This contribution discusses the physics potential of a future muon collider operating at a center-of-mass energy of √(s) = 10 TeV for precision studies in the Higgs sector. Using a detailed detector simulation that incorporates the dominant sources of machine-induced background, the expected sensitivity to key Higgs processes is evaluated. These include the measurement of production cross sections for H→ bb̅, H→ WW^*, and double-Higgs production HH→ bb̅bb̅. A central focus of the study is the determination of the Higgs boson trilinear self-coupling, a critical parameter for understanding the structure of the Higgs potential and electroweak symmetry breaking. The analysis is based on the MUSIC multi-purpose detector concept, specifically optimized for the muon collider environment, and assumes an integrated luminosity of 10 ab^-1 collected over five years. The results presented highlight the exceptional prospects of a multi-TeV muon collider for exploring the Higgs potential with a level of precision unattainable by any other proposed future collider within a comparable timeframe.

Abstract This work presents a proof of concept for MUSIC, a multi-purpose detector conceived for high-precision and ultra-high-energy physics studies in the challenging environment of $$\sqrt{s}=10$$ s = 10 TeV muon–antimuon collisions. The detector features a central tracking system, electromagnetic and hadronic calorimeters, and dedicated muon detectors. This paper outlines the main design elements of each subdetector, with an emphasis on the effects of machine-induced backgrounds and the reconstruction strategies employed for key physics objects. Performance results for electrons, photons, muons, and jets are reported, and studies of jet flavour identification are discussed.

The full exploitation of the physics potential of a multi-TeV muon collider will ultimately lie in the detector's ability to cope with unprecedented levels of machine-induced backgrounds. This contribution introduces the MUSIC (MUon System for Interesting Collisions) detector concept and presents its performance in the context of √(s) = 10 TeV muon-antimuon collisions. The MUSIC detector is designed to mitigate machine-induced background effects while maintaining high efficiency and accuracy in the reconstruction of physics events, in particular in the Higgs boson sector and in the search for new physics. It features an all-silicon tracking system, a semi-homogeneous lead-fluorite crystal electromagnetic calorimeter, an iron-scintillator sampling hadronic calorimeter, and a superconducting magnet providing a 5 T magnetic field. Detailed detector simulations, accounting for the dominant machine-induced backgrounds, demonstrate promising performance in track, muon, photon, electron, and jet reconstruction, as well as jet flavor identification, highlighting the detector's strong potential for high-energy muon collider experiments.

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.

Muons offer a unique opportunity to build a compact high-energy electroweak collider at the 10 TeV scale. A Muon Collider enables direct access to the underlying simplicity of the Standard Model and unparalleled reach beyond it. It will be a paradigm-shifting tool for particle physics representing the first collider to combine the high-energy reach of a proton collider and the high precision of an electron-positron collider, yielding a physics potential significantly greater than the sum of its individual parts. A high-energy muon collider is the natural next step in the exploration of fundamental physics after the HL-LHC and a natural complement to a future low-energy Higgs factory. Such a facility would significantly broaden the scope of particle colliders, engaging the many frontiers of the high energy community. The last European Strategy for Particle Physics Update and later the Particle Physics Project Prioritisation Panel in the US requested a study of the muon collider, which is being carried on by the International Muon Collider Collaboration. In this comprehensive document we present the physics case, the state of the work on accelerator design and technology, and propose an R&D project that can make the muon collider a reality.

We propose to explore the potential advantages of a new class of tracking algorithms loosely inspired by the Hough transform concept and where we include the time of arrival of each hit as an additional coordinate to be treated in the same way as a spatial coordinate. A remarkable property of this algorithm is that the execution time is proportional to the total number of hits to be processed, making it particularly attractive for high occupancy situations expected at future colliders. The particular structure of the algorithm also lends itself naturally to parallel hardware implementations which, combined to its intrinsic flexibility, should provide a powerful tool for triggering at future colliders. To probe the effectiveness of the algorithm, we apply it to a quasi-realistic simulated environment of a possible future muon collider experiment and report the performance.

This document is comprised of a collection of consolidated parameters for the key parts of the muon collider. These consolidated parameters follow on from the October 2024 Preliminary Parameters Report. Attention has been given to a high-level consistent set of baseline parameters throughout all systems of the complex, following a 10 TeV center-of-mass design. Additional details of the designs contributing to this baseline design are featured in the appendix. Likewise, explorative variations from this baseline set can be found in the appendix. The data is collected from a collaborative spreadsheet and transferred to overleaf.

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.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

Muon collisions at multi-TeV center-of-mass energies are ideal for studying Higgs boson properties. At these energies, the production rates will allow precise measurements of its couplings to fermions and bosons. In addition, the double Higgs boson production rate could be sufficiently high to directly measure the parameters of trilinear self-couplings, giving access to the determination of the Higgs potential. This communication aims to give an overview of the results that have been obtained so far on Higgs couplings by studying the mu (+)mu (-) -> H( bb)vv, mu (+)mu (- ) -> H(WW & lowast;)vv and mu (+)mu (-) -> H( bb) H(bb) vv processes. All the studies have been performed with a detailed simulation of the signal and physics background samples and by taking into account the effects of the beam-induced background on the detector performance. Evaluations of Higgs boson production cross-sections sensitivities and results on the uncertainty on double Higgs production cross-section, together with the trilinear self-coupling, will be discussed at a center-of-mass energy of 3 TeV.

A multi-TeV muon collider offers a spectacular opportunity in the direct exploration of the energy frontier. Offering a combination of unprecedented energy collisions in a comparatively clean leptonic environment, a high energy muon collider has the unique potential to provide both precision measurements and the highest energy reach in one machine that cannot be paralleled by any currently available technology. The topic generated a lot of excitement in Snowmass meetings and continues to attract a large number of supporters, including many from the early career community. In light of this very strong interest within the US particle physics community, Snowmass Energy, Theory and Accelerator Frontiers created a cross-frontier Muon Collider Forum in November of 2020. The Forum has been meeting on a monthly basis and organized several topical workshops dedicated to physics, accelerator technology, and detector R D. Findings of the Forum are summarized in this report.

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.

Experimental activities involving multi-TeV muon collisions are a relatively recent endeavor. The community has limited experience in designing detectors for lepton interactions at center-of-mass energies of 10 TeV and beyond. This review provides a short overview of the machine characteristics and outlines potential sources of beam-induced background that could impact the detector performance. The strategy for mitigating the effects of beam-induced background on the detector at $\sqrt{s}=3$ TeV is discussed, focusing on the machine-detector interface, detector design, and the implementation of reconstruction algorithms. The physics potential at this center-of-mass energy is evaluated using a detailed detector simulation that incorporates the effects of beam-induced background. This evaluation concerns the Higgs boson couplings and the Higgs field potential sensitivity, that then are used to get confidence on the expectations at 10 TeV. The physics and detector requirements for an experiment at $\sqrt{s}=10$ TeV, outlined here, form the foundation for the initial detector concept at that center-of-mass energy .

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

A search is reported for charge-parity D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ $CP$ violation in D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ decays, using data collected in proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by the CMS experiment in 2018. The analysis uses a dedicated data set that corresponds to an integrated luminosity of 41.6 fb$^{-1}$, which consists of about 10 billion events containing a pair of \b hadrons, nearly all of which decay to charm hadrons. The flavor of the neutral D meson is determined by the pion charge in the reconstructed decays D$^{*+}$ $\to$ D$^0\pi^+$ and D$^{*-}$ $\to$ D$^0\pi^-$. The D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ $CP$ asymmetry in D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ is measured to be $A_{CP}$( K$^0_\mathrm{S}$K$^0_\mathrm{S}$) = (6.2 $\pm$ 3.0 $\pm$ 0.2 $\pm$ 0.8)%, where the three uncertainties represent the statistical uncertainty, the systematic uncertainty, and the uncertainty in the measurement of the D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ $CP$ asymmetry in the D$^0$ $\to$ K$^0_\mathrm{S}\pi^+\pi^-$ decay. This is the first D$^0$ $\to$ K$^0_\mathrm{S}$K$^0_\mathrm{S}$ $CP$ asymmetry measurement by CMS in the charm sector as well as the first to utilize a fully hadronic final state.

A Muon Collider represents a promising possibility to combine the high energy and luminosity of hadron machines with very precise measurements of lepton colliders. The main challenges, that impact both the machine and detector design, arise from the short muon lifetime and the harsh Beam-induced Background (BIB). Therefore, a full simulation is crucial to understand the feasibility of the experiment implementation. Focusing in particular on the muon system, a preliminary simulation of sensitivity and hit rate reveals that the technology inherited from CLIC, i.e. glass Resistive Plate Chambers, is already at the limit of its rate capability. Thus, alternative MicroPattern Gaseous Detector solutions are under investigation to try to match the required performance. In parallel, studies of muon reconstruction are ongoing. Results of the muon reconstruction efficiency and BIB sensitivity are presented for multimuon final state processes at a centre-of-mass energy of 1.5 TeV. Besides, PICOSEC technology, based on a Micromegas detector coupled to a Cherenkov radiator and equipped with a photocathode, is discussed.

The design of a feasible multi-TeV muon collider facility is the mandate of the International Muon Collider Collaboration based at CERN and is considered with great interest along the presently on-going US Snowmass 2021 process. The physics potential of such a novel future collider is overwhelming, ranging from precision measurements to direct searches for new Physics. Despite the machine-design challenges, it gives access to the uncharted territory of leptonic collisions at a center-of-mass energy of 10 TeV or higher with an instantaneous luminosity up to a few 1035 cm−2 s−1. The experiment design, the detector technology choices, and the event reconstruction tools are strongly affected by the presence of the beam-induced background, generated by the interactions of the muon decay products with the machine elements. Full simulation studies at s=1.5 TeV and 3 TeV, adopting the CLIC experiment technologies, represent the starting point to optimize the detector design and propose future dedicated R&D.

A multi-TeV muon collider is a discovery machine and an invaluable tool for many new standard model precision measurements such as the shape of the Higgs boson potential. The update of the European Strategy for Particle Physics recognized the unique opportunity of a muon collider to reach the energy frontier, despite the challenges to produce intense collimated muon beams. The options of a collider at 3 TeV and a collider at 10 TeV or above are the main focus of the forming International Muon Collider Collaboration as well as of the discussion panels at the ongoing US Snowmass process.