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A<sc>bstract</sc> The coupling of the Higgs boson to first and second generation fermions has yet to be measured experimentally. There still could be very large deviations in these couplings, as the origin of flavor is completely unknown. Nevertheless, if Yukawa couplings are modified, especially for light generations, there are generically strong constraints from flavor-changing neutral currents (FCNCs). Therefore, it is imperative to understand whether there exists viable UV physics consistent with current data that motivates future Higgs coupling probes. In particular, the charm-quark Yukawa is the next quark coupling that could be measured at the LHCifit is a few times larger than the SM and compatible with flavor data. This is difficult to achieve in the context of standard ansatz such as Minimal Flavor Violation. In this paper we show that within the framework of Spontaneous Flavor Violation (SFV), using a Two Higgs Doublet Model as an example, the Higgs can be sufficiently charming that new LHC probes are relevant. In this charming region, we show that new Higgs states near the EW scale with large couplings to quarks are required, providing complementary observables or new constraints on the SM Yukawa couplings. The down-type SFV mechanism enabling the suppression of FCNCs also allows for independent modifications to the up-quark Yukawa coupling, which we explore in detail as well. 

A<sc>bstract</sc> The interpretation of Higgs data is typically based on different assumptions about whether there can be additional decay modes of the Higgs or if any couplings can be bounded by theoretical arguments. Going beyond these assumptions requires either a precision measurement of the Higgs width or an absolute measurement of a coupling to eliminate a flat direction in precision fits that occurs when$$ \left|{g}_{hVV}/{g}_{hVV}^{SM}\right| $$ $\left(g_{\mathrm{hVV}}/g_{\mathrm{hVV}}^{\mathrm{SM}}\right)$> 1, whereV=W^±,Z. In this paper we explore how well a high energy muon collider can test Higgs physics without having to make assumptions on the total width of the Higgs. In particular, we investigate off-shell methods for Higgs production used at the LHC and searches for invisible decays of the Higgs to see how powerful they are at a muon collider. We then investigate the theoretical requirements on a model which can exist in such a flat direction. Combining expected Higgs precision with other constraints, the most dangerous flat direction is described by generalized Georgi-Machacek models. We find that by combining direct searches with Higgs precision, a high energy muon collider can robustly test single Higgs precision down to the$$ \mathcal{O}\left(.1\%\right) $$ $O\left(.1\%\right)$level without having to assume SM Higgs decays. Furthermore, it allows one to bound new contributions to the width at the sub-percent level as well. Finally, we comment on how even in this difficult flat direction for Higgs precision, a muon collider can robustly test or discover new physics in multiple ways. Expanding beyond simple coupling modifiers/EFTs, there is a large region of parameter space that muon colliders can explore for EWSB that is not probed with only standard Higgs precision observables. 

A bstract Muon colliders are an exciting possibility for reaching the highest energies possible on the shortest timescale. They potentially combine the greatest strengths of e + e − and pp colliders by bridging the energy versus precision dichotomy. In this paper we study the sensitivity of Higgs properties that can be achieved with a future 3 or 10 TeV muon collider from single Higgs production. The results presented here represent the first comprehensive picture for the precision achievable including backgrounds and using fast detector simulation with Delphes. Additionally, we compare the results of fast detector simulation with available full simulation studies that include the muon collider specific Beam Induced Background, and show the results are largely unchanged. We comment on some of the strengths and weaknesses of a high energy muon collider for Higgs physics alone, and demonstrate the complementarity of such a collider with the LHC and e + e − Higgs factories. Furthermore, we discuss some of the exciting avenues for improving future results from both theoretical and detector R&D that could be undertaken. 

Abstract The Muon Collider is one of the most promising future collider facilities with the potential to reach multi-TeV center-of-mass energy and high luminosity. Due to the significant Higgs boson production cross section in muon-antimuon collisions at such high energies, the collider offers an excellent opportunity for in-depth exploration of Higgs boson properties. It holds the capability to significantly advance our understanding of the Higgs sector to a very high level of precision. However, the presence of beam-induced background resulting from the decay of the beam muons poses unique challenges for detector development and event reconstruction. In this paper, the prospects for measuring various Higgs boson properties at a center-of-mass energy of 3 TeV are presented, using a detailed detector simulation in a realistic environment. The study demonstrates the feasibility of achieving high precision results with the current state-of-the-art detector design. In addition, the paper discusses the detector requirements necessary to achieve this level of accuracy. 

Abstract We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models. 

Abstract A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.