate to the IMCC
and have the ambition to host a future collider.”

U.S. groups are very active and in leading roles in the IMCC, e.g., in the
Coordination Committee and the Publications and Speakers Committee, even
though in several cases the formal MoC signatures and effort ramp-up the will
need to wait for the forthcoming implementation planning of the P5
recommendations.

The collaboration plans to revise both the organisation and the workplan
together with U.S. colleagues. This will also impact the work programme laid
out in this report. In particular, the ambition of the U.S. to host such a
facility strengthens the motivation for R&D and demonstrator planning at a
fast pace.

The collaboration also plans to attempt further strengthen other regions’
participation during this process. There is at this moment an important
potential for substantial expansion of the collaboration, resources and
efforts in Asia, and several European countries, Canada and South America.

###  0.1.5 R&D programme

The novelty of the muon collider concept implies that the R&D programme
contains more uncertainty and challenges than for more conservative collider
approaches.

A concise set of work-packages has been developed for the European LDG roadmap
[2]. The programme aims to provide a broad basis for the global collaboration
and planning of future work towards a multi-TeV muon collider. The programme
is estimated to require about 450 full-time equivalent (FTE) years of labour
and 12 MEUR material budget for the accelerator studies.

Substantial progress has been made since the definition of the European LDG
roadmap. The approval of the EU co-funded design study MuCol, contributions
from the collaboration members as well from U.S. partners during the Snowmass
process and an increase of the budget at CERN were instrumental in supporting
the muon collider study.

With the existing funding until 2026, the R&D cannot cover the full programme
as described in the European LDG roadmap. The focus is on the most critical
challenges and is guided by the priorities established by the roadmap. The
planned effort is roughly consistent with the minimal scenario in the roadmap.

The focus is on the most critical challenges:

  * •

The development of the physics case.

  * •

The possibility to find a site and mitigate the neutrino flux.

  * •

The detector concept, in particular, the machine-detector interface which
drives the physics capabilities of the detector.

  * •

The development of the high energy accelerator design concepts, in particular
the pulsed synchrotrons and the collider ring. These are vital to reach the
high energy beyond the scale studied by MAP.

  * •

The further development of the muon production and cooling complex. The focus
is on an engineering design of the cooling cell and the evaluation of the
target concept. An overall optimisation of the complex is desirable but very
resource demanding.

  * •

The magnet technologies that drive the performance, cost and power
consumption.

  * •

The RF technologies that drive the performance, cost and power consumption.

  * •

Other key technologies, for example shielding and cryogenics.

#### Work organisation

The distribution of the work onto workpackages has been modified since the
publication of the European LDG roadmap to adjust to the availability of
effort and experts. The document reflects this change. The areas represented
in the coordination committee are:

  * •

The physics potential links to all studies of the muon collider physics
potential.

  * •

The detector and MDI Links to the detector design studies and to the machine
detector interface.

  * •

The proton complex addresses the key challenge of the accumulation of the
protons in very high-charge bunches, by addressing in detail the proton
complex design, and provides the basic parameters of the complex and the
characteristics of the beam impacting on the production target.

  * •

The muon production and cooling addresses the production of the muons by the
proton beam hitting a target and the subsequent cooling, including some of the
specific technologies, such as for the production target and the absorbers
that reduce the beam phase space volume.

  * •

The muon acceleration complex (in MuCol part of the high-energy complex)
studies the acceleration complex of the muons.

  * •

The muon collider ring and siting studies the design of the collider ring.
Because the muon collider siting is foremost driven by considerations on the
neutrino flux from the collider ring the package also contains these
activities.

  * •

Magnet systems will establish a complete inventory of the necessary magnets to
optimize and standardise the design, and address the most critical ones. In
particular it focuses on the solenoids of the muon production and cooling,
which are specific to the muon collider, and the fast-ramping magnet system,
which have ambitious requirements on power flow and power efficiency and
limits the energy reach of the collider.

  * •

Radio frequency (RF) systems addresses the muon cooling ensuring coherence in
frequency choice and synchronization among the various stages. It contributes
to sustainability studies by its work on high efficiency RF power sources.

  * •

The beam-matter interaction and target design links to the different shielding
studies, in particular for the muon production target and the collider ring.

  * •

The collective effects area includes all beam dynamics studies across the
complex.

  * •

The demonstrator area connects to all the activities regarding the muon
cooling demonstration.

  * •

Cooling cell integration addresses the design of the muon cooling cell, which
is a unique and novel design and that faces integration challenges.

#### Recent progress and studies until 2026

The studies are summarised below, largely following the European LDG roadmap
workpackages, which are indicated in brackets.

  * •

For the site and neutrino flux mitigation (MC.SITE, MC.NF) the following
studies are ongoing and planned by 2026:

    * –

Verification of the neutrino flux impact using FLUKA and radiation protection
knowledge.

    * –

Exploration of a site and orientation of the collider ring to mitigate the
neutrino flux, in particular from the experimental insertions. This is the
most difficult challenge.

    * –

Assessment of the mover concept to mitigate neutrino flux from the arcs.

    * –

An assessment if the neutrino flux mitigation with movers impacts beam
operation.

A number of important points cannot be covered with the current resources.
This includes an assessment of the neutrino flux mitigation for the other
parts of the complex, the development of a concept to measure and verify the
neutrino flux in operation and the alignment concept that allows to link the
machine reliably to the surface.

  * •

The MDI studies (MC.MDI) are progressing:

    * –

The simulation tools for the background prediction have been developed.

    * –

A masking system has been studied and optimisation is planned.

    * –

A programme to simulate beam-beam induced background has been developed.

    * –

Different lattice designs for the interaction region have been compared for
the beam-induced background and limited differences were found.

The main effort to mitigate the background will have to be carried by the
detector design.

  * •

The accelerator concept and beam dynamics (MC.ACC) studies cover the key
activities:

    * –

The combination of the high-power proton beam into short intense pulses.

    * –

A design of the experimental insertion and the arc lattices of the collider
ring for 10 TeV.

    * –

A design of the arc lattice of the pulses synchrotrons of the muon beam
acceleration system.

    * –

An improved concept of the muon cooling system.

    * –

Assessment of key collective effects and their impact on the performance and
specifications.

Studies that are not covered are the concepts of other parts of the collider
complex, e.g., the low energy muon acceleration or the proton complex as well
as full start-to-end simulations. Also alternatives for the muon cooling and
acceleration cannot be covered. Further the studies do not cover the 3 TeV
design. We anticipate that a solution for 10 TeV is also valid at 3 TeV.

  * •

The high-field magnet (MC.HFM) studies are ongoing

    * –

The muon production target solenoid concept is being developed, based on HTS
technology.

    * –

A database with the magnet performance specifications from the previous MAP
design has been developed and the resulting challenges identified. A tool to
systematically derive optimised magnet configurations that create similar
fields for the beam is under development and will be used on subsequent
lattice designs.

    * –

40 T has been identified as a realistic goal for the final cooling magnets and
is used in the lattice design effort. The magnet study addresses the
technology challenges that stem from this field.

    * –

Initial limits for the collider ring magnets have been identified and show the
need for improved magnet protection and stress management, which will be
addressed in further studies. Additional resources are required to perform
more cable tests and to build magnet models to verify the simulations and
improve the technology.

An experimental programme would be important to verify magnet performances and
to develop the technology, but the material budget for this is currently very
limited. Also measurement of the radiation hardness of the HTS magnets would
be instrumental in establishing the performance limits.

  * •

The design of the power converters and fast-ramping normal magnets (MC.FR) for
the RCSs is ongoing in close interaction with the RF design and the lattice
design. An overall optimisation will be performed of magnets, power converter
and RF systems. These systems have a very important impact on cost and
additional funding would allow experimental verification of the performances.
The development of HTS-based alternatives is not covered.

  * •

The RF system (MC.RF) studies are ongoing:

    * –

The acceleration of high-charge muon bunches to high energies is being
developed using superconducting cavities. The longitudinal beam dynamics
studies along the high-energy complex is progressing and shows that cavities
developed for the International Linear Collider (ILC) might be applicable.

    * –

The synchronisation is being studied between the RF and the ramping of the
magnets in the RCS together with its impact on the cost.

    * –

The design is progressing of normal conducting cavities for the muon cooling
cell.

  * •

The muon production target (MC.TAR) studies focus on the ability of the target
to withstand the beam power and the required shielding of the surrounding
solenoid. Indications are that a graphite target can sustain about 2 MW.
Higher power liquid metal target alternatives will be explored. The current
resources do not allow a complete design of the target and study of the muon
capture systems.

  * •

The engineering design of one muon cooling cell (MC.MOD) is ongoing and is
instrumental to maintain the option of a timely implementation of a
demonstrator facility. Currently the resources to actually build models of the
components and ultimately a prototype of the cell are not secured.

Concepts of an RF test stand are being developed and allow to apply for
funding to overcome the current lack of infrastructure of this type.

  * •

The initial scope for the muon cooling demonstrator (MC.DEM) has been
determined and high-level concepts of the facility are being developed to
understand the footprint requirements. Initially two potential sites at CERN
have been identified, further options exist at Fermilab and we will invite
more options. More resources are needed to develop a full conceptual design of
the facility.

The estimate of the cost scale (MC.INT) has started and will use a mixture of
high-level estimates with detailed estimates of key components.

The physics potential and detector R&D goals are not part of the European LDG
roadmap.

The physics potential requires sustained study to fully develop the
understanding of the different measurements that can be performed at the muon
collider, in particular also in view of synergies with other physics
instruments.

A set of physics benchmark processes is being developed that allows to assess
the key detector concept capabilities with a limited number of studies. The
aim is to use these benchmark processes to demonstrate that the detector
performance is adequate and that the background is well controlled.

Designs of the detector at 3 and 10 TeV detectors is being developed with
clear specifications for the technology performance. A systematic review is
important of these performance requirements and an assessment which current
technology developments will meet them on which timescale. Also an exploration
of alternative technologies is essential and the derivation of a prioritised
list of alternatives that should be further developed. Of particular concern
is the forward region, which suffers most from the background, as well as the
detection of small angle muons. Also some concept for the luminosity
monitoring is essential.

A 3 TeV detector concept exists based on a slightly modified version of the
CLIC detector concept. Performance studies with this concept show that the
measurement resolution for some processes is not strongly impacted by the
beam-induced background while important impact exists for other channels. A 10
TeV detector concept is under development.

A systematic performance study of the 10 TeV detector concept is required for
the benchmark processes to establish that the physics potential can be
realised. Therefore simulation of the detector is required without and with
beam-induced background in order to establish the latter has no significant
impact on the physics performance. The development of artificial intelligence-
based methods will be important to reduce the background at the reconstruction
and potentially the trigger level.

###  0.1.6 Timeline and staging

The potential of a muon collider to reach 10 TeV parton-parton collisions with
high luminosity makes it a very exciting future opportunity both on a longer
and shorter timescale.

A roadmap towards a muon collider must remain flexible, and is an important
part of a diverse international research programme in particle physics. New
results, from the HL-LHC or non-accelerator based experiments, and potentially
also lower energy experiments, might change the desired parameters for a
future muon collider. Societal changes and priorities might also influence
resource availability and hence timelines for investments in basic science as
needed for future colliders.

We already know that sustainability and environmental consideration needs to
guide the design process much more than projects decades back. Staging
scenarios, a clear focus on working with developing technologies (from HTS
magnets to machine learning (ML) and artificial intelligence (AI) methods)
with a wide impact and interest outside our field, synergetic studies and
projects as described in next subsection, and a broad international
collaboration, are all important to develop the muon collider as a
scientifically and technically novel but robust future facility when it comes
to implementation.

The current timeline considerations identified that three technical
developments are defining the minimum time to implement a muon collider:

  * •

The muon production and cooling technology and its demonstration in a test
facility. At this moment we expect that this development can be mature enough
for a decision in 15 years provided sufficient funding is made available.

  * •

The magnet technologies, in particular HTS superconductor technology. At this
moment, we expect that the different HTS solenoids for the muon production and
cooling are available within 15 years; the same is expected for the fast-
ramping magnets. For the collider ring, one can expect 11 T Nb3Sn magnets with
an aperture of 16 cm to be mature. Higher performant HTS or hybrid collider
ring magnets may take longer.

  * •

The detector and its technologies that impact the efficiency of background
suppression and the quality of the measurements. At this moment, we expect
this technology to be mature in 15 years.

Sufficient funding should enable to accelerate the R&D of the other
technologies and designs as to not constrain the timeline..

A staged implementation that anticipates use of Nb3Sn collider ring magnets
can provide a muon collider by 2050. The scenarios are possible, see also
Table 0.1.1:

  * •

In the energy-staging approach, the inital stage is at lower energy, for
example 3 TeV. There is an important physics case already at this energy. In
this strategy, the cost of the initial stage is substantially lower than for
the full project. This could accelerate the decision-making processes. The 3
TeV design is consistent with Nb3Sn magnets at 11 T. In the second stage the
whole complex will be reused with the exception of the collider ring. An RCS
to accelerate to full energy and a new collider ring will be added.

  * •

In the luminosity-staging approach, the initial stage is at the full energy
but using less performant collider ring magnets. This leads to an important
reduction of the luminosity. If 11 T Nb3Sn dipoles are used instead of 16 T
HTS dipoles, the resulting increase of collider ring circumference reduces the
luminosity by one third. In addition a further reduction arises from the
interaction regions. A detailed study is required to quantify the loss, but a
factor three reduction might be a good guess. In the luminosity upgrade, the
interaction region magnets will be replaced with more performant ones, similar
to the HL-LHC. However one most likely will not replace the other collider
ring magnets. In this scenario almost the complete project cost is required in
the first stage, which could have important implications on the timeline.

The choice between the staging options will depend on physics needs and
funding availability. Also the progress in magnet development will play an
important role. Faster progress, in particular of HTS for the collider ring
magnets, combined with strong funding support will make an earlier start of
the 10 TeV option more attractive.

###  0.1.7 Site considerations

Different sites for the muon collider will be explored in the longer run.
However, at this moment the international study to a large extent focuses on
the technical and design challenges with no specific site in consideration.
Specific sites however offer the benefit of existing infrastructure, e.g.,
existing proton complexes and collider tunnels. We will consider these
benefits later for the different potential sites. Specific sites also can
impose important constraints. For example, for Fermilab an option is preferred
where the accelerator rings all fit on the existing site. First considerations
indicate that this is possible. For CERN the most important consideration is
to ensure that the neutrino flux can be mitigated to a negligible level. A
first site and orientation of the collider ring that can achieve this has been
identified and requires further study. In this case the extension of the
experimental insertions point towards a steep uninhabited slope of the Jura on
the one side and to the Mediterranean sea on the other side.

###  0.1.8 Synergies and outreach

Particle physics and the associated accelerator development have made
important contributions to society; both in training of young people and in
developing technologies.

Many young people have developed their scientific and technical skills in the
field; they also learned to work in fully international collaborations.
Because the muon collider is a novel concept it opens opportunities for young
researchers to make original contributions to the development that are much
harder to make in long-established design approaches.

The muon collider needs technologies in several areas that differ from other
colliders. High-field solenoids are a prime example. In the past low-
temperature superconductors such as the very mature NbTi and still developing
Nb3Sn were the technologies of choice for accelerators and most other
applications. Now high-temperature superconductors (HTS) are becoming an
important technology. In particular they are of interest for fusion reactors,
that have similar requirements than the one for the muon collider target
solenoid. Highly-efficient superconducting motors and power generators, e.g.,
for off-shore windmills, also have strong synergy. Other relevant areas are
life and material sciences; in particular, applications for nuclear magnetic
resonance (NMR) and magnetic resonance imaging (MRI). In addition synergy
exists with magnets for neutron spectroscopy, physics detectors and magnets
for other particle colliders, such as hadron colliders.

The muon production target is synergetic with neutron spallation sources
targets, in particular the alternative liquid metal concept.

The muon collider RF power sources have synergy with other developments of
high-efficiency klystrons and superconducting cavities. Some RF systems need
to work in high magnetic fields, an issue that also exists in some fusion
reactor designs.

The test facility and the collider itself require a high power proton source.
This allows sharing technology and potentially even facilities. Neutron
spallation sources such as SNS and ESS are major examples; other examples are
neutrino facilities, such a NuSTORM, lepton flavour violation experiments,
such as mu2e and COMET and the generation of low-energy, highly polarised muon
beams.

## References

  * [1] The International Muon Collider Collaboration—IMCC, https://muoncollider.web.cern.ch/, last accessed 22 May 2024.
  * [2] European Large National Laboratories Directors Group (LDG), European Strategy for Particle Physics—Accelerator R&D Roadmap, edited by N. Mounet, CERN-2022-001 (CERN, Geneva, 2022), doi:10.23731/CYRM-2022-001.
  * [3] MuCol—A design study for a muon collider complex at 10 TeV center of mass, https://mucol.web.cern.ch/, last accessed 22 May 2024.
  * [4] S. Asai et al., Pathways to innovation and discovery in particle physics : Report of the 2023 Particle Physics Project Prioritization Panel (P5), https://inspirehep.net/literature/2772795 and website.
  * [5] M. A. Palmer and K. Long (eds.), Muon accelerators for particle physics (MUON), JINST special issue (2016–2021), Article collection; Muon accelerator program (MAP), http://map.fnal.gov (restricted access), archived version 5 May 2021 (free access).
  * [6] C. Aimé et al., Muon collider physics summary, arXiv:2203.07256v2 [hep-ph] (2022), doi:10.48550/arXiv.2203.07256.
  * [7] J. P. Delahaye et al. Muon colliders, arXiv:1901.06150 [physics.acc-ph] (2019), doi:10.48550/arXiv.1901.06150.
  * [8] H. Al Ali et al., The muon smasher’s guide, Rept. Prog. Phys. 85 (2022) 084201, doi:10.1088/1361-6633/ac6678, [arXiv:2103.14043 [hep-ph]] (2021), doi:10.48550/arXiv.2103.14043.
  * [9] C. Accettura et al., Towards a muon collider, Eur. Phys. J. C 83 (2023) 864, doi:10.1140/epjc/s10052-023-11889-x, [erratum: Eur. Phys. J. C 84 (2024) 36, doi:10.1140/epjc/s10052-023-12257-5].
  * [10] M. Bogomilov, et al., Demonstration of cooling by the Muon Ionization Cooling Experiment, Nature 578 (2020) 53–59, doi:10.1038/s41586-020-1958-9.

##  0.2 Physics opportunities

A muon collider with 10 TeV energy or more could discover new particles with
presently inaccessible mass, including WIMP dark matter candidates. It could
discover cracks in the SM by the precise study of the Higgs boson, including
the direct observation of double-Higgs production and the precise measurement
of the triple Higgs coupling. It will uniquely pursue the quantum imprint of
new phenomena in novel observables by combining precision with energy. It
gives unique access to new physics coupled to muons and delivers beams of
neutrinos with unprecendeted properties from the muons decay.

For these reasons, the new European interest on muon colliders that emerged
during the process and with the deliberation of the 2020 Strategy Update—and
the creation of the IMCC—triggered an enthusiastic reaction of the theory and
phenomenology community. Since 2019, INSPIRE-HEP has recorded more than 150
papers about muon colliders in the “Phenomenology-HEP” subject category [1].
This is about half of the papers ever written on this topic. The left panel of
Fig. 0.2.1 compares the time distribution of the phenomenology papers (in
blue), with the papers about muon colliders in all subjects (in grey). In the
past, muon collider phenomenology papers used to be a small fraction of the
total and the development of the field was almost entirely driven by the
advances in accelerator physics. Physics studies are instead a major component
and a driver of the activity in the last few years, indicating an
unprecedented enthusiasm on muon colliders physics opportunities. A small
fraction of these recent works is described below to exemplify some of the
achieved accomplishments. For an extensive overview, see Refs. [2, 3] and,
most recently, the review produced by the International Muon Collider
Collaboration [4].

Several workshops and seminars on muon colliders physics were held in the last
few years, including a very successful series of events organised by the “Muon
Forum” [5] in the context of the Snowmass 2021 Community Planning Exercise.
The activities and the work triggered by the Forum [3] strongly impacted the
Snowmass Energy Frontier outcome [6], which recognised the muon colliders
potential for the exploration of the energy frontier and advocated R&D
investments with the perspective of hosting a muon collider in the US. The P5
panel report confirmed and strengthened this view [7].

The rest of this section describes the work done, the open questions and the
future directions for the development of muon colliders physics. In Section
0.2.1 we outline the potential of a 10 TeV muon collider to explore the energy
frontier conclusively and systematically by a number of different strategies,
depicted on the right panel of Fig. 0.2.1. Section 0.2.1 describes the future
challenges for theory and phenomenology in the novel environment of multi-TeV
muon collisions. These challenges are in fact opportunities for the theory
frontier exploration of a new regime of the electroweak interactions. Section
0.2.2 is devoted to physics opportunities in addition to those entailed by the
10 TeV muons collisions. In particular, we illustrate the unprecendented
properties of the collimated beam of neutrinos that emerges from muon decays
close to the interaction point. Finally, we present in Section 0.2.2 a
physics-driven assessment of possible muon colliders energy or luminosity
staging plans.

Figure 0.2.1: Left: Time distribution of the papers on muon colliders (grey)
compared with those (blue) with subject “Phenomenology-HEP” [1]. Right:
Pictorial view of the muon colliders exploration opportunities.

###  0.2.1 Exploring the energy frontier

#### Motivations

The LHC confirmed an unprecedentedly complete framework—the Standard Model
(SM)—that enables a theoretical description of Nature up to extremely short
distance scales, which are still experimentally unexplored. Testing the SM
predictions at shorter and shorter scales is a prime motivation for studying
higher and higher energy collisions. On the other hand, the SM success should
not be overrated. The theoretical machinery of local field interactions the SM
formulation builds upon is compatible with the profound principles of
relativistic quantum field theory, but it is not uniquely selected by these
principles, nor it is sufficient for a truly complete description of Nature
that includes gravity. Even within this partial framework of local Lagrangian
field theory, the SM is highly non-unique and its field content is merely
engineered to accommodate the observed particles, and in fact not all of them
because the SM lacks a dark matter candidate. Since our present knowledge of
fundamental particles emerges from past observations, the existence or non-
existence of other particles can be only established by future observations.
If the new particles are heavy, this requires a high-energy collider.

The most mysterious sector of the SM is the one associated with the breaking
of the electroweak (EW) symmetry: the Higgs sector. The Higgs boson is not
only the most recently discovered SM particle. It is the first manifestation
of a description of the massive spin one EW force carriers—by the formalism of
spontaneously-broken gauge theories—that can be extrapolated up to energies
much above the EW bosons mass. Testing the SM predictions for the properties
and the couplings of the Higgs particle is an important but indirect way to
probe the validity of this novel description. The key innovation of the Higgs
theory is to offer a modelling of EW interactions in the multi-TeV energy
regime. Its most striking manifestations are thus the interplay between the
Higgs and the EW bosons—and also the fermions, as also their mass requires the
Higgs—in high energy collisions.

At variance with other theoretical possibilities, the SM Higgs achieves the
breaking of the EW symmetry by a fundamental scalar field, which results in an
elementary (point-like) Higgs boson. The naturalness paradox famously displays
the contradiction between the existence of elementary spin zero particles and
the Wilsonian interpretation of quantum field theory. We will thus learn
profound lessons by probing if the Higgs particle is elementary—namely, if its
size is much smaller than its Compton wavelenght—or instead composite. Less
radical possibilities to circumvent the naturalness paradox such as
supersymmetry should be also investigated for the same reason.

In this context, the muon colliders’ potential to explore Higgs and EW physics
at high energy and without large backgrounds from the QCD interaction appears
particularly appealing. A high-energy muon collider is arguably the best
response to the contemporary challenges of fundamental particles and
interactions physics.

#### Muon collider physics highlights

The motivations for studying short-distance physics are strong, but broad.
Therefore, a radical advance requires an equally broad and comprehensive
program of energy frontier exploration that leverages many diverse strategies
of investigation. The multiple exploration strategies available at a muon
collider—see Fig. 0.2.1—make it ideally suited for this task.

Figure 0.2.2: Left: The HL-LHC and FCC-hh exclusion mass-reach for several
beyond the Standard Model (BSM) particles. The exclusion (and discovery) reach
of 10, 14 and 30 TeV muon colliders are reported as horizontal lines. Right:
Sensitivity to the Higgs trilinear coupling modifier $\delta\kappa_{\lambda}$
of different future colliders proposals. The sensitivity of the 10 TeV muon
collider ($\mu 10$) is compared with the one of higher energy muon colliders
($\mu 14$ and $\mu 30$) and with the one of the low-energy stage at 3 TeV
($\mu 3$). Plots from Ref. [4].

The high available energy allows to search for new heavy particles, with a
reach in mass that strongly extends the one of the LHC. In fact, the muons are
elementary and their collision energy is entirely available to produce new
particles. The protons instead are composite and their effective energy reach
is limited to a fraction of the collider energy by the steep fall of the
parton distribution functions. This is the reason why a muon collider with 10
TeV energy can access heavier particles than the 14 TeV LHC, as illustrated on
the left panel of Fig. 0.2.2. The figure shows the projected exclusion mass
reach111We use the HL-LHC and FCC-hh sensitivity projections that have been
presented for the 2020 Update of the European Strategy for Particle Physics,
summarised in Ref. [8]. The particles are labeled with a standard BSM
notation; for instance $\widetilde{t}$ is the stop quark. See Ref. [4] for
additional details. for a number of BSM particles at the HL-LHC (solid bars)
and at the 100 TeV proton-proton collider FCC-hh (shaded bars). At a muon
collider, these particles are produced in pairs by EW interactions and their
production cross section does not depend on any BSM model detail other than
the EW and spin quantum numbers of the states. The EW cross-sections for the
particles considered in the figure range from $0.1$ to 10 fb [9, 10] at the 10
TeV MuC, for masses almost up to the kinematic threshold of 5 TeV. With the
target integrated luminosity of 10 ab-1, enough (more than 1000) events will
be available for discovery up to the threshold. The MuC mass-reach at 5 TeV is
above the HL-LHC exclusion limit for all the BSM candidates. The 10 TeV muon
collider has an even higher reach than a 100 TeV proton-proton collider on
QCD-neutral particles such as charginos ${\widetilde{\chi}}_{1}^{\pm}$ and tau
sleptons $\widetilde{\tau}$.

Along these lines, the “Energy” arrow in Fig. 0.2.1 represents the possibility
of searching for new heavy particles of very generic nature, or specific well-
motivated candidates. Past works investigated the MuC sensitivity to a number
of BSM scenarios ranging from WIMP dark matter, extended Higgs sectors, heavy
neutral leptons, composite resonances, solutions to the $\mathrm{g}-2$ anomaly
and more. An incomplete list of references include [11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 24, 34, 28, 35].
Few specific results are outlined below.

Reference [11] (see also Refs. [2, 12, 13]) studied one extra EW-singlet extra
Higgs scalar which is potentially responsible for the generation of a strong
first-order EW phase transition in the Early Universe, and is present in other
BSM scenarios as well. Such “scalar singlet” is a standard benchmark for
future colliders, also in light of its peculiar coupling to the SM, which
occurs only through a Higgs-portal interaction. The 10 TeV MuC mass-reach on
this BSM scenario has been found superior to the one of the FCC-hh in the most
motivated region of the parameter space of the model. In fact, the sensitivity
is superior in the whole parameter space, if including [4] the indirect MuC
reach from Higgs coupling measurements. The MuC advantage over FCC-hh stems
from the large MuC cross-section for the production of Higgs-portal coupled
new physics in vector boson fusion. Similar findings have been reported in
other Higgs-portal coupled BSM scenarios, making the muon collider an ideal
option to cover this class of models at the multi-TeV scale.

It should be emphasised that the results described above—as well as the other
findings reported in this section and the majority of the muon collider
studies in the literature—are based on detailed phenomenological analyses that
consider the relevant backgrounds as well as a parametric modeling of the
detector effects. The assumed detector performances are those of the IMCC muon
collider DELPHES card [36, 37], which match the performances of the CLIC
detector and lie in between (see Section 0.3.1) the “Baseline” and
“Aspirational” performances.

Several papers [31, 32, 33, 34, 28, 35] studied the observability of a variety
of WIMP DM candidates at the muon collider (see Ref. [4] for a summary).
Detection strategies include mono-photon (or, more generally mono-$X$)
searches, indirect searches from loop effects, and direct searches of the
disappearing tracks produced by the charged particle in the dark matter
multiplet. The beam-induced-background (BIB) from the decay of the muon beams
has a potentially large impact on the disappearing track search, which is
difficult to estimate and to parametrize faithfully in a fast detector
simulation. For this reason, a complete study of disappearing tracks was
performed in Ref. [35], based on realistic BIB Monte Carlo simulations. The
observability of long-sought dark matter candidates such as the Higgsino and
the Wino has been established up to the thermal mass.

The “Precision” arrow in Fig. 0.2.1 represents accurate measurements in the EW
and Higgs sector. These are possible at the muon collider exploiting the large
rate for EW-scale scattering processes initiated by effective vector bosons,
and the small QCD background that is typical of leptonic collisions. The
perspectives of exploiting the 10 million Higgs boson produced by the collider
in the vector boson fusion channel have been investigated in details [38, 2,
39, 40] based on fast simulation but also validated against the available
full-simulation studies [40]. These sensitivity projections for Higgs signal-
strength measurements were used in Ref. [4] for a Higgs couplings fit in the
same setup that was employed in Ref. [41] for a global comparative assessment
of future colliders sensitivity in preparation for the 2020 European Strategy
Update process222Reference [4] also presents an EFT fit, which includes
several additional muon collider observables like high-energy measurements..
The result is that a per mille level determination of the single Higgs boson
couplings will be possible at the 10 TeV MuC, similarly to future low-energy
$\mathrm{e}^{+}\mathrm{e}^{-}$ Higgs factories. A detailed inspection of the
sensitivity to different couplings reveals the complementarity between MuC and
low-energy Higgs factory couplings determinations.

The findings above refer to the “kappa-0” Higgs couplings fit [41], where no
BSM Higgs decay channel is allowed. The closure of the “kappa-1” fit, where
this assumption is relaxed, requires a measurement that is sensitive to the
absolute value of at least one of the couplings of the Higgs, without
dependence on the Higgs total width. The determination of the total
(inclusive) Higgs cross-section in the Z-boson fusion production channel could
provide such measurement at the MuC, enabling a very precise coupling
determination also in the kappa-1 scheme [42]. However, this measurement
relies on the observability of muons in the forward region by a dedicated
detector, whose feasibility is still to be assessed (see Section 0.3.1). If
such measurement turned out to be impossible, the closure of the kappa-1 fit
will have to rely on the inclusive cross-section measurement at a low-energy
$\mathrm{e}^{+}\mathrm{e}^{-}$ Higgs factory, providing one further element of
complementarity with such machine. The flat direction in the kappa-1 fit could
be also lifted by high-energy measurements at the MuC, by relying on extra
assumptions [43].

Unlike low-energy Higgs factories, the MuC can also measure the double-Higgs
production cross-section and determine the Higgs trilinear coupling at the
percent level, as shown on the right panel of Fig. 0.2.2. This result [38, 9]
is based on a parametric modeling of the detector effects—assuming CLIC-like
performances—validated against the CLIC full simulation sensitivity projection
[44]. Figure 0.2.2 also reports the expected sensitivity of FCC-hh [45], which
ranges from $3\%$ to $8\%$ depending on the assumed detector performances. The
MuC result has been found less sensitive to detector performances because the
background is lower.

A unique feature of the muon collider is the simultaneous availability of
energy and precision. This allows, very simply, to measure high-energy
scattering cross-sections precisely. The possibility of exploiting energy and
precision at once is represented by the “Energy&Precision” arrow in Fig. 0.2.1
and it corresponds to an exploration strategy that is typical of high energy
physics: higher energy observables are more sensitive to short-distance
physical laws and give access to novel effects that were too tiny to be
detected in previous experiments performed at lower energy. This mechanism
produced some of the most striking past discoveries, including the discovery
of neutral currents and the one of the finite radius—i.e., the composite
nature—of the nucleons. Sufficient statistics will be available at the muon
collider to measure 10 TeV $2\to 2$ scattering cross sections with percent-
level accuracy333Interestingly enough, the sensitivity is not limited to
neutral $\mu^{+}\mu^{-}$ scattering processes. The copious emission of charged
EW bosons at the 10 TeV scale gives effective access to charged $\mu\nu$
scattering, and to $\nu\bar{\nu}$ scattering., which roughly translates into
the sensitivity to new physics at the 100 TeV scale. Notice for comparison
that 100 TeV scale new physics produces unobservably small one part-per-millon
effects on EW-scale observables. This explains the superior sensitivity [4] to
EFT interactions of the muon collider in comparison with Z-pole measurements
at the FCC-ee.

Concrete illustrations of the physics potential from high-energy measurements
include (see [4] for an overview) the sensitivity to new neutral currents
mediated by a very heavy “$Z^{\prime}$” boson of order 100 TeV mass [46, 9]
and the possibility of observing new quark- or lepton-flavour breaking
transitions more effectively than low-energy experiments [2]. Furthermore,
high-energy measurements give direct access to the possible finite size of the
Higgs particle [46, 9] testing Higgs compositeness more effectively than any
other future collider project. This is shown on the left panel of Fig. 0.2.3
in the plane formed by the Higgs compositeness scale $m_{*}$—i.e., the inverse
of the Higgs radius—and the effective coupling $g_{*}$ of the new strongly-
interacting sector the Higgs emerges from. The “Others” line in the plot is
the envelope of the sensitivity attained by other future collider projects. It
assumes the entire FCC-ee physics program including EW precision tests at the
Z pole, and direct searches at FCC-hh for new states with order $m_{*}$ mass
that emerge in the Composite Higgs scenario under examination.

The “Muons and neutrinos” arrow in Fig. 0.2.1 reminds us that energetic muon
beams will be made available for the first time. Studying their collisions
offers self-evident opportunities to discover new physics coupled primarily to
muons and not for instance to electrons, whose collisions are extensively
studied. Specific illustrations [2, 4] of the potential in this direction stem
from the larger Yukawa coupling of the muon than of the electron, which
suggests a stronger coupling to muons of extended Higgs sectors [47], from the
connection with possible new physics in the muon anomalous magnetic moment
[19, 48, 49, 20, 21, 50, 22, 18, 51, 52], as well as opportunities to test
muon-philic scenarios [53, 14, 15, 54, 55, 56, 17, 57]. However, the agnostic
exploration of new physics coupled to muons is arguably the strongest
motivation.

Beyond collisions, energetic muon beams offer additional unique opportunities.
In particular, they produce a collimated beam of neutrinos with unprecedented
properties described in Section 0.2.2.

#### Future work and physics-detector integration

The future development of muon collider physics should proceed along three
complementary directions. First, by expanding the physics case with new
targets and sensitivity projections. We saw that previous work already
identified many promising avenues, but we are still far from a complete
assessment of the muon collider physics opportunities.

Second, by consolidating the physics case with increasingly detailed and
optimised sensitivity projections in close connection with the evolution of
the muon collider experiment and detector design. Current results assume the
CLIC-like detector performances implemented in the IMCC muon collider DELPHES
card [36, 37], as previously described. Novel and more specific (“Baseline”
and “Aspirational”) target performances are defined in Section 0.3.1.

The third direction in which progress is needed is the development of the
theoretical tools for making predictions at the muon collider. The next
section summarises the main open questions in this area.

#### Challenges and opportunities at the theory frontier

EW interactions at 10 TeV display novel phenomena associated with the large
separation between the collision energy and the mass of the EW particles, of
order $100$ GeV. The EW bosons start behaving as nearly massless producing IR-
enhanced radiative effects that are parametrically of order one at 10 TeV. The
corresponding “EW radiation” phenomena share some similarity with
electromagnetic and QCD radiation, but also remarkable differences that pose
profound theoretical challenges. Being the EW symmetry broken at low energy,
different particles in the same EW multiplet—i.e., with different EW gauge
color—are distinguishable. This invalidates the cancellation between real and
virtual radiation, obliging us to include the resummed effects of EW radiation
in all observables, also in inclusive cross sections. Moreover, the
resummation is needed for non color singlet observables that do not exist in
QCD. In analogy with QCD and unlike QED, the IR scale for EW radiation is
physical. However, at variance with QCD, the theory is weakly-coupled at the
IR scale. A first-principle and accurate modelling of EW radiation is thus
possible in principle, though based on all-orders resummation techniques that
are still to be developed. On top of being functional to the exploitation of
the MuC physics potential, this poses an interesting challenge to theory [58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77,
78, 79, 80, 81, 82, 83, 84, 46, 85].

Muon colliders will require at least as much theory progress as it was needed
and achieved in the past decades for the exploitation of the LHC data. LHC
studies greatly advanced fixed-order calculations, Monte Carlo showering and
resummation techniques and produced radical progress in the theoretical (and
later experimental) knowledge of the QCD interaction. Muon collider physics
requires similar tools but in the EW sector. Its development will entail an
equally radical advance of EW physics knowledge.

###  0.2.2 Synergies and staging

Most of the recent work focuses on the opportunities offered by muon
collisions at 10 TeV (or possibly higher) energy and with the target design
luminosity of $10\leavevmode\nobreak\ {\textrm{ab}}^{-1}$ (or higher, at
higher energy). Much less explored are instead alternative ways—other than
collisions—to exploit the muon beams (see however Ref. [86] for a first study
of physics at muon beam-dump experiments), or the opportunities that emerge
during the facility construction in a staged approach. This is the subject
Sections 0.2.2 and 0.2.2, respectively.

Figure 0.2.3:  Left: The sensitivity (from [4]) to Higgs compositeness. Right:
the number of neutrino DIS events as a function of $x$ and $Q^{2}$ for a 10
TeV MuC after one year of data taking with a small 10 kg detector.

#### Neutrinos

When the muons in the beam decay in the straight section close to the
Interaction Point (IP), they produce a collimated beam of very energetic
neutrinos. Based on the conservative estimate of the neutrino flux presented
in Section 0.3.3, we expect at least $9\times 10^{16}$ neutrinos of each
species emitted in a narrow cone of $0.6$ mrad average angle during one year
of run at the 10 TeV MuC, and $2.4\times 10^{17}$ neutrinos at the 3 TeV
collider. A far-forward detector with realistic geometry (e.g., a 10 cm radius
cylindrical target placed 100 m away from the IP, or a 1 m target at 1 km
distance) would intercept all the emitted neutrinos. Each neutrino would thus
have the chance to produce a detectable interaction, with probability

$p_{\rm{int}}\simeq 6\times
10^{-8}\,\frac{\rho\cdot{L}}{{\rm{g\,cm}}^{-2}}\,\frac{E}{\rm{TeV}}\,,$

where we assumed a typical cross-section on nucleons of
$10^{-35}{\rm{cm}}^{2}\cdot{E}/{\rm{TeV}}$ for all neutrino species, with $E$
the neutrino energy. In the equation, $\rho$ is the density of the neutrino
target and $L$ is the longitudinal extension of the target along the neutrino
beam.

No design is currently available for the neutrino detector. One concept was
developed long ago [87], with the purpose of studying the neutrinos produced
by a dedicated 250 GeV muons ring. The concept foresees a cylindrical target
with 1 m length and 10 cm radius composed of 750 silicon CCD tracking planes,
which would also act as a vertex detector. This would be followed by a
magnetized spectrometer and calorimeter. The design of Ref. [87] ensures
excellent tracking and reconstruction performances for all the particles that
are possibly produced in the interaction, including electrons, muons (and
perhaps $\tau$’s) as well as bottom and charm hadrons tagging and
discrimination. On the other hand, the target mass per unit area is relatively
small: $\rho\cdot{L}=50$ g$\cdot{\textrm{cm}}^{-2}$, for a total target mass
of only 10 kg. Contemporary neutrino detectors operating at similar energy and
with similar physics needs employ denser and bigger targets and attain masses
ranging from one ton (FASERv [88], SND@LHC [89], CHORUS [90]) to several
hundred tons (CHARM [91], NuTeV [92]). Waiting for dedicated studies, it seems
reasonable to assume a target mass of at least one ton for the neutrino
detector.

Figure 0.2.4 reports the energy distribution and the total number of neutrino
interactions that could be recorded by a 10 kg target (corresponding to Ref.
[87]) and by a 1 ton target during one year of run at the 10 TeV and 3 TeV
muon colliders. The neutrinos available for a number of past and planned
experiments (from Ref. [93]) are also reported for comparison. Notice that
only the anti-neutrinos from the decay of the $\mu^{+}$ are included in the
figure. A second detector would be needed to collect the neutrinos from the
$\mu^{-}$ decay, since they fly away from the IP in the opposite direction.
Electron (anti-)neutrinos with a similar spectrum are also present.

The figure shows that one single year of muon collider operations would enable
to collect orders of magnitude more interactions of TeV-energy neutrinos than
current facilities such as FASER$\nu$ and SND@LHC. Even with the very small 10
kg detector, more neutrinos will be collected than at the proposed Forward
Physics Facility (FPF) [95]. The energy spectrum peaks at 1 TeV for the 3 TeV
MuC, and at 4 TeV in the case of the 10 TeV collider, and more than 100
million interactions would be recorded at these energies by a 1 ton detector.
There are many orders of magnitude more neutrino interactions in this energy
range than any other past or planned neutrino experiment. Furthermore,
extremely small uncertainties are expected in the predictions for the energy
spectrum of the muon collider neutrinos, to be contrasted with the large
uncertainties in the spectrum of the neutrinos produced by the LHC arising
from forward hadron production. On top of the superior statistics, neutrino
physics measurements at a muon collider are thus expected to benefit from
reduced systematic uncertainties in comparison with LHC-based experiments such
as FASER or FPF.

Figure 0.2.4: The energy spectrum of neutrino interactions produced by the 3
TeV and 10 TeV MuC in one year, overlaid with the summary plot in Ref. [93]
for past and planned neutrino experiments. The solid and dashed lines assume,
respectively, a small 10 kg and a realistic 1 ton target mass.

The physics opportunities offered by the neutrino beams are still to be
explored. Ideas discussed long ago [87] include CKM quark mixing matrix,
nucleon structure, EW precision and charm quark physics measurements. The
contemporary relevance of these measurements should be assessed, and the
sensitivity projections adapted to the higher-energy neutrino beams that would
be available at the 3 and 10 TeV MuC.

Progress can also come from the extrapolation of the physics reach of modern
LHC-based neutrino experiments. For example, Ref. [96] studied the
opportunities for QCD and hadronic physics studies, and Parton Distribution
Functions (PDFs) [97] determination, offered by neutrino Deep Inelastic
Scattering (DIS) at these facilities. The right panel of Fig. 0.2.3 shows the
expected DIS event yields in the $x$–$Q^{2}$ plane at the 10 TeV muon
collider. The figure conservatively assumes the 10 kg target. The
unprecedented rate of events will make possible a very fine binning with
permille-level statistical uncertainties in the whole kinematic region covered
and enables multi-differential measurements, such as those required to access
the 3D structure of the proton in terms of non-perturbative quantities such as
transverse-momentum dependent PDFs or generalised PDFs. The large statistics
can be positively compared with the predicted event yields at the Electron-Ion
Collider (EIC) [98]. A far-forward neutrino detector at the muon collider
would therefore provide a charged-current analog of the EIC.

#### Stages

We conclude this section with a physics-driven assessment of the opportunities
of muon colliders of lower energy or lower luminosity, to be possibly operated
during the construction of the 10 TeV MuC facility in a staged approach.

At order 100 GeV energy the luminosity is not competitive with the one of
electron-positron colliders, however (see Ref. [4] and references therein)
muon colliders feature specific opportunities in this range of energy. One is
to operate at 125 GeV energy in the centre of mass, exploiting the large muon
Yukawa coupling to produce the Higgs boson in the $s$-channel. This would
enable a percent-level direct determination of the Higgs boson width, an
astonishingly precise Higgs mass measurement at one part per million and few
permille measurement of the muon Yukawa coupling. Alternatively, or in
addition, a muon collider operating at the threshold for the production of a
pair of tops (which muon colliders could reach with a very compact design)
would enable a conclusive assessment of the SM vacuum stability by a
measurement of the top mass with 50 MeV uncertainty. Focused projects with
specific and unique targets like the ones above would be definitely of
interest.

The current IMCC staging plan [4] foresees a first muon collider with 3 TeV
energy in the centre of mass and a target integrated luminosity of 1 ab-1
collected in five years, or of 2 ab-1 in 10 years if the 10 TeV collider
construction is delayed. Such 3 TeV muon collider stage features striking
physics opportunities, described in Ref. [99] in details. These include
probing Higgs compositeness at the 20 TeV scale (still competitive of better
than other future collider project) by high-energy measurements and
determining the Higgs trilinear coupling (see Fig. 0.2.2). It will be also
possible to improve HL-LHC single-Higgs couplings precision, but not to
surpass it radically. Studying muon collisions for the first time entails
strong opportunities, including those that stem from the neutrino beams
previously described.

The 3 TeV MuC can also search for new heavy particles. However, the window of
opportunities beyond the HL-LHC sensitivity is limited by the pair-production
mass reach of $1.5$ TeV. Progress could thus be possible only on relatively
light motivated targets like extended Higgs sectors and Higgsino dark matter.
Further studies and advances on the search of these specific scenarios would
be an important addition to the 3 TeV MuC physics case. Recently, R.
Capdevilla et al.,studied the possibility of observing the soft tracks from
the decay of the charged state in fully realistic experimental conditions
including the BIB, and demonstrated that the Higgsino with thermal mass could
be discovered by this strategy at the 3 TeV MuC [100].

An alternative plan is to operate the first muon collider directly at 10 TeV
energy, but employing less performant technologies—available on a shorter
timescale—which entail a luminosity reduction by around a factor of 10 or
less. The physics reach of such low-luminosity 10 TeV MuC stage can be
robustly extrapolated from the full-luminosity results.

The candidate BSM particles considered in Fig. 0.2.2 would still be discovered
or excluded up to the 5 TeV mass threshold. In fact, the particles considered
in the figure are produced at a very high rate with the full design
luminosity. More than $10^{3}$ or $10^{4}$ production events are expected with
the baseline integrated luminosity of 10 ab-1, which is collected in 5 years
with the full luminosity. Around one month of run would be enable a discovery.
With one tenth of the luminosity, discovery would merely take one year. The
reduced luminosity would of course affect the excellent perspectives of
characterising the properties of the newly discovered particles with
precision, but not the mass-reach.

The indirect physics reach described in Section 0.2.1 will be impacted by the
reduced luminosity because the corresponding measurements are dominated by
statistical uncertainties and not by systematics or theory errors. However,
the factor few increase of the uncertainties—by the square root of the
luminosity—will not have a dramatic impact on the physics reach. While a
detailed and comprehensive assessment is not yet available, it is expected
that the reduced performances would still allow for very competitive studies
of the Higgs single and trilinear couplings, and for probes of very heavy new
physics by high-energy measurements including Higgs compositeness at tens of
TeV. On the other hand, the total 10 ab-1 target luminosity is needed in order
to deliver the physics program described in Section 0.2.1 in its full breadth
and power.

## References

  * [1] Database query in INSPIRE-HEP for muon collider papers written from 2019 to 2024 and classified as “Phenomenology-HEP”, last visited 22 May 2024.
  * [2] H. Al Ali et al., The muon smasher’s guide, Rept. Prog. Phys. 85 (2022) 084201, doi:10.1088/1361-6633/ac6678, [arXiv:2103.14043 [hep-ph]] (2021), doi:10.48550/arXiv.2103.14043.
  * [3] K.M. Black et al., Muon Collider Forum report, JINST 19 (2024) T02015, doi:10.1088/1748-0221/19/02/.
  * [4] C. Accettura et al., Towards a muon collider, Eur. Phys. J. C 83 (2023) 864, doi:10.1140/epjc/s10052-023-11889-x, [erratum: Eur. Phys. J. C 84 (2024) 36, doi:10.1140/epjc/s10052-023-12257-5].
  * [5] The Snowmass 2021 Muon Forum, Wayback Machine, webpage archived 24 May 2023.
  * [6] M. Narain et al. The future of U.S. particle physics—The Snowmass 2021 energy frontier report, [arXiv:2211.11084v3 [hep-ex]], doi:10.48550/arXiv.2211.11084.
  * [7] S. Asai et al., Pathways to innovation and discovery in particle physics: Report of the 2023 particle physics project prioritization panel (P5), https://inspirehep.net/literature/2772795 and website.
  * [8] R.K. Ellis et al., Physics briefing book: Input for the European Strategy for Particle Physics Update 2020, [arXiv:1910.11775v2 [hep-ex]] (2019), doi:10.48550/arXiv.1910.11775.
  * [9] D. Buttazzo, R. Franceschini and A. Wulzer, Two paths towards precision at a very high energy lepton collider,” JHEP 05 (2021), 219, doi:10.1007/JHEP05(2021)219.
  * [10] A. Costantini et al., Vector boson fusion at multi-TeV muon colliders, JHEP 09 (2020) 080, doi:10.1007/JHEP09(2020)080.
  * [11] D. Buttazzo et al., Fusing vectors into scalars at high energy lepton colliders, JHEP 11 (2018) 144, doi:10.1007/JHEP11(2018)144.
  * [12] M. Ruhdorfer, E. Salvioni and A. Weiler, A global view of the off-shell Higgs portal, SciPost Phys. 8 (2020) 027, doi:10.21468/SciPostPhys.8.2.027.
  * [13] W. Liu and K. P. Xie, Probing electroweak phase transition with multi-TeV muon colliders and gravitational waves, JHEP 04 (2021) 015, doi:10.1007/JHEP04(2021)015.
  * [14] P. Asadi et al., Searching for leptoquarks at future muon colliders, JHEP 10 (2021) 182, doi:10.1007/JHEP10(2021)182.
  * [15] G.-y. Huang, F.S. Queiroz and W. Rodejohann, Gauged $L_{\mu}{-}L_{\tau}$ at a muon collider, Phys. Rev. D 103 (2021) 095005, doi:10.1103/PhysRevD.103.095005.
  * [16] W. Liu, K.P. Xie and Z. Yi, Testing leptogenesis at the LHC and future muon colliders: A Z′ scenario, Phys. Rev. D 105 (2022) 095034, doi:10.1103/PhysRevD.105.095034.
  * [17] S. Qian et al., Searching for heavy leptoquarks at a muon collider, JHEP 12 (2021) 047, doi:10.1007/JHEP12(2021)047.
  * [18] P. Bandyopadhyay et al., Distinguishing signatures of scalar leptoquarks at hadron and muon colliders, Eur. Phys. J. C 82 (2022) 916, doi:10.1140/epjc/s10052-022-10809-9.
  * [19] R. Capdevilla et al., Discovering the physics of $(g-2)_{\mu}$ at future muon colliders, Phys. Rev. D 103 (2021) 075028, doi:10.1103/PhysRevD.103.075028.
  * [20] R. Capdevilla et al., No-lose theorem for discovering the new physics of $(g-2)_{\mu}$ at muon colliders, Phys. Rev. D 105 (2022) 015028, doi:10.1103/PhysRevD.105.015028.
  * [21] R. Dermisek, K. Hermanek and N. McGinnis, Muon $g-2$ in two-Higgs-doublet models with vectorlike leptons, Phys. Rev. D 104 (2021) 055033, doi:10.1103/PhysRevD.104.055033.
  * [22] R. Capdevilla etal., Systematically testing singlet models for $(g-2)_{\mu}$, JHEP 04 (2022) 129, doi:10.1007/JHEP04(2022)129.
  * [23] S. Homiller, Q. Lu and M. Reece, Complementary signals of lepton flavor violation at a high-energy muon collider, JHEP 07 (2022) 036, doi:10.1007/JHEP07(2022)036.
  * [24] S. Bottaro, A. Strumia and N. Vignaroli, Minimal dark matter bound states at future colliders, JHEP 06 (2021) 143, doi:10.1007/JHEP06(2021)143.
  * [25] K. Mękała, J. Reuter and A. F. Żarnecki, Optimal search reach for heavy neutral leptons at a muon collider, Phys. Lett. B 841 (2023) 137945, doi:10.1016/j.physletb.2023.137945.
  * [26] P. Li, Z. Liu and K. F. Lyu, Heavy neutral leptons at muon colliders, JHEP 03 (2023) 231, doi:10.1007/JHEP03(2023)231.
  * [27] T. H. Kwok et al., Searching for heavy neutral leptons at a future muon collider, [arXiv:2301.05177v2 [hep-ph]] (2023), doi:10.48550/arXiv.2301.05177.
  * [28] S. Bottaro et al., The last complex WIMPs standing, Eur. Phys. J. C 82 (2022) 992, doi:10.1140/epjc/s10052-022-10918-5.
  * [29] A. Jueid and S. Nasri, Lepton portal dark matter at muon colliders: Total rates and generic features for phenomenologically viable scenarios, Phys. Rev. D 107 (2023) 115027, doi:10.1103/PhysRevD.107.115027.
  * [30] D. Liu, L. T. Wang and K. P. Xie, Composite resonances at a 10 TeV muon collider, JHEP 04 (2024) 084, doi:10.1007/JHEP04(2024)084.
  * [31] L. Di Luzio, R. Gröber and G. Panico, Probing new electroweak states via precision measurements at the LHC and future colliders, JHEP 01 (2019) 011, doi:10.1007/JHEP01(2019)011.
  * [32] R. Franceschini and X. Zhao, Going all the way in the search for WIMP dark matter at the muon collider through precision measurements, Eur. Phys. J. C 83 (2023) 552, doi:10.1140/epjc/s10052-023-11724-3.
  * [33] T. Han et al., WIMPs at high energy muon colliders, Phys. Rev. D 103 (2021) 075004, doi:10.1103/PhysRevD.103.075004.
  * [34] S. Bottaro et al., Closing the window on WIMP dark matter, Eur. Phys. J. C 82 (2022) 31, doi:10.1140/epjc/s10052-021-09917-9.
  * [35] R. Capdevilla et al., Hunting wino and higgsino dark matter at the muon collider with disappearing tracks, JHEP 06 (2021) 133, doi:10.1007/JHEP06(2021)133.
  * [36] J. de Favereau et al. [DELPHES 3 Collaboration], DELPHES 3, A modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057, doi:10.1007/JHEP02(2014)057.
  * [37] Muon collider detector Delphes card, https://github.com/delphes/delphes/blob/master/cards/delphes_card_MuonColliderDet.tcl, last accessed 13 June 2024.
  * [38] T. Han et al., Electroweak couplings of the Higgs boson at a multi-TeV muon collider, Phys. Rev. D 103 (2021) 013002, doi:10.1103/PhysRevD.103.013002.
  * [39] M. Forslund and P. Meade, High precision higgs from high energy muon colliders, JHEP 08 (2022) 185, doi:10.1007/JHEP08(2022)185.
  * [40] N. Bartosik et al. [International Muon Collider Collaboration], Simulated detector performance at the muon collider, [arXiv:2203.07964v2 [hep-ex]] (2022), doi:10.48550/arXiv.2203.07964.
  * [41] J. de Blas et al. Higgs boson studies at future particle colliders, JHEP 01 (2020) 139, doi:10.1007/JHEP01(2020)139.
  * [42] P. Li, Z. Liu and K. F. Lyu, Higgs boson width and couplings at high energy muon colliders with forward muon detection, Phys. Rev. D 109 (2024) 073009, doi:10.1103/PhysRevD.109.073009.
  * [43] M. Forslund and P. Meade, Precision Higgs width and couplings with a high energy muon collider, JHEP 01 (2024) 182, doi:10.1007/JHEP01(2024)182.
  * [44] J. de Blas et al. [CLIC Collaboration], The CLIC potential for new physics, CERN-2018-009-M (CERN, Geneva, 2018), doi:10.23731/CYRM-2018-003.
  * [45] M. L. Mangano, G. Ortona and M. Selvaggi, Measuring the Higgs self-coupling via Higgs-pair production at a 100 TeV p-p collider, Eur. Phys. J. C 80 (2020) 1030, doi:10.1140/epjc/s10052-020-08595-3.
  * [46] S. Chen et al., Learning from radiation at a very high energy lepton collider, JHEP 05 (2022) 180, doi:10.1007/JHEP05(2022)180.
  * [47] N. Chakrabarty et al., Radiative return for heavy Higgs boson at a muon collider, Phys. Rev. D 91 (2015) 015008, doi:10.1103/PhysRevD.91.015008.
  * [48] D. Buttazzo and P. Paradisi, Probing the muon $g-2$ anomaly with the Higgs boson at a muon collider, Phys. Rev. D 104 (2021) 075021, doi:10.1103/PhysRevD.104.075021.
  * [49] W. Yin and M. Yamaguchi, Muon $g-2$ at a multi-TeV muon collider, Phys. Rev. D 106 (2022) 033007, doi:10.1103/PhysRevD.106.033007.
  * [50] R. Dermisek, K. Hermanek and N. McGinnis, Di-Higgs and tri-Higgs boson signals of muon $g-2$ at a muon collider, Phys. Rev. D 104 (2021) L091301, doi:10.1103/PhysRevD.104.L091301.
  * [51] R. Dermisek et al., Ellipse of muon dipole moments, Phys. Rev. Lett. 129 (2022) 221801, doi:10.1103/PhysRevLett.129.221801.
  * [52] P. Paradisi, O. Sumensari and A. Valenti, High-energy frontier of the muon $g-2$ at a muon collider, Phys. Rev. D 106 (2022) 115038, doi:10.1103/PhysRevD.106.115038.
  * [53] G. y. Huang et al., Probing the R${}_{\mathrm{K}^{(*)}}$ anomaly at a muon collider, Phys. Rev. D 105 (2022) 015013, doi:10.1103/PhysRevD.105.015013.
  * [54] A. Azatov et al., New physics in b → s$\mu$$\mu$: FCC-hh or a muon collider?, JHEP 10 (2022) 149, doi:10.1007/JHEP10(2022)149.
  * [55] W. Altmannshofer, S. A. Gadam and S. Profumo, Snowmass White Paper: Probing new physics with $\mu^{+}\mu^{-}\to bs$ at a muon collider, [arXiv:2203.07495 [hep-ph]] (2022), doi:10.48550/arXiv.2203.07495.
  * [56] R. Bause et al., B-anomalies from flavorful U(1)′ extensions, safely, Eur. Phys. J. C 82 (2022) 42, doi:10.1140/epjc/s10052-021-09957-1.
  * [57] B. Allanach and E. Loisa, Flavonstrahlung in the B3$-$ L2Z′ model at current and future colliders, JHEP 03 (2023) 253, doi:10.1007/JHEP03(2023)253.
  * [58] S. Dawson, The effective W approximation, Nucl. Phys. B 249 (1985) 42–60, doi:10.1016/0550-3213(85)90038-0.
  * [59] G. L. Kane, W. W. Repko and W. B. Rolnick, The effective W±, Z0 approximation for high-energy collisions, Phys. Lett. B 148 (1984) 367–372, doi:10.1016/0370-2693(84)90105-9.
  * [60] Z. Kunszt and D. E. Soper, On the validity of the effective W approximation, Nucl. Phys. B 296 (1988) 253–289, doi:10.1016/0550-3213(88)90673-6.
  * [61] M. S. Chanowitz and M. K. Gaillard, The TeV physics of strongly interacting W’s and Z’s, Nucl. Phys. B 261 (1985) 379–431, doi:10.1016/0550-3213(85)90580-2.
  * [62] G. J. Gounaris, R. Kogerler and H. Neufeld, Relationship between longitudinally polarized vector bosons and their unphysical scalar partners, Phys. Rev. D 34 (1986) 3257–3259, doi:10.1103/PhysRevD.34.3257.
  * [63] W. B. Kilgore, The equivalence theorem in the Abelian Higgs theory, Phys. Lett. B 294 (1992) 257–262, doi:10.1016/0370-2693(92)90691-V.
  * [64] V. S. Fadin et al., Resummation of double logarithms in electroweak high-energy processes, Phys. Rev. D 61 (2000) 094002, doi:10.1103/PhysRevD.61.094002, [arXiv:hep-ph/9910338] (1999), doi:10.48550/arXiv.hep-ph/9910338.
  * [65] M. Ciafaloni, P. Ciafaloni and D. Comelli, Electroweak Bloch–Nordsieck violation at the TeV scale: “Strong” weak interactions?, Nucl. Phys. B 589 (2000) 359–380, doi:10.1016/S0550-3213(00)00508-3, [arXiv:hep-ph/0004071] (2000), doi:10.48550/arXiv.hep-ph/0004071.
  * [66] M. Ciafaloni, P. Ciafaloni and D. Comelli, Bloch–Nordsieck violating electroweak corrections to inclusive TeV scale hard processes, Phys. Rev. Lett. 84 (2000) 4810–4813, doi:10.1103/PhysRevLett.84.4810, [arXiv:hep-ph/0001142v2] (2000), doi:10.48550/arXiv.hep-ph/0001142.
  * [67] M. Melles, Subleading Sudakov logarithms in electroweak high-energy processes to all orders, Phys. Rev. D 63 (2001) 034003, doi:10.1103/PhysRevD.63.034003, [arXiv:hep-ph/0004056v2] (2000), doi:10.48550/arXiv.hep-ph/0004056.
  * [68] A. Manohar et al., Non-cancellation of electroweak logarithms in high-energy scattering, Phys. Lett. B 740 (2015) 179–187, doi:10.1016/j.physletb.2014.11.050.
  * [69] C. W. Bauer, N. Ferland and B. R. Webber, Standard Model parton distributions at very high energies, JHEP 08 (2017) 036, doi:10.1007/JHEP08(2017)036.
  * [70] C. W. Bauer, D. Provasoli and B. R. Webber, Standard Model fragmentation functions at very high energies, JHEP 11 (2018) 030, doi:10.1007/JHEP11(2018)030.
  * [71] A. V. Manohar and W. J. Waalewijn, Electroweak logarithms in inclusive cross sections, JHEP 08 (2018) 137, doi:10.1007/JHEP08(2018)137.
  * [72] B. Fornal, A. V. Manohar and W. J. Waalewijn, Electroweak gauge boson parton distribution functions, JHEP 05 (2018) 106, doi:10.1007/JHEP05(2018)106.
  * [73] J. y. Chiu et al., Electroweak corrections in high energy processes using effective field theory, Phys. Rev. D 77 (2008) 053004, doi:10.1103/PhysRevD.77.053004, [arXiv:0712.0396 [hep-ph]] (2007), 10.48550/arXiv.0712.0396.
  * [74] J. y. Chiu et al., Electroweak Sudakov corrections using effective field theory, Phys. Rev. Lett. 100 (2008) 021802, doi:10.1103/PhysRevLett.100.021802, [arXiv:0709.2377v2 [hep-ph]] (2007), doi:10.48550/arXiv.0709.2377.
  * [75] J. y. Chiu et al., Soft and collinear functions for the Standard Model, Phys. Rev. D 81 (2010) 014023, doi:10.1103/PhysRevD.81.014023, [arXiv:0909.0947v2 [hep-ph]], doi:10.48550/arXiv.0909.0947.
  * [76] A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 1. Results, Eur. Phys. J. C 18 (2001), 461–480, doi:10.1007/s100520100551, [arXiv:hep-ph/0010201v3] (2000), doi:10.48550/arXiv.hep-ph/0010201.
  * [77] A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 2. Factorization of collinear singularities, Eur. Phys. J. C 21 (2001) 63–79, doi:10.1007/s100520100721, [arXiv:hep-ph/0104127] (2001), doi:10.48550/arXiv.hep-ph/0104127.
  * [78] P. Borel et al., Probing the scattering of equivalent electroweak bosons, JHEP 06 (2012) 122, doi:10.1007/JHEP06(2012)122, [arXiv:1202.1904 [hep-ph]] (2012), doi:10.48550/arXiv.1202.1904.
  * [79] A. Wulzer, An equivalent gauge and the equivalence theorem, Nucl. Phys. B 885 (2014) 97–126, doi:10.1016/j.nuclphysb.2014.05.021.
  * [80] G. Cuomo, L. Vecchi and A. Wulzer, Goldstone equivalence and high energy electroweak physics, SciPost Phys. 8 (2020) 078, doi:10.21468/SciPostPhys.8.5.078.
  * [81] E. Bothmann and D. Napoletano, Automated evaluation of electroweak Sudakov logarithms in Sherpa, Eur. Phys. J. C 80 (2020) 1024, doi:10.1140/epjc/s10052-020-08596-2.
  * [82] J. Chen, T. Han and B. Tweedie, Electroweak splitting functions and high energy showering, JHEP 11 (2017) 093, doi:10.1007/JHEP11(2017)093.
  * [83] T. Han, Y. Ma and K. Xie, Quark and gluon contents of a lepton at high energies, JHEP 02 (2022) 154, doi:10.1007/JHEP02(2022)154.
  * [84] R. Ruiz et al., The effective vector boson approximation in high-energy muon collisions, JHEP 06 (2022) 114, doi:10.1007/JHEP06(2022)114.
  * [85] F. Garosi, D. Marzocca and S. Trifinopoulos, LePDF: Standard Model PDFs for high-energy lepton colliders, JHEP 09 (2023) 107, doi:10.1007/JHEP09(2023)107.
  * [86] C. Cesarotti and R. Gambhir, The new physics case for beam-dump experiments with accelerated muon beams, JHEP 05 (2024) 283, doi:10.1007/JHEP05(2024)283.
  * [87] B. J. King, Neutrino physics at a muon collider, AIP Conf. Proc. 435 (1998) 334–348, doi:10.1063/1.56211, [arXiv:hep-ex/9907033] (1999), doi:10.48550/arXiv.hep-ex/9907033.
  * [88] H. Abreu et al. [FASER Collaboration], The FASER detector, JINST 19 (2024) P05066, doi:10.1088/1748-0221/19/05/P05066.
  * [89] G. Acampora et al. [SND@LHC Collaboration], SND@LHC: The Scattering and Neutrino Detector at the LHC, JINST 19 (2024) P05067, doi:10.1088/1748-0221/19/05/P05067.
  * [90] G. Onengut et al. [CHORUS Collaboration], Measurement of nucleon structure functions in neutrino scattering, Phys. Lett. B 632 (2006) 65–75, doi:10.1016/j.physletb.2005.10.062.
  * [91] J. V. Allaby et al. [CHARM Collaboration], A precise determination of the electroweak mixing angle from semileptonic neutrino scattering, Z. Phys. C 36 (1987) 611–628, doi:10.1007/BF01630598.
  * [92] M. Tzanov et al. [NuTeV Collaboration], Precise measurement of neutrino and anti-neutrino differential cross sections, Phys. Rev. D 74 (2006) 012008, doi:10.1103/PhysRevD.74.012008, [arXiv:hep-ex/0509010] (2005), doi:10.48550/arXiv.hep-ex/0509010.
  * [93] C. Ahdida et al., Post-LS3 experimental options in ECN3, CERN-PBC Report-2023-003, [arXiv:2310.17726 [hep-ex]] (2023), doi:10.48550/arXiv.2310.17726.
  * [94] H. Abreu et al. [FASER Collaboration], Detecting and studying high-energy collider neutrinos with FASER at the LHC, Eur. Phys. J. C 80 (2020) 61, doi:10.1140/epjc/s10052-020-7631-5.
  * [95] J. L. Feng et al., The forward physics facility at the High-Luminosity LHC, J. Phys. G 50 (2023) 030501, doi:10.1088/1361-6471/ac865e.
  * [96] J. M. Cruz-Martinez et al., The LHC as a neutrino-ion collider, Eur. Phys. J. C 84 (2024) 369, doi:10.1140/epjc/s10052-024-12665-1.
  * [97] J. Gao, L. Harland-Lang and J. Rojo, The structure of the proton in the LHC precision era, Phys. Rept. 742 (2018) 1–121, doi:10.1016/j.physrep.2018.03.002, [arXiv:1709.04922v2 [hep-ph]] (2017), doi:10.48550/arXiv.1709.04922.
  * [98] R. Abdul Khalek et al., Science requirements and detector concepts for the Electron-Ion Collider: EIC yellow report, Nucl. Phys. A 1026 (2022) 122447, doi:10.1016/j.nuclphysa.2022.122447, [arXiv:2103.05419v3 [physics.ins-det]] (2021), doi:10.48550/arXiv.2103.05419.
  * [99] J. de Blas et al. [International Muon Collider Collaboration], The physics case of a 3 TeV muon collider stage, FERMILAB-CONF-22-317-AD-ND-PPD-SCD-TD (2022), [arXiv:2203.07261v2 [hep-ph]] (2022), doi:10.48550/arXiv.2203.07261.
  * [100] R. Capdevilla, F. Meloni and J. Zurita, Discovering electroweak interacting dark matter at muon colliders using soft tracks, FERMILAB-PUB-23-0832-T, DESY-24-069, [arXiv:2405.08858 [hep-ph]] (2024), doi:10.48550/arXiv.2405.08858.