# Higgs and BSM Physics at the Future Muon Collider

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Low-Energy Muon Collider

#### 2.1. Higgs Boson Resonant Production

#### 2.2. Numerical Results on the ISR and BES on Resonance

#### 2.3. Outlook on Low-Energy Options

## 3. High-Energy Muon Collider

#### 3.1. First of a New Kind

#### 3.2. Multiplexing the Search for New Physics

- Direct production of new physics, e.g., the on-shell production of new states ${\ell}^{+}{\ell}^{-}\to \chi \chi $ where $\chi $ is a new physics particle, for instance, a dark matter particle;
- Indirect effects from off-shell new physics, e.g., the modification to the angular distribution of ${\ell}^{+}{\ell}^{-}\to f\overline{f}$ Drell–Yan processes due to contact interactions ${\overline{\psi}}_{\ell}{\psi}_{\ell}{\overline{\psi}}_{f}{\psi}_{f}$ beyond the SM;
- Copious production of SM states in (effective) $2\to 1$ annihilations, $2\to 2$ scatterings, or 3-body and multi-body productions. These include for instance the effective W boson annihilation to produce Higgs bosons in ${\ell}^{+}{\ell}^{-}\to \nu \nu h,$ ${\ell}^{+}{\ell}^{-}\to t\overline{t}$ and ${\ell}^{+}{\ell}^{-}\to t\overline{t}h$ processes.

#### 3.3. Direct Production of New Physics

#### 3.4. Indirect Effects from Off-Shell New Physics

#### The Size of the Higgs Boson

_{★}as strong as what indicated by the shade of blue in the figure. The orange line for our baseline luminosity runs parallel to these lines of iso-S/B and corresponds to be sensitive to around 10% deviations at 95% CL. Thus, if we imagine to run the same energy with lower luminosity we would be effectively probing theories for which the EFT expansion parameter Equation (6) has grown to be close to O(1), hence in a regime in which the EFT may not be valid. A simple way to fall in this case is to reduce the mass of the new physics in Equation (6), which eventually leads to M < $\sqrt{s}/2$ and thus makes the indirect search strategy no longer meaningful. All in all, if we want to pursue indirect new physics searches we need to push the energy of the machine, as to profit from the growth with energy of the new physics effects, but at the same time, we need to keep a target luminosity around Equation (5), or else the whole strategy of indirect new physics searches collapses. In this eventuality the high-energy muon collider would be a machine suitable for direct new physics exploration, up to its kinematical limit $\sqrt{s}/2$ for pair production, and with no meaningful sensitivity whatsoever to new physics heavier than that.

_{★}, therefore we give combined results in a plane (m

_{★}, g

_{★}) in Figure 6. Additionally, in this more refined setting it is clear that the high-energy muon collider options in the multi-TeV regime can improve by orders of magnitude our knowledge of the point-like nature of the Higgs boson. Thus, a high-energy muon collider operating at 10 TeV can be said to be a magnifying glass a factor above 10 more powerful than even the most powerful traditional colliders in discussion in the future collider landscape.

#### 3.5. Copious Production of SM States

#### 3.5.1. A Giga-Higgs Boson Program

#### 3.5.2. A Mega-Top Quark Program

#### Low-Energy Top Quarks

#### High-Energy Top Quarks

#### Further Production Modes and Measurements: ${e}^{+}{e}^{-}\to t\overline{t}h+X$ the Yukawa Coupling ${y}_{t}$ and More

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Budker, G.I. Accelerators and colliding beams. Conf. Proc. C
**1969**, 690827, 33–39. [Google Scholar] - Budker, G.I. Research work on the colliding beams of the Novosibirsk Institute of Nuclear Physics (present state of experiments and perspectives). AIP Conf. Proc.
**1996**, 352, 5. [Google Scholar] - Skrinsky, A.N. Polarized muon beams for muon collider. Nucl. Phys. B Proc. Suppl.
**1996**, 51, 201–203. [Google Scholar] [CrossRef] - Neuffer, D. Multi-TeV muon colliders. AIP Conf. Proc.
**1987**, 156, 201–208. [Google Scholar] [CrossRef] [Green Version] - Blondel, A.; Ellis, J.R.; Autin, B. Prospective Study of Muon Storage Rings at CERN. In CERN Yellow Reports: Monographs; CERN: Geneva, Switzerland, 1999. [Google Scholar] [CrossRef]
- Ankenbrandt, C.M.; Atac, M.; Autin, B.; Balbekov, V.I.; Barger, V.D. Status of muon collider research and development and future plans. Phys. Rev. ST Accel. Beams
**1999**, 2, 081001. [Google Scholar] [CrossRef] [Green Version] - Geer, S. Muon Colliders and Neutrino Factories. Ann. Rev. Nucl. Part. Sci.
**2009**, 59, 347–365. [Google Scholar] [CrossRef] [Green Version] - Rubbia, C. A complete demonstrator of a muon cooled Higgs factory. arXiv
**2013**, arXiv:1308.6612. [Google Scholar] - Palmer, R.B. Muon Colliders. Rev. Accel. Sci. Technol.
**2014**, 7, 137–159. [Google Scholar] [CrossRef] - Boscolo, M.; Delahaye, J.P.; Palmer, M. The future prospects of muon colliders and neutrino factories. Rev. Accel. Sci. Technol.
**2019**, 10, 189–214. [Google Scholar] [CrossRef] [Green Version] - Barger, V.D.; Berger, M.S.; Gunion, J.F.; Han, T. Higgs Boson physics in the s channel at μ
^{+}μ^{−}colliders. Phys. Rep.**1997**, 286, 1–51. [Google Scholar] [CrossRef] [Green Version] - Long, K.; Lucchesi, D.; Palmer, M.; Pastrone, N.; Schulte, D.; Shiltsev, V. Muon colliders to expand frontiers of particle physics. arXiv
**2020**, arXiv:2007.15684. [Google Scholar] - ATLAS Collaboration; Aad, G.; Abajyan, T.; Abbott, B.; Abdallah, J.; Khalek, S.A.; Abdelalim, A.A.; Abdinov, O.; Aben, R.; Abi, B.; et al. Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B
**2012**, 716, 1–29. [Google Scholar] [CrossRef] - Chatrchyan, S.; Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Aguilo, E.; Bergauer, T.; Dragicevic, M.; Erö, J.; et al.; CMS Collaboration Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC. Phys. Lett. B
**2012**, 716, 30–61. [Google Scholar] [CrossRef] - Robson, A.; Burrows, P.N.; Catalan Lasheras, N.; Linssen, L.; Petric, M.; Schulte, D.; Sicking, E.; Stapnes, S.; Wuensch, W. The Compact Linear e
^{+}e^{−}Collider (CLIC): Accelerator and Detector. arXiv**2018**, arXiv:1812.07987. [Google Scholar] - Abada, A.; Abbrescia, M.; AbdusSalam, S.S.; Abdyukhanov, I.; Fernandez, J.A.; Abramov, A.; Aburaia, M.; Acar, A.O.; Adzic, P.R.; Agrawal, P.; et al. FCC-ee: The Lepton Collider: Future Circular Collider Conceptual Design Report Volume 2. Eur. Phys. J. ST
**2019**, 228, 261–623. [Google Scholar] [CrossRef] - Greco, M.; Han, T.; Liu, Z. ISR effects for resonant Higgs production at future lepton colliders. Phys. Lett. B
**2016**, 763, 409–415. [Google Scholar] [CrossRef] [Green Version] - CLIC and CLICdp Collaborations. The Compact Linear e
^{+}e^{−}Collider (CLIC): Accelerator and Detector. arXiv**2018**, arXiv:1812.07987. [Google Scholar] - Ruth, R.D. CTF3 Design Report; SLAC: Stanford, CA, USA, 2003; Available online: http://cds.cern.ch/record/747483 (accessed on 13 March 2003).
- European Strategy for Particle Physics Preparatory Group. Physics Briefing Book—Input for the European Strategy for Particle Physics Update 2020. In Physics Briefing Book; CERN: Geneva, Switzerland, 2019. [Google Scholar]
- Shiltsev, V. Will There Be Energy Frontier Colliders After LHC? In Proceedings of the 38th International Conference on High Energy Physics (ICHEP 2016), Chicago, IL, USA, 3–10 August 2016. [Google Scholar]
- Shiltsev, V. Considerations On Energy Frontier Colliders After LHC. arXiv
**2017**, arXiv:1705.02011. [Google Scholar] - The CEPC Study Group. CEPC Conceptual Design Report: Volume 2—Physics and Detector. arXiv
**2018**, arXiv:1811.10545. [Google Scholar] - The CEPC Study Group. CEPC Conceptual Design Report: Volume 1—Accelerator. arXiv
**2018**, arXiv:1809.00285. - Benedikt, M.; Blondel, A.; Brunner, O.; Capeans Garrido, M.; Cerutti, F.; Gutleber, J.; Janot, P.; Jimenez, J.M.; Mertens, V.; Milanese, A.; et al. Future Circular Collider—Volume 2—The Lepton Collider FCC-ee Conceptual Design Report; Technical Report CERN-ACC-2018-0057; CERN: Geneva, Switzerland, 2018. [Google Scholar]
- Barna, D. High field septum magnet using a superconducting shield for the Future Circular Collider. Phys. Rev. Accel. Beams
**2017**, 20, 041002. [Google Scholar] [CrossRef] - Barna, D.; Novak, M.; Brunner, K.; Petrone, C.; Atanasov, M.; Feuvrier, J.; Pascal, M. NbTi/Nb/Cu multilayer shield for the superconducting shield (SuShi) septum. arXiv
**2018**, arXiv:1809.04330v1. [Google Scholar] [CrossRef] [Green Version] - Delahaye, J.P.; Diemoz, M.; Long, K.; Mansoulié, B.; Pastrone, N.; Rivkin, L.; Schulte, D.; Skrinsky, A.; Wulzer, A. Muon Colliders. arXiv
**2019**, arXiv:1901.06150. [Google Scholar] - Bernardini, C.; Corazza, G.F.; Ghigo, G.; Touschek, B. The Frascati storage ring. IL Nuovo C
**1960**, 18, 1293–1295. [Google Scholar] [CrossRef] - Cabibbo, N.; Gatto, R. Electron Positron Colliding Beam Experiments. Phys. Rev.
**1961**, 124, 1577–1595. [Google Scholar] [CrossRef] - Bernardini, C. AdA: The first electron-positron collider. Phys. Perspect.
**2004**, 6, 156–183. [Google Scholar] [CrossRef] - Schmueser, P. Superconductivity in high energy particle accelerators. Prog. Part. Nucl. Phys.
**2002**, 49, 155–244. [Google Scholar] [CrossRef] [Green Version] - Marriner, J. Stochastic cooling overview. Nucl. Instrum. Methods Phys. Res. Sect. A
**2004**, 532, 11–18. [Google Scholar] [CrossRef] [Green Version] - MICE Collaboration. Demonstration of cooling by the Muon Ionization Cooling Experiment. Nature
**2020**, 578, 53–59. [Google Scholar] [CrossRef] [Green Version] - Rubbia, C. Further searches of the Higgs scalar sector at the ESS. arXiv
**2019**, arXiv:1908.05664. [Google Scholar] - Antonelli, M.; Boscolo, M.; Di Nardo, R.; Raimondi, P. Novel proposal for a low emittance muon beam using positron beam on target. Nucl. Instrum. Meth. A
**2016**, 807, 101–107. [Google Scholar] [CrossRef] [Green Version] - Amapane, N.; Antonelli, M.; Anulli, F.; Ballerini, G.; Bandiera, L.; Bartosik, N.; Bertolin, A.; Biino, C.; Blanco-Garcia, O.R.; Boscolo, M.; et al. LEMMA approach for the production of low-emittance muon beams. Nuovo Cim. C
**2020**, 42, 259. [Google Scholar] [CrossRef] - Augustin, J.E.; Boyarski, A.M.; Breidenbach, M.; Bulos, F.; Dakin, J.T.; Feldman, G.J.; Fischer, G.E.; Fryberger, D.; Hanson, G.; Jean-Marie, B.; et al. Discovery of a Narrow Resonance in e
^{+}e^{−}Annihilation. Phys. Rev. Lett.**1974**, 33, 1406–1408. [Google Scholar] [CrossRef] [Green Version] - Greco, M.; Pancheri-Srivastava, G.; Srivastava, Y. Radiative Corrections for Colliding Beam Resonances. Nucl. Phys. B
**1975**, 101, 234–262. [Google Scholar] [CrossRef] - Greco, M.; Pancheri-Srivastava, G.; Srivastava, Y. Radiative Corrections to e
^{+}e^{−}→μ^{+}μ^{−}Around the Z^{0}. Nucl. Phys. B**1980**, 171, 118. [Google Scholar] [CrossRef] - Nicrosini, O.; Trentadue, L. Soft Photons and Second Order Radiative Corrections to e
^{+}e^{−}→Z^{0}. Phys. Lett. B**1987**, 196, 551. [Google Scholar] [CrossRef] - Greco, M. On the study of the Higgs properties at a muon collider. Mod. Phys. Lett. A
**2015**, 30, 1530031. [Google Scholar] [CrossRef] [Green Version] - Jadach, S.; Kycia, R.A. Lineshape of the Higgs boson in future lepton colliders. Phys. Lett. B
**2016**, 755, 58–63. [Google Scholar] [CrossRef] [Green Version] - Kuraev, E.A.; Fadin, V.S. On Radiative Corrections to e
^{+}e^{−}Single Photon Annihilation at High-Energy. Sov. J. Nucl. Phys.**1985**, 41, 466–472. [Google Scholar] - Blas, J.D.; Cepeda, M.; D’Hondt, J.; Ellis, R.K.; Grojean, C.; Heinemann, B.; Maltoni, F.; Nisati, A.; Petit, E.; Rattazzi, R.; et al. Higgs Boson Studies at Future Particle Colliders. arXiv
**2019**, arXiv:1905.03764v1. [Google Scholar] [CrossRef] [Green Version] - Han, T.; Liu, Z. Potential precision of a direct measurement of the Higgs boson total width at a muon collider. Phys. Rev. D
**2013**, 87, 033007. [Google Scholar] [CrossRef] [Green Version] - Conway, A.; Wenzel, H. Higgs Measurements at a Muon Collider. arXiv
**2013**, arXiv:1304.5270v1. [Google Scholar] - Janot, P. Higgs Properties at Circular Lepton Colliders. CERN Faculty Meeting June 1st 2018. Available online: https://indico.cern.ch/event/716380/ (accessed on 1 March 2021).
- Liu, Z. Physics at Higgs Factories. Available online: https://indico.cern.ch/event/969815/contributions/4098170/ (accessed on 1 March 2021).
- An, F.; Bai, Y.; Chen, C.; Chen, X.; Chen, Z.; da Costa, J.G.; Cui, Z.; Fang, Y.; Fu, C.; Gao, J.; et al. Precision Higgs Physics at CEPC. arXiv
**2018**, arXiv:1810.09037v2. [Google Scholar] [CrossRef] - Benedikt, M.; Blondel, A.; Brunner, O.; Capeans Garrido, M.; Cerutti, F.; Gutleber, J.; Janot, P.; Jimenez, J.M.; Mertens, V.; Milanese, A.; et al. Future Circular Collider—The Lepton Collider (FCC-ee)—European Strategy Update Documents. 2019. Available online: https://cds.cern.ch/record/2653669 (accessed on 1 March 2021).
- Abada, A.; Abbrescia, M.; AbdusSalam, S.S.; Abdyukhanov, I.; Fernandez, J.A.; Abramov, A.; Aburaia, M.; Acar, A.O.; Adzic, P.R.; Agrawal, P.; et al. FCC Physics Opportunities: Future Circular Collider Conceptual Design Report Volume 1. Future Circular Collider. Eur. Phys. J. C
**2019**, 474. [Google Scholar] [CrossRef] [Green Version] - De Blas, J.; Gu, J.; Liu, Z. Understinging the Higgs Precision at Muon Collider Higgs Factory. 2021; in preparation. [Google Scholar]
- Abramowicz, H.; Abusleme, A.; Afanaciev, K.; Alipour Tehrani, N.; Balázs, C.; Benhammou, Y.; Benoit, M.; Bilki, B.; Blaising, J.-J.; Boland, M.J.; et al. Higgs physics at the CLIC electron–positron linear collider. Eur. Phys. J.
**2017**, C77, 475. [Google Scholar] [CrossRef] [Green Version] - Dainese, A.; Mangano, M.; Meyer, A.B.; Nisati, A.; Salam, G.; Vesterinen, M.A. Report on the Physics at the HL-LHC, and Perspectives for the HE-LHC. CERN Yellow Rep. Monogr.
**2019**, 7. [Google Scholar] [CrossRef] - Ohnishi, Y.; Abe, T.; Adachi, T.; Akai, K.; Arimoto, Y.; Ebihara, K.; Egawa, K.; Flanagan, J.; Fukuma, H.; Funakoshi, Y.; et al. Accelerator design at SuperKEKB. PTEP
**2013**, 2013, 03A011. [Google Scholar] [CrossRef] - Rossi, L.; Badel, A.; Bajko, M.; Ballarino, A.; Bottura, L.; Dhallé, M.M.J.; Durante, M.; Fazilleau, P.; Fleiter, J.; Goldacker, W.; et al. The EuCARD-2 Future Magnets European Collaboration for Accelerator-Quality HTS Magnets. IEEE Trans. Appl. Supercond.
**2015**, 25, 1–7. [Google Scholar] [CrossRef] - Gourlay, S. Superconducting accelerator magnet technology in the 21st century: A new paradigm on the horizon? Nucl. Instrum. Methods Phys. Res. Sect. A
**2018**, 893, 124–137. [Google Scholar] [CrossRef] [Green Version] - The European Strategy Group. Deliberation Document on the 2020 Update of the European Strategy for Particle Physics; Technical Report CERN-ESU-014; CERN: Geneva, Switzerland, 2020. [Google Scholar] [CrossRef]
- The European Strategy Group. 2020 Update of the European Strategy for Particle Physics; Technical Report CERN-ESU-013; CERN: Geneva, Switzerland, 2020. [Google Scholar] [CrossRef]
- Asadi, P.; Capdevilla, R.; Cesarotti, C.; Homiller, S. Searching for Leptoquarks at Future Muon Colliders. arXiv
**2021**, arXiv:2104.05720v1. [Google Scholar] - Ali, H.A.; Arkani-Hamed, N.; Banta, I.; Benevedes, S.; Buttazzo, D.; Cai, T.; Cheng, J.; Cohen, T.; Craig, N.; Ekhterachian, M.; et al. The Muon Smasher’s Guide. arXiv
**2021**, arXiv:2103.14043v1. [Google Scholar] - Bottaro, S.; Strumia, A.; Vignaroli, N. Minimal Dark Matter bound states at future colliders. arXiv
**2021**, arXiv:2103.12766v1. [Google Scholar] - Han, T.; Ma, Y.; Xie, K. Quark and Gluon Contents of a Lepton at High Energies. arXiv
**2021**, arXiv:2103.09844v1. [Google Scholar] - Serra, J. Opportunities for Studying Top Compositeness at a Muon Collider. Available online: https://indico.cern.ch/event/1008639/ (accessed on 1 March 2021).
- Huang, G.Y.; Jana, S.; Queiroz, F.S.; Rodejohann, W. Probing the R
_{K(•)}Anomaly at a Muon Collider. arXiv**2021**, arXiv:2103.01617v1. [Google Scholar] - Capdevilla, R.; Meloni, F.; Simoniello, R.; Zurita, J. Hunting wino and higgsino dark matter at the muon collider with disappearing tracks. arXiv
**2021**, arXiv:2102.11292v1. [Google Scholar] - Han, T.; Li, S.; Su, S.; Su, W.; Wu, Y. Heavy Higgs Bosons in 2HDM at a Muon Collider. arXiv
**2021**, arXiv:2102.08386v1. [Google Scholar] - Liu, W.; Xie, K.P. Probing electroweak phase transition with multi-TeV muon colliders and gravitational waves. arXiv
**2021**, arXiv:2101.10469v1. [Google Scholar] - Capdevilla, R.; Curtin, D.; Kahn, Y.; Krnjaic, G. A No-Lose Theorem for Discovering the New Physics of (g − 2)
_{μ}at Muon Colliders. arXiv**2021**, arXiv:2101.10334v1. [Google Scholar] - Huang, G.Y.; Queiroz, F.S.; Rodejohann, W. Gauged L
_{μ}− L_{τ}at a muon collider. arXiv**2021**, arXiv:2101.04956v1. [Google Scholar] - Buttazzo, D.; Franceschini, R.; Wulzer, A. Two Paths Towards Precision at a Very High Energy Lepton Collider. arXiv
**2020**, arXiv:2012.11555v1. [Google Scholar] - Yin, W.; Yamaguchi, M. Muon g − 2 at multi-TeV muon collider. arXiv
**2020**, arXiv:2012.03928v1. [Google Scholar] - Buttazzo, D.; Paradisi, P. Probing the muon g − 2 anomaly at a Muon Collider. arXiv
**2020**, arXiv:2012.02769v1. [Google Scholar] - Banelli, G.; Salvioni, E.; Serra, J.; Theil, T.; Weiler, A. The Present and Future of Four Tops. arXiv
**2020**, arXiv:2010.05915v1. [Google Scholar] - Craig, N.; Levi, N.; Mariotti, A.; Redigolo, D. Ripples in Spacetime from Broken Supersymmetry. arXiv
**2020**, arXiv:2011.13949v1. [Google Scholar] - Gu, J.; Wang, L.T.; Zhang, C. An unambiguous test of positivity at lepton colliders. arXiv
**2020**, arXiv:2011.03055v1. [Google Scholar] - Han, T.; Liu, D.; Low, I.; Wang, X. Electroweak Couplings of the Higgs Boson at a Multi-TeV Muon Collider. arXiv
**2020**, arXiv:2008.12204v1. [Google Scholar] - Han, T.; Liu, Z.; Wang, L.T.; Wang, X. WIMPs at High Energy Muon Colliders. arXiv
**2020**, arXiv:2009.11287v1. [Google Scholar] - Han, T.; Ma, Y.; Xie, K. High Energy Leptonic Collisions and Electroweak Parton Distribution Functions. arXiv
**2020**, arXiv:2007.14300v2. [Google Scholar] - Capdevilla, R.; Curtin, D.; Kahn, Y.; Krnjaic, G. A Guaranteed Discovery at Future Muon Colliders. arXiv
**2020**, arXiv:2006.16277v1. [Google Scholar] - Costantini, A.; Lillo, F.D.; Maltoni, F.; Mantani, L.; Mattelaer, O.; Ruiz, R.; Zhao, X. Vector boson fusion at multi-TeV muon colliders. arXiv
**2020**, arXiv:2005.10289v1. [Google Scholar] [CrossRef] - Chiesa, M.; Maltoni, F.; Mantani, L.; Mele, B.; Piccinini, F.; Zhao, X. Measuring the quartic Higgs self-coupling at a multi-TeV muon collider. arXiv
**2020**, arXiv:2003.13628. [Google Scholar] [CrossRef] - Bartosik, N.; Bertolin, A.; Buonincontri, L.; Casarsa, M.; Collamati, F.; Ferrari, A.; Ferrari, A.; Gianelle, A.; Lucchesi, D.; Mokhov, N.; et al. Detector and Physics Performance at a Muon Collider. arXiv
**2020**, arXiv:2001.04431v1. [Google Scholar] - Ruhdorfer, M.; Salvioni, E.; Weiler, A. A Global View of the Off-Shell Higgs Portal. arXiv
**2019**, arXiv:1910.04170. [Google Scholar] [CrossRef] [Green Version] - Di Luzio, L.; Gröber, R.; Panico, G. Probing new electroweak states via precision measurements at the LHC and future colliders. arXiv
**2018**, arXiv:1810.10993. [Google Scholar] [CrossRef] [Green Version] - Buttazzo, D.; Redigolo, D.; Sala, F.; Tesi, A. Fusing Vectors into Scalars at High Energy Lepton Colliders. arXiv
**2018**, arXiv:1807.04743. [Google Scholar] [CrossRef] [Green Version] - Fornal, B.; Manohar, A.V.; Waalewijn, W.J. Electroweak Gauge Boson Parton Distribution Functions. arXiv
**2018**, arXiv:1803.06347. [Google Scholar] [CrossRef] - Chakrabarty, N.; Han, T.; Liu, Z.; Mukhopadhyaya, B. Radiative return for heavy Higgs boson at a muon collider. Phys. Rev. D
**2015**, 91, 015008. [Google Scholar] [CrossRef] [Green Version] - Robson, A.; Roloff, P. Updated CLIC luminosity staging baseline and Higgs coupling prospects. arXiv
**2018**, arXiv:1812.01644. [Google Scholar] - TASSO Collaboration; Brandelik, R.; Braunschweig, W.; Gather, K.; Kirschfink, F.J.; Lü belsmeyer, K.; Martyn, H.-U.; Peise, G.; Rimkus, J.; Sander, H.G.; et al. Charge Asymmetry and Weak Interaction Effects in e
^{+}e^{−}→μ^{+}μ^{−}and e^{+}e^{−}→τ^{+}τ^{−}. Phys. Lett. B**1982**, 110, 173–180. [Google Scholar] [CrossRef] - Grzadkowski, B.; Iskrzynski, M.; Misiak, M.; Rosiek, J. Dimension-Six Terms in the Standard Model Lagrangian. JHEP
**2010**, 10, 085. [Google Scholar] [CrossRef] [Green Version] - Giudice, G.F.; Grojean, C.; Pomarol, A.; Rattazzi, R. The strongly-interacting light Higgs. J. High Energy Phys.
**2007**, 6, 045. [Google Scholar] [CrossRef] [Green Version] - International Muon Collider Design Study. Physics and Detector Simulation. Available online: https://indico.cern.ch/category/13145/ (accessed on 1 March 2021).
- International Muon Collider Design Study. Available online: https://muoncollider.web.cern.ch/ (accessed on 1 March 2021).
- Abramowicz, H.; Alipour Tehrani, N.; Arominski, D.; Benhammou, Y.; Benoit, M.; Blaising, J.-J.; Boronat, M.; Borysov, O.; Bosley, R.R.; Božović Jelisavčić, I.; et al. Top-Quark Physics at the CLIC Electron-Positron Linear Collider. arXiv
**2018**, arXiv:1807.02441v1. [Google Scholar] [CrossRef] [Green Version] - Zarnecki, A.F. Top physics at CLIC and ILC. arXiv
**2016**, arXiv:1611.04492. [Google Scholar] - Janot, P. Top-quark electroweak couplings at the FCC-ee. J. High Energy Phys.
**2015**, 4, 182. [Google Scholar] [CrossRef] [Green Version] - Janot, P. Precision measurements of the top quark couplings at the FCC. arXiv
**2015**, arXiv:1510.09056v1. [Google Scholar] - Alwall, J.; Frederix, R.; Frixione, S.; Hirschi, V.; Maltoni, F.; Mattelaer, O.; Shao, H.S.; Stelzer, T.; Torrielli, P.; Zaro, M. The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. JHEP
**2014**, 7, 79. [Google Scholar] [CrossRef] [Green Version] - Barklow, T.; Brau, J.; Fujii, K.; Gao, J.; List, J.; Walker, N.; Yokoya, K. ILC Operating Scenarios. arXiv
**2015**, arXiv:1506.07830. [Google Scholar] - Franceschini, R. A global picture of BSM physics in the top quark sector at the future muon collider. in preparation.

**Figure 1.**The line shapes of the resonances production of the SM Higgs boson as a function of the beam energy $\sqrt{s}$ at a ${\mu}^{+}{\mu}^{-}$ collider (

**left panel**) and an ${e}^{+}{e}^{-}$ collider (

**right panel**). The blue curve is the Breit–Wigner resonance line-shape. The orange line-shape includes the ISR effect alone. The green curves include the BES only with two different energy spreads. The red line shapes take into account all the Breit–Wigner resonance, ISR effect and BES in solid and dashed lines, respectively.

**Figure 3.**Rates for direct production of new states. The labels follow standard nomenclature of composite Higgs models and supersymmetric models. However, we computed cross-sections using only gauge interactions, whereas in these models each state may have specific model dependent interactions that can increase their production rate. Therefore our labels are shorthand for $SU\left(3\right)\otimes SU\left(2\right)\otimes U\left(1\right)$ charges: fermions ${X}_{5/3}\sim {(3,2)}_{7/6}$, $\tilde{W}\sim {(1,3)}_{0}$, $\tilde{h}\sim {(1,2)}_{\pm 1/2}$, ${T}_{2/3}\sim {(3,1)}_{2/3}$ and scalars ${\tilde{t}}_{L}\sim {(3,2)}_{1/6}$, ${\tilde{t}}_{R}\sim {(3,1)}_{2/3}$.

**Figure 4.**Partonic flux for transverse-transverse (red), transverse-longitudinal (green), longitudinal-longitudinal (blue) W boson in $pp$ (hatched) and $\mu \mu $ (solid shading) collisions.

**Figure 5.**Lower-bounds on ${m}_{\u2605}=1/{\ell}_{H}$ expressed as upper bounds on $\widehat{S}={({m}_{W}/{m}_{\u2605})}^{2}$ (blue shades and labels). Dashed lines correspond to limits on the same quantity from the combination of $ee$ Higgs factory and high-energy $pp$ colliders $FCC-\mathrm{ee}$ an $FCC-\mathrm{hh}$ [20].

**Figure 6.**Bounds from Ref. [72] on the size of the Higgs bosons ${\ell}_{H}\simeq 1/{m}_{\u2605}$ from a 10 TeV (blue), 14 TeV (orange), 30 TeV (red) ${\mu}^{+}{\mu}^{-}$ collider using the luminosity Equation (5). The vertical lines are from di-boson and multi-boson production (e.g., ${W}^{+}{W}^{-},Z{W}^{+}{W}^{-}h)$. Diagonal lines are from hh production. Bounds con m

_{★}depend on a generic coupling g

_{★}as suggested by the SILH power counting. The dashed line corresponds to the limits projected for the CLIC 3 TeV stage [20]. The solid shade corresponds to the bounds from HL-LHC [20].

**Figure 7.**Higgs boson direction (as angle $\theta $ or pseudo-rapidity $\eta $) and energy distributions in the laboratory frame for ${\ell}^{+}{\ell}^{-}\to \nu \overline{\nu}h$.

**Table 1.**Effective cross-sections in units of pb at the resonance $\sqrt{s}={m}_{h}=125\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{GeV}$, with Breit–Wigner resonance profile alone, with ISR alone, with BES alone for two choices of beam energy resolutions, and both the BES and ISR effects included.

$\mathit{\sigma}$(BW) | ISR Alone | R (%) | BES Alone | BES+ISR |
---|---|---|---|---|

71 pb | 37 | $0.01$ | 17 | 10 |

$0.003$ | 41 | 22 |

**Table 2.**Signal and background effective cross-sections at the resonance $\sqrt{s}={m}_{h}=125\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{GeV}$ in pb, for two choices of beam energy resolutions R and two leading decay channels with ISR effects taken into account, with the SM branching fractions ${\mathrm{Br}}_{b\overline{b}}=58\%$ and ${\mathrm{Br}}_{{WW}^{*}}=21\%$. For the $b\overline{b}$ background, a conservative cut on the $b\overline{b}$ invariant mass to be greater than 100 GeV is applied.

${\mathit{\mu}}^{+}{\mathit{\mu}}^{-}\to \mathit{h}$ | $\mathit{h}\to \mathit{b}\overline{\mathit{b}}$ | $\mathit{h}\to {\mathit{WW}}^{*}$ | |||
---|---|---|---|---|---|

R (%) | ${\mathit{\sigma}}_{\mathbf{eff}}$ (pb) | ${\mathit{\sigma}}_{\mathit{Sig}}$ | ${\mathit{\sigma}}_{\mathit{Bkg}}$ | ${\mathit{\sigma}}_{\mathit{Sig}}$ | ${\mathit{\sigma}}_{\mathit{Bkg}}$ |

$0.01$ | 10 | $5.6$ | 20 | $2.1$ | 0.051 |

$0.003$ | 22 | 12 | 4.6 |

**Table 3.**Top quark production cross-section in Drell–Yan (

**A**) and W boson fusion (

**B**) at $\sqrt{s}=0.5\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$, $3\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$, $30\phantom{\rule{0.166667em}{0ex}}\mathrm{TeV}$. These numbers are obtained at LO in perturbation theory using $\mathrm{MadGraph}5\_\mathrm{aMC}@\mathrm{NLO}$ [100]. The luminosities used are those following Equation (5) for 30 TeV, whereas we use projected luminosities for top quark factory operation of ILC at 0.5 TeV [101] and CLIC 3 TeV [90]. Radiative corrections and beam energy spreads should be taken into account in a realistic setup but are not expected to change the overall picture (e.g., at 3 TeV $\sigma ({\ell}^{+}{\ell}^{-}\to t\overline{t})=25\phantom{\rule{0.166667em}{0ex}}\mathrm{fb}$ if radiative corrections are included [96]).

(A) | |||
---|---|---|---|

$\sqrt{s}$ | $\sigma ({\ell}^{+}{\ell}^{-}\to t\overline{t})$ | $\mathcal{L}$ | $\sigma \xb7\mathcal{L}$ |

0.5 TeV | 548 fb | 4/ab | $2.2\mathrm{M}$ |

3 TeV | 19 fb | $2.5$/ab | $47\mathrm{K}$ |

30 TeV | 0.19 fb | 90/ab | $17\mathrm{K}$ |

(B) | |||

$\sqrt{s}$ | $\sigma ({\ell}^{+}{\ell}^{-}\to \nu \nu t\overline{t})$ | $\mathcal{L}$ | $\sigma \xb7\mathcal{L}$ |

0.5 TeV | 0.23 fb | 4/ab | $0.9\mathrm{K}$ |

3 TeV | 5.4 fb | 5/ab | $27\mathrm{K}$ |

30 TeV | 31 fb | 90/ab | $2.7\mathrm{M}$ |

**Table 4.**Expected rates for $t\overline{t}+X$ reactions and an estimate on the sensitivity to energy-independent effects, such as a shift in the Yukawa coupling of the top quark.

$\sqrt{\mathit{s}}$ | $\mathit{\sigma}({\mathit{\ell}}^{+}{\mathit{\ell}}^{-}\to \mathit{t}\overline{\mathit{t}}\mathit{h})$ | $\mathcal{L}$ | $\mathit{\sigma}\xb7\mathcal{L}$ | $\frac{\mathit{\delta}\mathit{\sigma}}{\mathit{\sigma}}$ at 68% CL | $\frac{\mathit{\delta}{\mathit{y}}_{\mathit{t}}}{{\mathit{y}}_{\mathit{t}}}$ at 68% CL |

30 TeV | 7 ab | 90/ab | 630 | 4.0% | 2.0% |

$\sigma ({\ell}^{+}{\ell}^{-}\to t\overline{t}h\nu \nu )$ | $\mathcal{L}$ | $\sigma \xb7\mathcal{L}$ | $\frac{\delta \sigma}{\sigma}$ at 68% CL | $\frac{\delta {y}_{t}}{{y}_{t}}$ at 68% CL | |

30 TeV | 100 ab | 90/ab | 9000 | 1% | 0.5% |

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Franceschini, R.; Greco, M.
Higgs and BSM Physics at the Future Muon Collider. *Symmetry* **2021**, *13*, 851.
https://doi.org/10.3390/sym13050851

**AMA Style**

Franceschini R, Greco M.
Higgs and BSM Physics at the Future Muon Collider. *Symmetry*. 2021; 13(5):851.
https://doi.org/10.3390/sym13050851

**Chicago/Turabian Style**

Franceschini, Roberto, and Mario Greco.
2021. "Higgs and BSM Physics at the Future Muon Collider" *Symmetry* 13, no. 5: 851.
https://doi.org/10.3390/sym13050851