Muon Collider Physics Summary arXiv:2203.07256v2 [hep-ph ...

May 30 2022httpsmuoncolliderwebcernch

Muon Collider Physics Summary

Submitted to the Proceedings of the US Community Studyon the Future of Particle Physics (Snowmass 2021)

AbstractThe perspective of designing muon colliders with high energy and luminositywhich is being investigated by the International Muon Collider Collaborationhas triggered a growing interest in their physics reachWe present a concise summary of the muon collider potential to explore newphysics leveraging on the unique possibility of combining high available en-ergy with very precise measurements

This is one of the five reports submitted to Snowmass by the muon colliders community at large The re-ports preparation effort has been coordinated by the International Muon Collider Collaboration Authorsand Signatories have been collected with a subscription page and are defined as follows

ndash An ldquoAuthorrdquo contributed to the results documented in the report in any form including eg byparticipating to the discussions of the community meetings and sending comments on the draft orplans to contribute to the future work

ndash A ldquoSignatoryrdquo expresses support to the efforts described in the report and endorses the Collabora-tion plans

AuthorsC Aimegrave129 A Apyan2 MA Mahmoud3 N Bartosik4 A Bertolin5 M Bonesini679 S Bottaro78D Buttazzo8 R Capdevilla920 M Casarsa10 L Castelli11 MG Catanesi12 FG Celiberto1380A Cerri14 C Cesarotti15 G Chachamis16 S Chen17 Y-T Chien18 M Chiesa129 G Collazuol511M Costa78 N Craig19 D Curtin20 S Dasu21 J de Blas22 D Denisov23 H Denizli24R Dermisek25 L Luzio115 B Di Micco2681 K R Dienes2782 T Dorigo5 A Ferrari28 D Fiorina29R Franceschini2681 F Garosi30 A Glioti17 M Greco26 A Greljo31 R Groumlber325 C Grojean3383J Gu34 T Han35 B Henning17 K Hermanek25 TR Holmes36 S Homiller15 S Jana37S Jindariani38 Y Kahn39 I Karpov40 W Kilian41 K Kong42 P Koppenburg43 K Krizka44 L Lee36Q Li45 R Lipton38 Z Liu46 KR Long4784 I Low4885 D Lucchesi115 Y Ma35 L Ma49F Maltoni5086 B Mansoulieacute51 L Mantani52 D Marzocca10 N McGinnis53 B Mele54 F Meloni33C Merlassino55 A Montella10 M Nardecchia5654 F Nardi115 P Panci578 S Pagan Griso44G Panico5860 R Paparella59 P Paradisi325 N Pastrone4 F Piccinini29 K Potamianos55E Radicioni12 R Rattazzi17 D Redigolo60 L Reina61 J Reuter33 C Riccardi129 L Ricci17L Ristori38 T Robens62 R Ruiz63 F Sala64 J Salko31 P Salvini29 E Salvioni325 D Schulte40M Selvaggi40 A Senol24 L Sestini5 V Sharma21 J Shu65 R Simoniello40 G Stark66D Stolarski67 S Su27 W Su68 O Sumensari69 X Sun70 R Sundrum71 J Tang7287 A Tesi60B Thomas73 R Torre74 S Trifinopoulos10 I Vai29 A Valenti325 L Vittorio78 L-T Wang75Y Wu76 A Wulzer11 X Zhao2681 J Zurita77

arX

iv2

203

0725

6v2

[he

p-ph

] 2

7 M

ay 2

022

SignatoriesD Acosta88 K Agashe82 BC Allanach52 F Anulli54 A Apresyan38 P Asadi89 D Athanasakos90A Azatov3010 JJ Back91 L Bandiera92 R J Barlow93 E Barzi38148 F Batsch40 M Bauce5456J S Berg23 J Berryhill38 A Bersani74 KM Black21 C Booth94 L Bottura D Bowring38A Braghieri29 G Brooijmans95 A Bross38 E Brost23 L Buonincontri511 B Caiffi74G Calderini96149 S Calzaferri29 P Cameron23 A Canepa38 F Casaburo G Cavoto5654L Celona97 G Cesarini Z Chacko82 A Chanceacute51 R T Co98 A Colaleo9912 D J Colling47G Corcella100 L M Cremaldi A Crivellin101150 Y Cui102 C Curatolo6 R T DrsquoAgnolo103F DrsquoEramo115 G Da Molin11 M Dam6 H Damerau40 E De Matteis59 A Deandrea104J Delahaye40 A Delgado105 C Densham84 K F Di Petrillo38 J Dickinson38 M Dracos106J Duarte107 F Errico9912 R Essig90 P Everaerts21 L Everett21 M Fabbrichesi10 J Fan108S Farinon74 J F Somoza40 G Ferretti109 F Filthaut110 M Forslund90 P Franchini111151M Frigerio112 E Gabrielli11310 M Gallinaro16 I Garcia Garcia114 L Giambastiani115AS Giannakopoulou115 D Giove59 C Giraldin11 L Gladilin S Goldfarb116 HM Gray11744L Gray38 HE Haber66 J Haley76 C Han72 J Hauptman118 M Herndon21 H Jia21 C Jolly84D M Kaplan119 D Kelliher84 GK Krintiras42 G Krnjaic38 N Kumar120 P Kyberd121R LOSITO40 J-B Lagrange84 S Levorato W Li88 R L Voti54 D Liu122 M Liu123 S Lomte21Q Lu15 R Mahbubani62 A Mariotti124 S Mariotto12559 P Mastrapasqua50 K Matchev126A Mazzacane38 P Meade90 P Merkel38 F Mescia127152 R K Mishra15 A Mohammadi21R Mohapatra N Mokhov38 P Montagna129 R Musenich74 MS Neubauer39 D Neuffer38H Newman128 Y Nomura117 I Ojalvo129 JL Oliver130 G Ortona4 D Pagani131 M Palmer23A Pellecchia99 A Perloff132 M Pierini40 M Prioli59 M Procura133 R Radogna9912RA Rimmer134 F Riva135 C Rogers84 L Rossi12559 R Ryne136 J Santiago13822 E Santopinto74I Sarra J Schieck139153 R Schwiehorst140 D Sertore59 V Shiltsev38 L Silvestris12F M Simone9912 K Skoufaris40 P Snopok119 FJP Soler141 M Sorbi12559 A Stamerra9912M Statera59 D Stratakis38 N Strobbe46 J Stupak142 M Swiatlowski53 A Sytov92 A Taffard130T Tait130 J Tang87 M Taoso4 J Thaler89 E A Thompson33 L Tortora81 Y Torun119 M Valente53R U Valente59 N Valle129 R Venditti9912 P Verwilligen12 N Vignaroli143 P Vitulo129E Vryonidou144 C Vuosalo21 H Weber83 CG Whyte145 K Xie35 A Yamamoto146 W Yin147K Yonehara38 H-B Yu102 M Zanetti11 A Zaza9912 J Zhang Y J Zheng42 A Zlobin38D Zuliani115

1Universitagrave di Pavia Italy 2Department of Physics Brandeis University United States 3Center for High EnergyPhysics (CHEP-FU) Fayoum University Egypt 4INFN Sezione di Torino Italy 5INFN Sezione di Padova Italy6Istituto Nazionale di Fisica Nucleare Italy 7Scuola Normale Superiore Italy 8INFN Sezione di Pisa Italy9Perimeter Institute Canada 10INFN Sezione di Trieste Italy 11Dipartimento di Fisica e AstronomiaUniversitrsquoa di Padova Italy 12INFN Sezione di Bari Italy 13European Centre for Theoretical Studies in NuclearPhysics and Related Areas (ECT) Italy 14MPS School University of Sussex United Kingdom 15Departmentof Physics Harvard University United States 16Laboratoacuterio de Instrumentaccedilatildeo e Fiacutesica Experimental dePartiacuteculas (LIP) Portugal 17Theoretical Particle Physics Laboratory (LPTP) Institute of Physics EPFLSwitzerland 18Physics and Astronomy Department Georgia State University United States 19University ofCalifornia Santa Barbara United States 20Department of Physics University of Toronto Canada 21Universityof Wisconsin United States 22CAFPE and Departamento de Fiacutesica Teoacuterica y del Cosmos Universidad deGranada Spain 23Brookhaven National Laboratory United States 24Department of Physics Bolu Abant IzzetBaysal University Turkey 25Physics Department Indiana University United States 26Dipartimento diMatematica e Fisica Universitagrave Roma Tre Italy 27Department of Physics University of Arizona United States28Helmholtz-Zentrum Dresden-Rossendorf Germany 29INFN Sezione di Pavia Italy 30SISSA Italy 31Albert

2

Einstein Center for Fundamental Physics Institute for Theoretical Physics University of Bern Switzerland32Universitagrave di Padova Italy 33Deutsches Elektronen-Synchrotron DESY Germany 34Department of PhysicsFudan University China 35University of Pittsburgh United States 36University of Tennessee United States37Max-Planck-Institut fuumlr Kernphysik Germany 38Fermi National Accelerator Laboratory United States39Department of Physics University of Illinois at Urbana-Champaign United States 40CERN Switzerland41Department of Physics University of Siegen Germany 42Department of Physics and Astronomy University ofKansas United States 43Nikhef National Institute for Subatomic Physics The Netherlands 44Physics DivisionLawrence Berkeley National Laboratory United States 45Peking University China 46School of Physics andAstronomy University of Minnesota United States 47Imperial College London United Kingdom 48HighEnergy Physics Division Argonne National Laboratory United States 49Shandong University China 50Centerfor Cosmology Particle Physics and Phenomenology Universiteacute catholique de Louvain Belgium 51IRFU CEAUniversity Paris-Saclay France 52DAMTP University of Cambridge United Kingdom 53TRIUMF Canada54INFN Sezione di Roma Italy 55Particle Physics Department University of Oxford United Kingdom56Sapienza University of Rome Italy 57Pisa University Italy 58Dipartimento di Fisica e Astronomia Universitagravedegli Studi di Firenze Italy 59INFN Sezione di Milano LASA Italy 60INFN Sezione di Firenze Italy61Florida State University United States 62Rudjer Boskovic Institute Croatia 63Institute of Nuclear Physics ndashPolish Academy of Sciences (IFJ PAN) Poland 64Laboratoire de Physique Theacuteorique et Hautes EacutenergiesSorbonne Universiteacute CNRS France 65CAS Key Laboratory of Theoretical Physics Insitute of TheoreticalPhysics Chinese Academy of Sciences PRChina 66SCIPP UC Santa Cruz United States 67Ottawa-CarletonInstitute for Physics Carleton University Canada 68Korea Institute for Advanced Study South Korea 69IJCLabPocircle Theacuteorie (Bacirct 210) CNRSIN2P3 et Universiteacute Paris-Saclay France 70State Key Laboratory of NuclearPhysics and Technology Peking University China 71Maryland Center for Fundamental Physics University ofMaryland United States 72Sun Yat-sen University China 73Department of Physics Lafayette College UnitedStates 74INFN Sezione di Genova Italy 75Department of Physics University of Chicago United States76Department of Physics Oklahoma State University United States 77Instituto de Fiacutesica CorpuscularCSIC-Universitat de Valeacutencia Spain 78Institut fuumlr Allgemeine Elektrotechnik Universitaumlt Rostock Germany79Dipartimento di Fisica Universitagrave Milano Bicocca Italy 80INFN-TIFPA Trento Institute of FundamentalPhysics and Applications Italy 81INFN Sezione di Roma Tre Italy 82Department of Physics University ofMaryland United States 83Humboldt-Universitaumlt zu Berlin Institut fuumlr Physik Germany 84STFC UnitedKingdom 85Department of Physics and Astronomy Northwestern University United States 86Dipartimento diFisica e Astronomia Universitagrave di Bologna Italy 87Institute of High-Energy Physics China 88Physics ampAstronomy Department Rice University United States 89Center for Theoretical Physics Massachusetts Instituteof Technology United States 90YITP Stony Brook United States 91Department of Physics University ofWarwick United Kingdom 92INFN Sezione di Ferrara Italy 93The University of Huddersfield UnitedKingdom 94Department of Physics and Astronomy University of Sheffield United Kingdom 95ColumbiaUniversity United States 96CNRSIN2P3 France 97INFN Sezione di Catania Italy 98University of MinnesotaUnited States 99Department of Physics Universitagrave degli Studi di Bari Italy 100INFN Laboratori Nazionali diFrascati Italy 101University of Zurich Switzerland 102University of California-Riverside United States103Universitegrave Paris Saclay CNRS CEA Institut de Physique Thegraveorique France 104IP2I Universiteacute Lyon 1CNRSIN2P3 France 105University of Notre Dame United States 106IPHC Universiteacute de StrasbourgCNRSIN2P3 France 107University of California San Diego United States 108Brown University United States109Chalmers University of Technology Sweden 110Radboud University and Nikhef The Netherlands111University of Lancaster Department of Physics United Kingdom 112Laboratoire Charles Coulomb CNRSand University of Montpellier France 113Physics Department University of Trieste Italy 114Kavli Institute forTheoretical Physics University of California Santa Barbara United States 115SUNY at Stony Brook UnitedStates 116School of Physics University of Melbourne Australia 117UC Berkeley United States 118Iowa StateUniversity United States 119Illinois Institute of Technology United States 120Delhi University India121College of Engineering Design and Physical Sciences Brunel University United Kingdom 122Center forQuantum Mathematics and Physics (QMAP) University of California Davis United States 123PurdueUniversity United States 124Theoretische Natuurkunde and IIHEELEM Vrije Universiteit Brussel Belgium

3

125Dipartimento di Fisica Aldo Pontremoli Universitaacute degli Studi di Milano Italy 126Physics DepartmentUniversity of Florida United States 127Universitat de Barcelona Spain 128California Institute of TechnologyUnited States 129Princeton University United States 130UC Irvine United States 131INFN Sezione di BolognaItaly 132Department of Physics University of Colorado United States 133University of Vienna Faculty ofPhysics Austria 134JLab United States 135Deacutepartment de Physique Theacuteorique Universiteacute de GenegraveveSwitzerland 136Lawrence Berkeley National Laboratory United States 137International Institute of PhysicsUniversidade Federal do Rio Grande do Norte Brazil 138CAFPE Spain 139Institut fuumlr Hochenergiephysik derOumlsterreichischen Akademie der Wissenschaften Austria 140Michigan State University United States 141Schoolof Physics and Astronomy University of Glasgow United Kingdom 142University of Oklahoma United States143Universitaacute di Napoli ldquoFederico II and INFN Napoli Italy 144University of Manchester United Kingdom145Physics SUPA United Kingdom 146High Energy Accelerator Research Organization KEK Japan 147TohokuUniversity Japan 148Ohio State University United States 149LPNHE Sorbonne Universiteacute France 150PaulScherrer Institute Switzerland 151Royal Holloway University of London Department of Physics UnitedKingdom 152Institut de Ciencies del Cosmos (ICC) Spain 153Atominstitut Technische Universitaumlt WienAustria

1 OverviewColliders are microscopes that explore the structure and the interactions of particles at the shortest pos-sible length scale Their goal is not to chase discoveries that are inevitable or perceived as such based oncurrent knowledge On the contrary their mission is to explore the unknown in order to acquire radicallynovel knowledge

The current experimental and theoretical situation of particle physics is particularly favorable tocollider exploration No inevitable discovery diverts our attention from pure exploration and we canfocus on the basic questions that best illustrate our ignorance Why is electroweak symmetry broken andwhat sets the scale Is it really broken by the Standard Model Higgs or by a more rich Higgs sector Isthe Higgs an elementary or a composite particle Is the top quark in light of its large Yukawa couplinga portal towards the explanation of the observed pattern of flavor Is the Higgs or the electroweak sectorconnected with dark matter Is it connected with the origin of the asymmetry between baryons andanti-baryons in the Universe

The next collider should offer broad and varied opportunities for exploration It should deepenour understanding of the questions above and be ready to tackle novel challenges that might emergefrom future discoveries at the LHC or other experiments The current g-2 and lepton flavor universalityviolation anomalies which are both related to muons are examples of tensions with the Standard Model(SM) that the next collider might be called to elucidate by accessing the corresponding microscopicexplanation

A comprehensive exploration must exploit the complementarity between energy and precisionPrecise measurements allow us to study the dynamics of the particles we already know looking for theindirect manifestation of yet unknown new physics With a very high energy collider we can access thenew physics particles directly These two exploration strategies are normally associated with two distinctmachines either colliding electronspositrons (ee) or protons (pp)

With muons instead both strategies can be effectively pursued at a single collider that combinesthe advantages of ee and of ppmachines Moreover the simultaneous availability of energy and precisionoffers unique perspectives of indirect sensitivity to new physics at the 100 TeV scale as well as uniqueperspectives for the characterization of new heavy particles discovered at the muon collider itself Thisis the picture that emerges from the studies of the muon colliders physics potential performed so far tobe reviewed in this document

2 Why muonsMuons like protons can be made to collide with a center of mass energy of 10 TeV or more in arelatively compact ring without fundamental limitations from synchrotron radiation However beingpoint-like particles unlike protons their nominal center of mass collision energyEcm is entirely availableto produce high-energy reactions that probe lengths scale as short as 1Ecm The relevant energy forproton colliders is instead the center of mass energy of the collisions between the partons that constitutethe protons The partonic collision energy is distributed statistically and approaches a significant fractionof the proton collider nominal energy with very low probability A muon collider with a given nominalenergy and luminosity is thus evidently way more effective than a proton collider with comparable energyand luminosity

This concept is made quantitative in Figure 1 The figure displays the center of mass energyradicsp

that a proton collider must possess to be ldquoequivalentrdquo to a muon collider of a given energy Ecm =radicsmicro

Equivalence is defined [124] in terms of the pair production cross-section for heavy particles with massclose to the muon collider kinematical threshold of

radicsmicro2 The equivalent

radicsp is the proton collider

center of mass energy for which the cross-sections at the two colliders are equal

The estimate of the equivalentradicsp depends on the relative strength β of the heavy particle inter-

action with the partons and with the muons If the heavy particle only possesses electroweak quantum

5

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

gg

qq

β=1

β=10

β=100

0 10 20 30 40 50 60 70 80 90 100

200

400

600

800

1000

1200

1400

1600

sμ [TeV]

s p[TeV

]

Fig 1 Equivalent proton collider energy The left plot [1] assumes that qq and gg partonic initial statesboth contribute to the production In the orange and blue lines β = 1 and β = 10 respectively In theright panel [4] production from qq and from gg are considered separately

numbers β = 1 is a reasonable estimate because the particles are produced by the same interaction at thetwo colliders If instead it also carries QCD color the proton collider can exploit the QCD interaction toproduce the particle and a ratio of β = 10 should be considered owing to the large QCD coupling andcolor factors The orange line on the left panel of Figure 1 obtained with β = 1 is thus representativeof purely electroweak particles The blue line with β = 10 is instead a valid estimate for particles thatalso possess QCD interactions as it can be verified in concrete examples

The general lesson we learn from the left panel of Figure 1 (orange line) is that at a proton colliderwith around 100 TeV energy the cross-section for processes with an energy threshold of around 10 TeVis much smaller than the one of a muon collider operating at Ecm =

radicsmicro sim 10 TeV The gap can be

compensated only if the process dynamics is different and more favorable at the proton collider like inthe case of QCD production The general lesson has been illustrated for new heavy particles productionwhere the threshold is provided by the particle mass But it also holds for the production of light SMparticles with energies as high as Ecm which are very sensitive indirect probes of new physics Thismakes exploration by high energy measurements more effective at muon than at proton colliders aswe will see in Section 5 Moreover the large luminosity for high energy muon collisions producesthe copious emission of effective vector bosons In turn they are responsible at once for the tremendousdirect sensitivity of muon colliders to ldquoHiggs portalrdquo type new physics and for their excellent perspectivesto measure single and double Higgs couplings precisely as we will see in Section 3 and 4 respectively

On the other hand no quantitative conclusion can be drawn from Figure 1 on the comparisonbetween the muon and proton colliders discovery reach for the heavy particles That assessment will beperformed in the following section based on available proton colliders projections

3 Direct reachThe left panel of Figure 2 displays the number of expected events at a 10 TeV muon collider with10 abminus1 integrated luminosity for the pair production due to electroweak interactions of Beyond theStandard Model (BSM) particles with variable mass M The particles are named with a standard BSMterminology however the results do not depend on the detailed BSM model (such as Supersymmetryor Composite Higgs) in which these particles emerge but only on their Lorentz and gauge quantumnumbers The dominant production mechanism at high mass is the direct micro+microminus annihilation whosecross-section flattens out below the kinematical threshold at M = 5 TeV The cross-section increase atlow mass is due to the production from effective vector bosons annihilation

The figure shows that with the target luminosity of 10 abminus1 a Ecm = 10 TeV muon collider canproduce the BSM particles abundantly If they decay to energetic and detectable SM final states the new

6

ltlatexit sha1_base64=8RLmpAJ4CPiKR4h1tOFVZrXME=gtAAAB8nicbVBNSwMxEJ2tX7V+VT16CRbBU9mVoh6LvSh4qGAYLuUbJq2odlkSbJCWfZnePGgiFdjTfjWm7B219MPB4b4aZeWHMmTau++0U1tY3NreK26Wd3b39gLhUVvLRBHaIpJL1Q2xppwJ2jLMcNqNFcVRyGknnDRmfueJKs2keDTTmAYRHgk2ZAQbKlpT0Vp46ukWX9csWtunOgVeLlpAI5mv3yV28gSRJRYQjHWvueG5sgxcowwmlW6iWaxphM8Ij6lgocUR2k85MzdGaVARpKZUsYNFdT6Q40noahbYzwmasl72Z+JnJ2Z4HaRMxImhgiwWDROOjESz9GAKUoMn1qCiWL2VkTGWGFibEolG4K3PIqaV9Uvctq7aFWqdkcRThBE7hHDy4gjrcQhNaQEDCM7zCm2OcF+fd+Vi0Fpx85hj+wPn8ATTtkTc=ltlatexitgt

CLIC

ltlatexit sha1_base64=bIpzZIofHgtYS9eH8iBKNDDTp8=gtAAAB+nicdVDJSgNBEO2JW4xbokcvjUHwYugJISa3YEA8RjALJCH0dHoyTXoWumvUMOZTvHhQxKtf4s2sbMIKvqg4PFeFVX1nEgKDYR8WKmV1bX1jfRmZmt7Z3cvm9tv6TBWjDdZKEPVcajmUgS8CQIk70SKU9+RvO2M6zOfcOVFmFwDZOI9306CoQrGAUjDbK5pAf8DpSfXNTrp543nQ6yeVIgBuUynhG7QmxDqtVKsVjF9twiJI+WaAyy771hyGKfB8Ak1bprkwj6CVUgmOTTTCWPKJsTEe8a2hAfa77yfz0KT42yhC7oTIVAJ6r3ycS6ms98R3T6VPw9G9vJv7ldWNwK1EBFEMPGCLRW4sMYR4lgMeCsUZyIkhlClhbsXMo4oyMGllTAhfn+LSatYsMuF0lUpXztfxpFGh+gInSAbnaEaukQN1EQM3aIH9ISerXvr0XqxXhetKWs5c4B+wHr7BLoklFQ=ltlatexitgt

FCC-hh


CLIC


FCC-hh

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b

Figure 1 Diagrammatic contributions to the qq q0q0WW process On the left the scatteringtopology On the right one representative ldquoradiationrdquo diagram

that factorization fails for massive vector particles On the other because it suggests that it

simply does not make sense even in an ideal experimental situation to extract in a model

independent way the on-shell hWWWW i correlator from experimental data the interesting

physics of WW scattering would always be mixed up in an intricate way with SM ecrarrects

We thus believe that studying the conditions for the applicability of EWA is important and

timely as well Obviously the goal is not to find a fast and clever way to do computations

One should view EWA as a selection tool that allows to identify the relevant kinematic region

of the complete process the one which is more sensitive to the EWSB dynamics One would

want to focus on the kinematics where EWA applies not to speed up the computations but

to gain sensitivity to the relevant physics

In this paper we shall analyze in detail the applicability of EWA We will find not

surprisingly that in the proper kinematic regime factorization is valid and EWA works

egregiously In order to prove that we shall not need to focus as KS did on the case of

a heavy Higgs or a strongly interacting EWSB sector actually we shall not even need to

restrict on the specific sub-process WW WW Factorization indeed does not rely in any

way on the detailed nature of the hard sub-process It relies instead on the existence of a

large separation of virtuality scales between the sub-process and the collinear W emission

That only depends on kinematics and corresponds to requiring forward energetic jets and

hard high P outgoing W rsquos When those conditions are imposed EWA works well for both

longitudinally and transversely polarized W rsquos also including the case of weakly-coupled

EWSB (light and elementary Higgs) where all helicities interact with the same strength

gW at all energies

One serious issue in the applicability of EWA is the size of the subleading corrections

2

s

dagger

AbstractThe perspective of designing muon colliders with high energy and luminositywhich is being investigated by the International Muon Collider Collaborationhas triggered a growing interest in their physics reach

We present a concise summary of the muon collider potential to explore newphysics leveraging on the unique possibility of combining high available en-ergy with very precise measurements

dagger The low FCC-hh mass reach on Top Partnerscould be due to a non-optimal analysis

4

Fig 2 Left panel the number of expected events (from Ref [6] see also [2]) at a 10 TeV muon colliderwith 10 abminus1 luminosity for several BSM particles Right panel 95 CL mass reach from Ref [5] atthe HL-LHC (solid bars) and at the FCC-hh (shaded bars) The tentative discovery reach of a 10 14 and30 TeV muon collider are reported as horizontal lines

particles can be definitely discovered up to the kinematical threshold Taking into account that entiretarget integrated luminosity will be collected in 5 years a few months of run could be sufficient for adiscovery Afterwards the large production rate will allow us to observe the new particles decayingin multiple final states and to measure kinematical distributions We will thus be in the position ofcharacterizing the properties of the newly discovered states precisely Similar considerations hold formuon colliders with higher Ecm up to the fact that the kinematical mass threshold obviously grows toEcm2 Notice however that the production cross-section decreases as 1E2

cm1 Therefore we obtain asmany events as in the left panel of Figure 2 only if the integrated luminosity grows as

Lint = 10 abminus1(

Ecm

10 TeV

)2

(1)

A luminosity that is lower than this by a factor of around 10 would not affect the discovery reach but itmight in some cases slightly reduce the potential for characterizing the discoveries

The direct reach of muon colliders vastly and generically exceeds the sensitivity of the High-Luminosity LHC (HL-LHC) This is illustrated by the solid bars on the right panel of Figure 2 wherewe report the projected HL-LHC mass reach [5] on several BSM states The 95 CL exclusion isreported instead of the discovery as a quantification of the physics reach Specifically we considerComposite Higgs fermionic top-partners T (eg the X53 and the T23) and supersymmetric particlessuch as stops t charginos χplusmn1 stau leptons τ and squarks q For each particle we report the highestpossible mass reach as obtained in the configuration for the BSM particle couplings and decay chainsthat maximizes the hadron colliders sensitivity The reach of a 100 TeV proton-proton collider (FCC-hh)is shown as shaded bars on the same plot The muon collider reach displayed as horizontal lines forEcm = 10 14 and 30 TeV exceeds the one of the FCC-hh for several BSM candidates and in particularas expected for purely electroweak charged states

Several interesting BSM particles do not decay to easily detectable final states and an assessmentof their observability requires dedicated studies A clear case is the one of minimal WIMP Dark Matter(DM) candidates (see eg [4] and references therein) The charged state in the DM electroweak multipletis copiously produced but it decays to the invisible DM plus a soft undetectable pion owing to the

1The scaling is violated by the vector boson annihilation channel which however is relevant only at low mass

7

Indirect detection 0333

FCC-hh 1602FCC-hh 11

MuC 10 TeV 137MuC 10 TeV 11

CLIC 3 TeV 15

ILC 05 TeV 0326ILC 05 TeV 0249

FCC-ee 0293FCC-ee 0174

CEPC 0261CEPC 0119

Direct detection projection 2004





CLIC 3 TeV 1677CLIC 3 TeV 149



CEPC 0359CEPC 0119

m(χplusmn1 ) [TeV]10minus1 1

Higgsino

Wino

No collider2σ disappearing track5σ disappearing track

kinematic limitradic

s22σ indirect limit

-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ

Fig 3 Left panel exclusion and discovery mass reach on Higgsino and Wino Dark Matter candidates atmuon colliders from disappearing tracks and at other facilities The plot is adapted from Ref [9] Rightexclusion contour [4] for a scalar singlet of mass mφ mixed with the Higgs boson with strength sin γ

small mass-splitting WIMP DM can be studied at muon colliders in several channels (such as mono-photon) without directly observing the charged state [7 8] Alternatively one can instead exploit thedisappearing tracks produced by the charged particle [9] The result is displayed on the left panel ofFigure 3 for the simplest candidates known as Higgsino and Wino A 10 TeV muon collider reachesthe ldquothermalrdquo mass marked with a dashed line for which the observed relic abundance is obtained bythermal freeze out Other minimal WIMP candidates become kinematically accessible at higher muoncollider energies [78] Muon colliders could actually even probe some of these candidates when they areabove the kinematical threshold by studying their indirect effects on high-energy SM processes [1011]

New physics particles are not necessarily coupled to the SM by gauge interaction One setupthat is relevant in several BSM scenarios (including models of baryogenesis dark matter and neutralnaturalness) is the ldquoHiggs portalrdquo one where the BSM particles interact most strongly with the Higgsfield By the Goldstone Boson Equivalence Theorem Higgs field couplings are interactions with thelongitudinal polarizations of the SM massive vector bosonsW and Z which enable Vector Boson Fusion(VBF) production of the new particles A muon collider is extraordinarily sensitive to VBF productionowing to the large luminosity for effective vector bosons This is illustrated on the right panel of Figure 3in the context of a benchmark model [412] (see also [1314]) where the only new particle is a real scalarsinglet with Higgs portal coupling The coupling strength is traded for the strength of the mixing withthe Higgs particle sin γ that the interaction induces The scalar singlet is the simplest extension of theHiggs sector Extensions with richer structure such as involving a second Higgs doublet are a priorieasier to detect as one can exploit the electroweak production of the new charged Higgs bosons as wellas their VBF production See Refs [15ndash17] for dedicated studies and Ref [18] for a review

We have seen that in several cases the muon collider direct reach compares favorably to the oneof the most ambitious future proton collider project This is not a universal statement in particular it isobvious that at a muon collider it is difficult to access heavy particles that carry only QCD interactionsOne might also expect a muon collider of 10 TeV to be generically less effective than a 100 TeV protoncollider for the detection of particles that can be produced singly For instance for additional Z prime massivevector bosons that can be probed at the FCC-hh well above the 10 TeV mass scale We will see inSection 5 that the situation is slightly more complex and that in the case of Z primes a 10 TeV muon collidersensitivity actually exceeds the one of the FCC-hh dramatically (see the right panel of Fig 6)

8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s

Fig 4 Left panel schematic representation of vector boson fusion or scattering processes The collinearV bosons emitted from the muons participate to a process with hardness

radics Ecm Right panel num-

ber of expected events for selected SM processes at a muon collider with variable Ecm and luminosityscaling as in eq (1)

4 A vector bosons colliderWhen two electroweak charged particles like muons collide at an energy much above the electroweakscale mW sim 100 GeV they have a high probability to emit ElectroWeak (EW) radiation There aremultiple types of EW radiation effects that can be observed at a muon collider and play a major rolein muon collider physics Actually we will argue in Section 7 that the experimental observation andthe theoretical description of these phenomena emerges as a self-standing reason of scientific interest inmuon colliders

Here we focus on the practical implications [1 2 4 6 19 20] of the collinear emission of nearlyon-shell massive vector bosons which is the analog in the EW context of the WeizsaeckerndashWilliamsemission of photons The vector bosons V participate as depicted in Figure 4 to a scattering processwith a hard scale

radics that is much lower than the muon collision energy Ecm The typical cross-section

for V V annihilation processes is thus enhanced by E2cms relative to the typical cross-section for micro+microminus

annihilation whose hard scale is instead Ecm The emission of the V bosons from the muons is sup-pressed by the EW coupling but the suppression is mitigated or compensated by logarithms of the sep-aration between the EW scale and Ecm (see [2 4] for a pedagogical overview) The net result is a verylarge cross-section for VBF processes that occur at

radics sim mW with a tail in

radics up to the TeV scale

We already emphasized (see Figure 2) the importance of VBF for the direct production of newphysics particles The relevance of VBF for probing new physics indirectly simply stems for the hugerate of VBF SM processes summarized on the right panel of Figure 4 In particular we see that a 10 TeVmuon collider produces ten million Higgs bosons which is around 10 times more than future e+eminus

Higgs factories Since the Higgs bosons are produced in a relatively clean environment a 10 TeV muoncollider (over-)qualifies as a Higgs factory [419ndash22] Unlike e+eminus Higgs factories a muon collider alsoproduces Higgs pairs copiously enabling accurate measurements of the Higgs trilinear coupling [2619]and possibly also of the quadrilinear coupling [23]

The opportunities for Higgs physics at a muon collider are summarized elsewhere [18] In Figure 5we report for illustration the results of a 10-parameter fit to the Higgs couplings in the κ-framework ata 10 TeV muon collider and the sensitivity projections on the anomalous Higgs trilinear coupling δκλThe table shows that a 10 TeV muon collider will improve significantly and broadly our knowledge ofthe properties of the Higgs boson The combination with the measurements performed at an e+eminus Higgsfactory reported on the third column does not affect the sensitivity to several couplings appreciablyshowing the good precision that a muon collider alone can attain However it also shows complementar-ity with an e+eminus Higgs factory program More examples of this complementarity are discussed in [18]

9

HL-LHC HL-LHC HL-LHC+10 TeV +10 TeV

+ eeκW 17 01 01κZ 15 04 01κg 23 07 06κγ 19 08 08κZγ 10 72 71κc - 23 11κb 36 04 04κmicro 46 34 32κτ 19 06 04κlowastt 33 31 31lowast No input used for micro collider


CLIC


FCC-hh

Fig 5 Left panel 1σ sensitivities (in ) from a 10-parameter fit in the κ-framework at a 10 TeV muoncollider with 10 abminus1 [18] compared with HL-LHC The effect of measurements from a 250 GeV e+eminus

Higgs factory is also reported Right panel sensitivity to δκλ for different Ecm The luminosity is as ineq (1) for all energies apart fromEcm=3 TeV where doubled luminosity (of 18 abminus1) is assumed [18]

In the right panel of the figure we see that the performances of muon colliders in the measurementof δκλ are similar or much superior to the one of the other future colliders where this measurementcould be performed In particular CLIC measures δκλ at the 10 level [24] and the FCC-hh sensitivityranges from 35 to 8 depending on detector assumptions [25] A determination of δκλ that is way moreaccurate than the HL-LHC projections is possible already at a low energy stage of a muon collider withEcm = 3 TeV

The potential of a muon collider as a vector boson collider has not been explored fully In particulara systematic investigation of vector boson scattering processes such as WW rarrWW has not beenperformed The key role played by the Higgs boson to eliminate the energy growth of the correspondingFeynman amplitudes could be directly verified at a muon collider by means of differential measurementsthat extend well above one TeV for the invariant mass of the scattered vector bosons Along similarlines differential measurements of the WWrarrHH process has been studied in [6 19] (see also [2]) asan effective probe of the composite nature of the Higgs boson with a reach that is comparable or superiorto the one of Higgs coupling measurements A similar investigation was performed in [24] (see also [2])for WWrarrtt aimed at probing Higgs-top interactions

5 High-energy measurementsDirect micro+microminus annihilation such as HZ and tt production reported in Figure 4 displays a number ofexpected events of the order of several thousands These are much less than the events where a Higgs ora tt pair are produced from VBF but they are sharply different and easily distinguishable The invariantmass of the particles produced by direct annihilation is indeed sharply peaked at the collider energyEcmwhile the invariant mass rarely exceeds one tenth of Ecm in the VBF production mode

The good statistics and the limited or absent background thus enables percent of few-percent levelmeasurements of SM cross sections for hard scattering processes of energy Ecm = 10 TeV or moreAn incomplete list of the many possible measurements is provided in Ref [26] including the resummedeffects of EW radiation on the cross section predictions It is worth emphasizing that also charged finalstates such as WH or `ν are copiously produced at a muon collider The electric charge mismatch withthe neutral micro+microminus initial state is compensated by the emission of soft and collinearW bosons that occurswith high probability because of the large energy

10

Fig 6 Left panel 95 reach on the Composite Higgs scenario from high-energy measurements in di-boson and di-fermion final states [26] The green contour display the sensitivity from ldquoUniversalrdquo effectsrelated with the composite nature of the Higgs boson and not of the top quark The red contour includesthe effects of top compositeness Right panel sensitivity to a minimal Z prime [26] Discovery contours at 5σare also reported in both panels

High energy scattering processes are as unique theoretically as they are experimentally [1 6 26]They give direct access to the interactions among SM particles with 10 TeV energy which in turn provideindirect sensitivity to new particles at the 100 TeV scale of mass In fact the effects on high-energy crosssections of new physics at energy Λ Ecm generically scale as (EcmΛ)2 relative to the SM Percent-level measurements thus give access to Λ sim 100 TeV This is an unprecedented reach for new physicstheories endowed with a reasonable flavor structure Notice in passing that high-energy measurementsare also useful to investigate flavor non-universal phenomena as we will see below and in Section 6

This mechanism is not novel Major progress in particle physics always came from raising theavailable collision energy producing either direct or indirect discoveries For instance precisely becauseof the quadratic energy scaling outlined above the inner structure of nucleons and a first determinationof their radius could be achieved only when the transferred energy in electron scattering could reach asignificant fraction of the ldquonew physicsrdquo scale Λ = ΛQCD = 300 MeV [27]

Figure 6 illustrates the tremendous reach on new physics of a 10 TeV muon collider with 10 abminus1

integrated luminosity The left panel (green contour) is the sensitivity to a scenario that explains themicroscopic origin of the Higgs particle and of the scale of EW symmetry breaking by the fact that theHiggs is a composite particle In the same scenario the top quark is likely to be composite as well whichin turn explains its large mass and suggest a ldquopartial compositenessrdquo origin of the SM flavour structureTop quark compositeness produces additional signatures that extend the muon collider sensitivity up tothe red contour The sensitivity is reported in the plane formed by the typical coupling glowast and of thetypical mass mlowast of the composite sector that delivers the Higgs The scale mlowast physically corresponds tothe inverse of the geometric size of the Higgs particle The coupling glowast is limited from around 1 to 4πas in the figure In the worst case scenario of intermediate glowast a 10 TeV muon collider can thus probethe Higgs radius up to the inverse of 50 TeV or discover that the Higgs is as tiny as (35 TeV)minus1 Thesensitivity improves in proportion to the center of mass energy of the muon collider

The figure also reports as blue dash-dotted lines denoted as ldquoOthersrdquo the envelop of the 95 CLsensitivity projections of all the future collider projects that have been considered for the 2020 updateof the European Strategy for Particle Physics summarized in Ref [5] These lines include in particularthe sensitivity of very accurate measurements at the EW scale performed at possible future e+eminus HiggsElectroweak and Top factories These measurements are not competitive because new physics at Λ sim100 TeV produces unobservable one part per million effects on 100 GeV energy processes High-energy

11

measurements at a 100 TeV proton collider are also included in the dash-dotted lines They are notcompetitive either because the effective parton luminosity at high energy is much lower than the one ofa 10 TeV muon collider as explained in Section 1 For example the cross-section for the production ofan e+eminus pair with more than 9 TeV invariant mass at the FCC-hh is of only 40 ab while it is of 900 ab ata 10 TeV muon collider Even with a somewhat higher integrated luminosity the FCC-hh just does nothave enough statistics to compete with a 10 TeV muon collider

The right panel of Figure 6 considers a simpler new physics scenario where the only BSM stateis a heavy Z prime spin-one particle The ldquoOthersrdquo line also includes the sensitivity of the FCC-hh from directZ prime production The line exceeds the 10 TeV muon collider sensitivity contour (in green) only in a tinyregion with MZ

prime around 20 TeV and small Z prime coupling This result substantiates our claim in Section 3that a reach comparison based on the 2rarr1 single production of the new states is simplistic Single2rarr1 production couplings can produce indirect effect in 2rarr 2 scattering by the virtual exchange ofthe new particle and the muon collider is extraordinarily sensitive to these effects Which collider winsis model-dependent In the simple benchmark Z prime scenario and in the motivated framework of Higgscompositeness that future colliders are urged to explore the muon collider is just a superior device

We have seen that high energy measurements at a muon collider enable the indirect discoveryof new physics at a scale in the ballpark of 100 TeV However the muon collider also offers amazingopportunities for direct discoveries at a mass of several TeV and unique opportunities to characterize theproperties of the discovered particles as emphasized in Section 3 High energy measurements will enableus take one step further in the discovery characterization by probing the interactions of the new particleswell above their mass For instance in the Composite Higgs scenario one could first discover Top Partnerparticles of few TeV mass and next study their dynamics and their indirect effects on SM processesThis might be sufficient to pin down the detailed theoretical description of the newly discovered sectorwhich would thus be both discovered and theoretically characterized at the same collider Higgs couplingdeterminations and other precise measurements that exploit the enormous luminosity for vector bosoncollisions described in Section 4 will also play a major role in this endeavour

Obviously we can dream of such glorious outcome of the project only because energy and preci-sion are simultaneously available at a muon collider

6 Muon-specific opportunities

In the quest for generic exploration engineering collisions between muons and anti-muons for the firsttime is in itself a unique opportunity offered by the muon collider project The concept can be madeconcrete by considering scenarios where the sensitivity to new physics stems from colliding muonsrather than electrons or other particles An extensive overview of such ldquomuon-specificrdquo opportunities isprovided in Ref [18] based on the available literature [4 16 28ndash45] A concise summary is reportedbelow

It is perhaps worth emphasizing in this context that lepton flavour universality is not a fundamentalproperty of Nature Therefore new physics could exist coupled to muons that we could not yet discoverusing electrons In fact it is not only conceivable but even expected that new physics could couple morestrongly to muons than to electrons Even in the SM lepton flavour universality is violated maximallyby the Yukawa interaction with the Higgs field that is larger for muons than for electrons New physicsassociated to the Higgs or to flavour will most likely follow the same pattern offering a competitiveadvantage of muon over electron collisions at similar energies The comparison with proton collidersis less straightforward By the same type of considerations one expects larger couplings with quarksespecially with the ones of the second and third generation This expectation should be folded in withthe much lower luminosity for heavier quarks at proton colliders than for muons at a muon collider Theperspectives of muon versus proton colliders are model-dependent and of course strongly dependent onthe energy of the muon and of the proton collider

12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr

Fig 7 Summary from Ref [18] of the muon collider sensitivity to putative new physics responsible forthe muon anomalies Left panel reach on the muon g-2 from high-energy measurements (solid lines)and from direct searches for new particles in explicit models (dashed lines) Right panel reach frommicromicrorarr jj (solid line) on the scale Λ of semi-leptonic interactions that can account for the B-anomalies

The current g-2 and B-physics anomalies offer experimental hints for flavour non-universal newphysics that point strongly and specifically to muons The discrepancy of the muon g-2 measurementswith the theoretical prediction is subject to intense investigation If confirmed by further measurementsand theoretical calculations elucidating its origin might become a priority of particles physics in a fewyearsrsquo time Similar considerations hold for the persistent flavour anomalies including the most recentLHCb measurements of the B-meson decay ratios to muons over electrons R

K(lowast) These anomalies will

be further probed and potentially strengthened by the LHCb and Belle II experiments on a timescale offew years

A muon collider offers excellent prospects to probe putative new physics scenarios responsible forthe muon anomalies as schematically summarized in Figure 7 The left panel reports the minimal muoncollider energy that is needed to probe different types of new physics potentially responsible for the g-2anomaly The solid lines correspond to limits on contact interaction operators due to unspecified newphysics that contribute at the same time to the muon g-2 and to high-energy scattering processes Semi-leptonic muon-charm (muon-top) interactions that can account for the g-2 discrepancy can be probedby di-jets at a 3 TeV (10 TeV) muon collider whereas a 30 TeV collider could even probe a tree-levelcontribution to the muon electromagnetic dipole operator directly through micromicro rarr hγ These sensitivityestimates are agnostic on the specific new physics model responsible for the anomaly Explicit modelstypically predict light particles that can be directly discovered at the muon collider and correlated de-viations in additional observables In the figure dashed lines illustrate the sensitivity to three classesof models those featuring EW-singlet scalars or vectors the ones including EW-charged particles inmodels with minimal flavour violation (MFV) and heavy lepton-like particles that mix with the muonA complete coverage of several models is possible already at a 3 TeV muon collider and a collider oftens of TeV could provide a full-fledged no-lose theorem

The right panel of Figure 7 exemplifies instead the muon collider potential to probe explanationsof the flavour anomalies in an effective field theory description of the associated new physics Thegreen band labeled ldquob rarr smicromicro onlyrdquo represents the scale Λ of the interaction operator responsible forthe R

K(lowast) anomaly (with 1Λ2 being the Wilson coefficient) This scenario would not be testable at the

FCC-hh proton collider but it would be within the reach of a muon collider with 7 TeV energy or moreby measuring the micro+microminusrarr jets cross-section induced by the same operator Moreover in realistic newphysics models the (bs)(micromicro) interaction is unavoidably accompanied by flavour-conserving (bb)(micromicro)and (ss)(micromicro) interactions with a larger Wilson coefficient corresponding to a smaller Λ scale reportedin the ldquoCKM-likerdquo band In particular the band assumes a Vts suppression of the (bs) operator relative tothe operators that are diagonal in the quark flavour as it would emerge in models with a realistic flavour

13

structure The new physics scale Λ is in this case within the reach of a 3 TeV muon collider while itcannot be probed by the HL-LHC Of course these considerations hold if the new particles are heavy andthe EFT description is valid If the new physics is weakly coupled and the new states are light enoughthey can be directly produced at a muon collider or a hadron collider of suitable energy See Ref [18]for more details for a comprehensive investigation of explicit models and for an assessment of the muoncollider direct sensitivity

The muon-related anomalies should be regarded as of today as a specific illustration of the genericadded value for new physics exploration of a collider that employs second-generation particles Howeverin a few years these anomalies might turn if confirmed into a primary driver of particle physics researchMuon colliders offers excellent perspectives for progress on the anomalies already at 3 TeV with a verycompetitive time scale This scenario further supports the urgency of investing in a complete muoncollider design study

7 Electroweak radiationThe novel experimental setup offered by lepton collisions at 10 TeV energy or more outlines offerspossibilities for theoretical exploration that are at once novel and speculative yet robustly anchored toreality and to phenomenological applications

The muon collider will probe for the first time a new regime of EW interactions where the scalemWsim100 GeV of EW symmetry breaking plays the role of a small IR scale relative to the much largercollision energy This large scale separation triggers a number of novel phenomena that we collectivelydenote as ldquoEW radiationrdquo effects Since they are prominent at muon collider energies the comprehensionof these phenomena is of utmost importance not only for developing a correct physical picture but alsoto achieve the needed accuracy of the theoretical predictions

The EW radiation effects that the muon collider will observe which will play a crucial in theassessment of its sensitivity to new physics can be broadly divided in two classes

The first class includes the initial-state radiation of low-virtuality vector bosons It effectivelymakes the muon collider a high-luminosity vector bosons collider on top of a very high-energy lepton-lepton machine The compelling associated physics studies described in Section 4 pose challenges forfixed-order theoretical predictions and Monte Carlo event generation even at tree-level owing to thesharp features of the Monte Carlo integrand induced by the large scale separation and the need tocorrectly handle QED and weak radiation at the same time respecting EW gauge invariance Strate-gies to address these challenges are available in WHIZARD [46] they have been recently implementedin MadGraph5_aMCNLO [2 47] and applied to several phenomenological studies in the muon collidercontext Dominance of such initial-state collinear radiation will eventually require a systematic theo-retical modeling in terms of EW Parton Distribution Function where multiple collinear radiation effectsare resummed First studies show that EW resummation effects can be significant at a 10 TeV muoncollider [3]

The second class of effects are the virtual and real emissions of soft and soft-collinear EW radia-tion They affect most strongly the measurements performed at the highest energy described in Section 5and impact the corresponding cross-section predictions at order one [26] They also give rise to novelprocesses such as the copious production of charged hard final states out of the neutral micro+microminus initialstate and to new opportunities to detect new short distance physics by studying for one given hard fi-nal state different patterns of radiation emission [26] The deep connection with the sensitivity to newphysics makes the study of EW radiation an inherently multidisciplinary enterprise that overcomes thetraditional separation between ldquoSM backgroundrdquo and ldquoBSM signalrdquo studies

At very high energies EW radiation displays similarities with QCD and QED radiation but alsoremarkable differences that pose profound theoretical challenges First being EW symmetry broken atlow energy particles with different ldquoEW colorrdquo are easily distinguishable In particular the beam parti-

14

cles (eg charged left-handed leptons) carry definite color thus violating the KLN theorem assumptionsTherefore no cancellation takes place between virtual and real radiation contributions regardless of thefinal state observable inclusiveness [48 49] Furthermore the EW color of the final state particles can bemeasured and it must be measured for a sufficiently accurate exploration of the SM and BSM dynamicsFor instance distinguishing the top from the bottom quark or the W from the Z boson (or photon) isnecessary to probe accurately and comprehensively new short-distance physical laws that can affect thedynamics of the different particles differently When dealing with QCD and QED radiation only it issufficient instead to consider ldquoinclusiverdquo observables where QCDQED radiation effects can be system-atically accounted for and organized in well-behaved (small) corrections The relevant observables forEW physics at high energy are on the contrary dramatically affected by EW radiation effects Second inanalogy with QCD and unlike QED for EW radiation the IR scale is physical However at variance withQCD the theory is weakly-coupled at the IR scale and the EW ldquopartonsrdquo do not ldquohadroniserdquo EW show-ering therefore always ends at virtualities of order 100 GeV where heavy EW states (tWZH) coexistwith light SM ones and then decay Having a complete and consistent description of the evolution fromhigh virtualities where EW symmetry is restored to the weak scale where EW is broken to GeV scalesincluding also leading QEDQCD effects in all regimes is a new challenge [50]

Such a strong phenomenological motivation and the peculiarities of the problem stimulate workand offer a new perspective on resummation and showering techniques or more in general trigger theo-retical progress on IR physics Fixed-order calculations will also play an important role Indeed whilethe resummation of the leading logarithmic effects of radiation is mandatory at muon collider ener-gies [26 51] subleading logarithms could perhaps be included at fixed order Furthermore one shouldeventually develop a description where resummation is merged with fixed-order calculations in a exclu-sive way providing the most accurate predictions in the corresponding regions of the phase space ascurrently done for QCD computations

A significant literature on EW radiation exists starting from the earliest works on double-logarithmresummations based on Asymptotic Dynamics [4849] or on the IR evolution equation [5253] The fac-torization of virtual massive vector boson emissions leading to the notion of effective vector boson is alsoknown since long [54ndash57] More recent progress includes resummation at the next to leading logarithmin the Soft-Collinear Effective Theory framework [58ndash62] the operatorial definition of the distributionfunctions for EW partons [51 63 64] and the calculation of the corresponding evolution as well as thecalculation of the EW splitting functions [65] for EW showering and the proof of collinear EW emissionfactorization [66ndash68] Additionally fixed-order virtual EW logarithms are known for generic process atthe 1-loop order [6970] and are implemented in Sherpa [71] and MadGraph5_aMCNLO [72] Exact EWcorrections at NLO are available in an automatic form for arbitrary processes in the SM for examplein MadGraph5_aMCNLO [73] and in Sherpa+Recola [74] Implementations of EW showering are alsoavailable through a limited set of splittings in Pythia 8 [75 76] and in a complete way in Vincia [77]

While we are still far from an accurate systematic understanding of EW radiation the present-day knowledge is sufficient to enable rapid progress in the next few years The outcome will be anindispensable toolkit for muon collider predictions Moreover while we do expect that EW radiationphenomena can in principle be described by the Standard Model they still qualify as ldquonew phenomenardquountil when we will be able to control the accuracy of the predictions and verify them experimentallySuch investigation is a self-standing reason of scientific interest in the muon collider project

15

8 The path to a new generation of experimentsThe rich program enabled by colliding bunches of muons requires novel detectors and reconstructiontechniques to successfully exploit the physics potential of the machine

The main challenge to operating a detector at a muon collider is the fact that muons are unstableparticles As such it is impossible to study the muon interactions without being exposed to decays of themuons forming the colliding beams From the moment the collider is turned on and the muon bunchesstart to circulate in the accelerator complex the products of the in-flight decays of the muon beamsand the results of their interactions with beamline material or the detectors themselves will reach theexperiments contributing to polluting the otherwise clean collision environment The ensemble of allthese particles is usually known as ldquoBeam Induced Backgroundsrdquo or BIB The composition flux andenergy spectra of the BIB entering a detector is closely intertwined with the design of the experimentalapparatus such as the beam optics that integrate the detectors in the accelerator complex or the presenceof shielding elements and the collision energy However two general features broadly characterize theBIB it is composed of low-energy particles with a broad arrival time in the detector

The design of an optimized detector is still in its infancy but it is already clear that the physicsgoals will require a fully hermetic detector able to resolve the trajectories of the outgoing particles andtheir energies While the final design might look similar to those taking data at the LHC the technologiesat the heart of the detector will have to be new The large flux of BIB particles sets requirements on theneed to withstand radiation over long periods of time and the need to disentangle the products of thebeam collisions from the particles entering the sensitive regions from uncommon directions calls forhigh-granularity measurements in space time and energy The development of these new detectors willprofit from the consolidation of the successful solutions that were pioneered for example in the HighLuminosity LHC upgrades as well as brand new ideas New solutions are being developed for use in themuon collider environment spanning from tracking detectors calorimeters systems and dedicated muonsystems The whole effort is part of the push for the next generation of high-energy physics detectorsand new concepts targeted to the muon collider environment might end up revolutionizing other futureproposed collider facilities as well

Together with a vibrant detector development program new techniques and ideas needs to bedeveloped in the interpretation of the energy depositions recorded by the instrumentation The contri-butions from the BIB add an incoherent source of backgrounds that affect different detector systems indifferent ways and that are unprecedented at other collider facilities The extreme multiplicity of en-ergy depositions in the tracking detectors create a complex combinatorial problem that challenges thetraditional algorithms for reconstructing the trajectories of the charged particles as these were designedfor collisions where sprays of particles propagate outwards from the centre of the detector At the sametime the potentially groundbreaking reach into the high-energy frontier will lead to strongly collimatedjets of particles that need to be resolved by the calorimeter systems while being able to subtract withprecision the background contributions The challenging environment of the muon collider offers fertileground for the development of new techniques from traditional algorithms to applications of artificialintelligence and machine learning to brand new computing technologies such as quantum computers

References[1] J P Delahaye M Diemoz K Long B Mansoulieacute N Pastrone L Rivkin D Schulte

A Skrinsky and A Wulzer Muon Colliders arXiv190106150 [physicsacc-ph][2] A Costantini F De Lillo F Maltoni L Mantani O Mattelaer R Ruiz and X Zhao Vector

boson fusion at multi-TeV muon colliders JHEP 09 (2020) 080 arXiv200510289 [hep-ph][3] T Han Y Ma and K Xie High energy leptonic collisions and electroweak parton distribution

functions Phys Rev D 103 (2021) no 3 L031301 arXiv200714300 [hep-ph][4] H Al Ali et al The Muon Smasherrsquos Guide arXiv210314043 [hep-ph]

16

[5] R K Ellis et al Physics Briefing Book Input for the European Strategy for Particle PhysicsUpdate 2020 arXiv191011775 [hep-ex]

[6] D Buttazzo R Franceschini and A Wulzer Two Paths Towards Precision at a Very High EnergyLepton Collider JHEP 05 (2021) 219 arXiv201211555 [hep-ph]

[7] T Han Z Liu L-T Wang and X Wang WIMPs at High Energy Muon Colliders Phys Rev D103 (2021) no 7 075004 arXiv200911287 [hep-ph]

[8] S Bottaro D Buttazzo M Costa R Franceschini P Panci D Redigolo and L Vittorio Closingthe window on WIMP Dark Matter Eur Phys J C 82 (2022) no 1 31 arXiv210709688[hep-ph]

[9] R Capdevilla F Meloni R Simoniello and J Zurita Hunting wino and higgsino dark matter atthe muon collider with disappearing tracks JHEP 06 (2021) 133 arXiv210211292 [hep-ph]

[10] L Di Luzio R Groumlber and G Panico Probing new electroweak states via precisionmeasurements at the LHC and future colliders JHEP 01 (2019) 011 arXiv181010993[hep-ph]

[11] R Franceschini and X Zhao in progress [12] D Buttazzo D Redigolo F Sala and A Tesi Fusing Vectors into Scalars at High Energy Lepton

Colliders JHEP 11 (2018) 144 arXiv180704743 [hep-ph][13] M Ruhdorfer E Salvioni and A Weiler A Global View of the Off-Shell Higgs Portal SciPost

Phys 8 (2020) 027 arXiv191004170 [hep-ph][14] W Liu and K-P Xie Probing electroweak phase transition with multi-TeV muon colliders and

gravitational waves JHEP 04 (2021) 015 arXiv210110469 [hep-ph][15] T Han S Li S Su W Su and Y Wu Heavy Higgs bosons in 2HDM at a muon collider Phys

Rev D 104 (2021) no 5 055029 arXiv210208386 [hep-ph][16] N Chakrabarty T Han Z Liu and B Mukhopadhyaya Radiative Return for Heavy Higgs Boson

at a Muon Collider Phys Rev D 91 (2015) no 1 015008 arXiv14085912 [hep-ph][17] J Kalinowski T Robens D Sokolowska and A F Zarnecki IDM Benchmarks for the LHC and

Future Colliders Symmetry 13 (2021) no 6 991 arXiv201214818 [hep-ph][18] J De Blas et al The physics case of a 3 TeV muon collider stage in 2022 Snowmass Summer

Study 3 2022 arXiv220307261 [hep-ph][19] T Han D Liu I Low and X Wang Electroweak couplings of the Higgs boson at a multi-TeV

muon collider Phys Rev D 103 (2021) no 1 013002 arXiv200812204 [hep-ph][20] M Forslund and P Meade In preparation arXiv22xxxxx [hep-ph][21] N Bartosik et al Preliminary Report on the Study of Beam-Induced Background Effects at a

Muon Collider arXiv190503725 [hep-ex][22] N Bartosik et al Detector and Physics Performance at a Muon Collider JINST 15 (2020) no 05

P05001 arXiv200104431 [hep-ex][23] M Chiesa F Maltoni L Mantani B Mele F Piccinini and X Zhao Measuring the quartic

Higgs self-coupling at a multi-TeV muon collider JHEP 09 (2020) 098 arXiv200313628[hep-ph]

[24] J de Blas et al The CLIC Potential for New Physics arXiv181202093 [hep-ph][25] 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) no 11 1030 arXiv200403505[hep-ph]

[26] S Chen A Glioti R Rattazzi L Ricci and A Wulzer Learning from Radiation at a Very HighEnergy Lepton Collider arXiv220210509 [hep-ph]

[27] R Hofstadter The electron-scattering method and its application to the structure of nuclei andnucleons httpswwwnobelprizeorguploads201806hofstadter-lecturepdf

17

Nobel Lecture 1961 [28] R Capdevilla D Curtin Y Kahn and G Krnjaic Discovering the physics of (g minus 2)micro at future

muon colliders Phys Rev D 103 (2021) no 7 075028 arXiv200616277 [hep-ph][29] D Buttazzo and P Paradisi Probing the muon g minus 2 anomaly with the Higgs boson at a muon

collider Phys Rev D 104 (2021) no 7 075021 arXiv201202769 [hep-ph][30] W Yin and M Yamaguchi Muon g minus 2 at multi-TeV muon collider arXiv201203928

[hep-ph][31] R Capdevilla D Curtin Y Kahn and G Krnjaic No-lose theorem for discovering the new

physics of (g-2)micro at muon colliders Phys Rev D 105 (2022) no 1 015028 arXiv210110334[hep-ph]

[32] R Dermisek K Hermanek and N McGinnis Muon g-2 in two-Higgs-doublet models withvectorlike leptons Phys Rev D 104 (2021) no 5 055033 arXiv210305645 [hep-ph]

[33] R Dermisek K Hermanek and N McGinnis Di-Higgs and tri-Higgs boson signals of muon g-2at a muon collider Phys Rev D 104 (2021) no 9 L091301 arXiv210810950 [hep-ph]

[34] R Capdevilla D Curtin Y Kahn and G Krnjaic Systematically Testing Singlet Models for(g minus 2)micro arXiv211208377 [hep-ph]

[35] G-y Huang S Jana F S Queiroz and W Rodejohann Probing the RK() anomaly at a muoncollider Phys Rev D 105 (2022) no 1 015013 arXiv210301617 [hep-ph]

[36] P Asadi R Capdevilla C Cesarotti and S Homiller Searching for leptoquarks at future muoncolliders JHEP 10 (2021) 182 arXiv210405720 [hep-ph]

[37] A Azatov F Garosi A Greljo D Marzocca J Salko and S Trifinopoulos To appear soon(2022) arXiv2202yyyy [hep-ph]

[38] G-y Huang F S Queiroz and W Rodejohann Gauged LmicrominusLτ at a muon collider Phys Rev D103 (2021) no 9 095005 arXiv210104956 [hep-ph]

[39] S Homiller and L Qianshu To appear soon (2022) arXiv2202xxxx [hep-ph][40] M Casarsa M Fabbrichesi and E Gabrielli Mono-chromatic single photon events at the muon

collider arXiv211113220 [hep-ph][41] T Han W Kilian N Kreher Y Ma J Reuter T Striegl and K Xie Precision test of the

muon-Higgs coupling at a high-energy muon collider JHEP 12 (2021) 162 arXiv210805362[hep-ph]

[42] F Garosi D Marzocca and S Trifinopoulos (in progress) [43] A Azatov F Garosi A Greljo D Marzocca J Salko and S Trifinopoulos New physics in RK

FCC-hh or a Muon Collider (in progress) [44] W Liu K-P Xie and Z Yi Testing leptogenesis at the LHC and future muon colliders a Z prime

scenario arXiv210915087 [hep-ph][45] C Cesarotti S Homiller R K Mishra and M Reece Probing New Gauge Forces with a

High-Energy Muon Beam Dump arXiv220212302 [hep-ph][46] W Kilian T Ohl and J Reuter WHIZARD Simulating Multi-Particle Processes at LHC and

ILC Eur Phys J C 71 (2011) 1742 arXiv07084233 [hep-ph][47] R Ruiz A Costantini F Maltoni and O Mattelaer The Effective Vector Boson Approximation in

High-Energy Muon Collisions arXiv211102442 [hep-ph][48] M Ciafaloni P Ciafaloni and D Comelli Bloch-Nordsieck violating electroweak corrections to

inclusive TeV scale hard processes Phys Rev Lett 84 (2000) 4810ndash4813arXivhep-ph0001142

[49] M Ciafaloni P Ciafaloni and D Comelli Electroweak Bloch-Nordsieck violation at the TeVscale rsquoStrongrsquo weak interactions Nucl Phys B 589 (2000) 359ndash380 arXivhep-ph0004071

[50] T Han Y Ma and K Xie Quark and gluon contents of a lepton at high energies JHEP 02 (2022)

18

154 arXiv210309844 [hep-ph][51] C W Bauer D Provasoli and B R Webber Standard Model Fragmentation Functions at Very

High Energies JHEP 11 (2018) 030 arXiv180610157 [hep-ph][52] V S Fadin L N Lipatov A D Martin and M Melles Resummation of double logarithms in

electroweak high-energy processes Phys Rev D 61 (2000) 094002 arXivhep-ph9910338[53] M Melles Subleading Sudakov logarithms in electroweak high-energy processes to all orders

Phys Rev D 63 (2001) 034003 arXivhep-ph0004056[54] G L Kane W W Repko and W B Rolnick The Effective Wplusmn Z Approximation for

High-Energy Collisions Phys Lett B 148 (1984) 367ndash372[55] S Dawson The Effective W Approximation Nucl Phys B 249 (1985) 42ndash60[56] M S Chanowitz and M K Gaillard The TeV Physics of Strongly Interacting Wrsquos and Zrsquos Nucl

Phys B 261 (1985) 379ndash431[57] Z Kunszt and D E Soper On the Validity of the Effective W Approximation Nucl Phys B 296

(1988) 253ndash289[58] J-y Chiu F Golf R Kelley and A V Manohar Electroweak Sudakov corrections using effective

field theory Phys Rev Lett 100 (2008) 021802 arXiv07092377 [hep-ph][59] J-y Chiu F Golf R Kelley and A V Manohar Electroweak Corrections in High Energy

Processes using Effective Field Theory Phys Rev D 77 (2008) 053004 arXiv07120396[hep-ph]

[60] J-y Chiu A Fuhrer R Kelley and A V Manohar Soft and Collinear Functions for the StandardModel Phys Rev D 81 (2010) 014023 arXiv09090947 [hep-ph]

[61] A Manohar B Shotwell C Bauer and S Turczyk Non-cancellation of electroweak logarithmsin high-energy scattering Phys Lett B 740 (2015) 179ndash187 arXiv14091918 [hep-ph]

[62] A V Manohar and W J Waalewijn Electroweak Logarithms in Inclusive Cross Sections JHEP08 (2018) 137 arXiv180208687 [hep-ph]

[63] C W Bauer N Ferland and B R Webber Standard Model Parton Distributions at Very HighEnergies JHEP 08 (2017) 036 arXiv170308562 [hep-ph]

[64] B Fornal A V Manohar and W J Waalewijn Electroweak Gauge Boson Parton DistributionFunctions JHEP 05 (2018) 106 arXiv180306347 [hep-ph]

[65] J Chen T Han and B Tweedie Electroweak Splitting Functions and High Energy ShoweringJHEP 11 (2017) 093 arXiv161100788 [hep-ph]

[66] P Borel R Franceschini R Rattazzi and A Wulzer Probing the Scattering of EquivalentElectroweak Bosons JHEP 06 (2012) 122 arXiv12021904 [hep-ph]

[67] A Wulzer An Equivalent Gauge and the Equivalence Theorem Nucl Phys B 885 (2014)97ndash126 arXiv13096055 [hep-ph]

[68] G Cuomo L Vecchi and A Wulzer Goldstone Equivalence and High Energy ElectroweakPhysics SciPost Phys 8 (2020) no 5 078 arXiv191112366 [hep-ph]

[69] A Denner and S Pozzorini One loop leading logarithms in electroweak radiative corrections 1Results Eur Phys J C 18 (2001) 461ndash480 arXivhep-ph0010201

[70] A Denner and S Pozzorini One loop leading logarithms in electroweak radiative corrections 2Factorization of collinear singularities Eur Phys J C 21 (2001) 63ndash79arXivhep-ph0104127

[71] E Bothmann and D Napoletano Automated evaluation of electroweak Sudakov logarithms inSherpa Eur Phys J C 80 (2020) no 11 1024 arXiv200614635 [hep-ph]

[72] D Pagani and M Zaro One-loop electroweak Sudakov logarithms a revisitation and automationJHEP 02 (2022) 161 arXiv211003714 [hep-ph]

[73] R Frederix S Frixione V Hirschi D Pagani H S Shao and M Zaro The automation of

19

next-to-leading order electroweak calculations JHEP 07 (2018) 185 arXiv180410017[hep-ph] [Erratum JHEP 11 085 (2021)]

[74] B Biedermann S Braumluer A Denner M Pellen S Schumann and J M Thompson Automationof NLO QCD and EW corrections with Sherpa and Recola Eur Phys J C 77 (2017) 492arXiv170405783 [hep-ph]

[75] J R Christiansen and T Sjoumlstrand Weak Gauge Boson Radiation in Parton Showers JHEP 04(2014) 115 arXiv14015238 [hep-ph]

[76] J R Christiansen and S Prestel Merging weak and QCD showers with matrix elements EurPhys J C 76 (2016) no 1 39 arXiv151001517 [hep-ph]

[77] H Brooks P Skands and R Verheyen Interleaved Resonance Decays and ElectroweakRadiation in Vincia arXiv210810786 [hep-ph]

20

1 Overview

2 Why muons

3 Direct reach

4 A vector bosons collider

5 High-energy measurements


7 Electroweak radiation

8 The path to a new generation of experiments

References

SignatoriesD Acosta88 K Agashe82 BC Allanach52 F Anulli54 A Apresyan38 P Asadi89 D Athanasakos90A Azatov3010 JJ Back91 L Bandiera92 R J Barlow93 E Barzi38148 F Batsch40 M Bauce5456J S Berg23 J Berryhill38 A Bersani74 KM Black21 C Booth94 L Bottura D Bowring38A Braghieri29 G Brooijmans95 A Bross38 E Brost23 L Buonincontri511 B Caiffi74G Calderini96149 S Calzaferri29 P Cameron23 A Canepa38 F Casaburo G Cavoto5654L Celona97 G Cesarini Z Chacko82 A Chanceacute51 R T Co98 A Colaleo9912 D J Colling47G Corcella100 L M Cremaldi A Crivellin101150 Y Cui102 C Curatolo6 R T DrsquoAgnolo103F DrsquoEramo115 G Da Molin11 M Dam6 H Damerau40 E De Matteis59 A Deandrea104J Delahaye40 A Delgado105 C Densham84 K F Di Petrillo38 J Dickinson38 M Dracos106J Duarte107 F Errico9912 R Essig90 P Everaerts21 L Everett21 M Fabbrichesi10 J Fan108S Farinon74 J F Somoza40 G Ferretti109 F Filthaut110 M Forslund90 P Franchini111151M Frigerio112 E Gabrielli11310 M Gallinaro16 I Garcia Garcia114 L Giambastiani115AS Giannakopoulou115 D Giove59 C Giraldin11 L Gladilin S Goldfarb116 HM Gray11744L Gray38 HE Haber66 J Haley76 C Han72 J Hauptman118 M Herndon21 H Jia21 C Jolly84D M Kaplan119 D Kelliher84 GK Krintiras42 G Krnjaic38 N Kumar120 P Kyberd121R LOSITO40 J-B Lagrange84 S Levorato W Li88 R L Voti54 D Liu122 M Liu123 S Lomte21Q Lu15 R Mahbubani62 A Mariotti124 S Mariotto12559 P Mastrapasqua50 K Matchev126A Mazzacane38 P Meade90 P Merkel38 F Mescia127152 R K Mishra15 A Mohammadi21R Mohapatra N Mokhov38 P Montagna129 R Musenich74 MS Neubauer39 D Neuffer38H Newman128 Y Nomura117 I Ojalvo129 JL Oliver130 G Ortona4 D Pagani131 M Palmer23A Pellecchia99 A Perloff132 M Pierini40 M Prioli59 M Procura133 R Radogna9912RA Rimmer134 F Riva135 C Rogers84 L Rossi12559 R Ryne136 J Santiago13822 E Santopinto74I Sarra J Schieck139153 R Schwiehorst140 D Sertore59 V Shiltsev38 L Silvestris12F M Simone9912 K Skoufaris40 P Snopok119 FJP Soler141 M Sorbi12559 A Stamerra9912M Statera59 D Stratakis38 N Strobbe46 J Stupak142 M Swiatlowski53 A Sytov92 A Taffard130T Tait130 J Tang87 M Taoso4 J Thaler89 E A Thompson33 L Tortora81 Y Torun119 M Valente53R U Valente59 N Valle129 R Venditti9912 P Verwilligen12 N Vignaroli143 P Vitulo129E Vryonidou144 C Vuosalo21 H Weber83 CG Whyte145 K Xie35 A Yamamoto146 W Yin147K Yonehara38 H-B Yu102 M Zanetti11 A Zaza9912 J Zhang Y J Zheng42 A Zlobin38D Zuliani115

1Universitagrave di Pavia Italy 2Department of Physics Brandeis University United States 3Center for High EnergyPhysics (CHEP-FU) Fayoum University Egypt 4INFN Sezione di Torino Italy 5INFN Sezione di Padova Italy6Istituto Nazionale di Fisica Nucleare Italy 7Scuola Normale Superiore Italy 8INFN Sezione di Pisa Italy9Perimeter Institute Canada 10INFN Sezione di Trieste Italy 11Dipartimento di Fisica e AstronomiaUniversitrsquoa di Padova Italy 12INFN Sezione di Bari Italy 13European Centre for Theoretical Studies in NuclearPhysics and Related Areas (ECT) Italy 14MPS School University of Sussex United Kingdom 15Departmentof Physics Harvard University United States 16Laboratoacuterio de Instrumentaccedilatildeo e Fiacutesica Experimental dePartiacuteculas (LIP) Portugal 17Theoretical Particle Physics Laboratory (LPTP) Institute of Physics EPFLSwitzerland 18Physics and Astronomy Department Georgia State University United States 19University ofCalifornia Santa Barbara United States 20Department of Physics University of Toronto Canada 21Universityof Wisconsin United States 22CAFPE and Departamento de Fiacutesica Teoacuterica y del Cosmos Universidad deGranada Spain 23Brookhaven National Laboratory United States 24Department of Physics Bolu Abant IzzetBaysal University Turkey 25Physics Department Indiana University United States 26Dipartimento diMatematica e Fisica Universitagrave Roma Tre Italy 27Department of Physics University of Arizona United States28Helmholtz-Zentrum Dresden-Rossendorf Germany 29INFN Sezione di Pavia Italy 30SISSA Italy 31Albert

2


3
















5

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

gg

qq

β=1

β=10

β=100

0 10 20 30 40 50 60 70 80 90 100

200

400

600

800

1000

1200

1400

1600

sμ [TeV]

s p[TeV

]









6


CLIC


FCC-hh


CLIC


FCC-hh

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s

dagger




4




Lint = 10 abminus1(

Ecm

10 TeV

)2

(1)





7




CLIC 3 TeV 15



CEPC 0261CEPC 0119









CEPC 0359CEPC 0119


Higgsino

Wino




-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ





8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References


3
















5

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

gg

qq

β=1

β=10

β=100

0 10 20 30 40 50 60 70 80 90 100

200

400

600

800

1000

1200

1400

1600

sμ [TeV]

s p[TeV

]









6


CLIC


FCC-hh


CLIC


FCC-hh

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s

dagger




4




Lint = 10 abminus1(

Ecm

10 TeV

)2

(1)





7




CLIC 3 TeV 15



CEPC 0261CEPC 0119









CEPC 0359CEPC 0119


Higgsino

Wino




-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ





8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References
















5

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

gg

qq

β=1

β=10

β=100

0 10 20 30 40 50 60 70 80 90 100

200

400

600

800

1000

1200

1400

1600

sμ [TeV]

s p[TeV

]









6


CLIC


FCC-hh


CLIC


FCC-hh

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s

dagger




4




Lint = 10 abminus1(

Ecm

10 TeV

)2

(1)





7




CLIC 3 TeV 15



CEPC 0261CEPC 0119









CEPC 0359CEPC 0119


Higgsino

Wino




-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ





8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

gg

qq

β=1

β=10

β=100

0 10 20 30 40 50 60 70 80 90 100

200

400

600

800

1000

1200

1400

1600

sμ [TeV]

s p[TeV

]









6


CLIC


FCC-hh


CLIC


FCC-hh

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s

dagger




4




Lint = 10 abminus1(

Ecm

10 TeV

)2

(1)





7




CLIC 3 TeV 15



CEPC 0261CEPC 0119









CEPC 0359CEPC 0119


Higgsino

Wino




-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ





8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References


CLIC


FCC-hh


CLIC


FCC-hh

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s

dagger




4




Lint = 10 abminus1(

Ecm

10 TeV

)2

(1)





7




CLIC 3 TeV 15



CEPC 0261CEPC 0119









CEPC 0359CEPC 0119


Higgsino

Wino




-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ





8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References




CLIC 3 TeV 15



CEPC 0261CEPC 0119









CEPC 0359CEPC 0119


Higgsino

Wino




-

-

-

-

ϕ []

γ

-

-

γ = ϕγ = ϕ





8

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

5 10 15 20 25 3020

50

100

200

500

s [TeV]

s p[TeV

]

qq

q

q

V1

V2

1a

qq

q

q1b























gW at all energies


2

s














9




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References




CLIC


FCC-hh







10







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References







11









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References









12

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References

-

-

-

-

-

-

-

-

[]

Δ μ

μ[middot

]

μ+μ-

rarr

μ+μ- rarr γ

μ+μ- rarr

Δμ

() ()

[]

Λ

[

]

rarr μμ

-

-

-

μ+ μ

- rarr









13









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References









14





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References





15









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References









16























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References























17

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References

























18
























19






20

1 Overview

2 Why muons

3 Direct reach






References
























19






20

1 Overview

2 Why muons

3 Direct reach






References






20

1 Overview

2 Why muons

3 Direct reach






References

Muon Collider Physics Summary arXiv:2203.07256v2 [hep-ph ...

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Transcript of Muon Collider Physics Summary arXiv:2203.07256v2 [hep-ph ...