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.

Rare b hadron decays are considered excellent probes of new semileptonic four-fermion interactions of microscopic origin. However, the same interactions also correct the high-mass Drell-Yan tails. In this work, we revisit the first statement in the context of this complementarity and chart the space of short-distance new physics that could show up in rare b decays. We analyze the latest b → qℓ ^+ ℓ ^ − measurements, where q = d or s and ℓ = e or μ , including the most recent LHCb R K ∗ $$ {R}_{K^{\left(\ast \right)}} $$ update, together with the latest charged and neutral current high-mass Drell-Yan data, pp → ℓν and pp → ℓ ^+ ℓ ^ − . We implement a sophisticated interpretation pipeline within the flavio framework, allowing us to investigate the multidimensional SMEFT parameter space thoroughly and efficiently. To showcase the new functionalities of flavio, we construct several explicit models featuring either a Z ′ or a leptoquark, which can explain the tension in b → sμ ^+ μ ^ − angular distributions and branching fractions while predicting lepton flavor universality (LFU) ratios to be SM-like, R K ∗ ≈ R K ∗ SM $$ {R}_{K^{\left(\ast \right)}}\approx {R}_{K^{\left(\ast \right)}}^{\textrm{SM}} $$ , as indicated by the recent data. Those models are then confronted against the global likelihood, including the high-mass Drell-Yan, either finding tensions or compatibility.

This note gives an overview of the tools for the precision matching of ultraviolet theories to the Standard Model effective field theory (SMEFT) at the tree level and one loop. Several semi- and fully automated codes are presented, as well as some supplementary codes for the basis conversion and the subsequent running and matching at low energies. A suggestion to collect information for cross-validations of current and future codes is made.

Recent progress in calculating lepton density functions inside the proton and simulating lepton showers laid the foundations for precision studies of resonant leptoquark production at hadron colliders. Direct quark-lepton fusion into a leptoquark is a novel production channel at the LHC that has the potential to probe a unique parameter space for large masses and couplings. In this work, we build the first Monte Carlo event generator for a full-fledged simulation of this process at NLO for production, followed by a subsequent decay using the POWHEG method and matching to the parton showers utilizing HERWIG. The code can handle all scalar leptoquark models with renormalisable quark-lepton interactions. We then comprehensively study the differential distributions, including higher-order effects, and assess the corresponding theoretical uncertainties. We also quantify the impact of the improved predictions on the projected (HL-)LHC sensitivities and initiate the first exploration of the potential at the FCC-hh. Our work paves the way toward performing LHC searches using this channel.

Rare flavour-changing neutral-current transitions b → sμ+μ− probe higher energy scales than what is directly accessible at the LHC. Therefore, the presence of new physics in such transitions, as suggested by the present-day LHCb anomalies, would have a major impact on the motivation and planning of future high-energy colliders. The two most prominent options currently debated are a proton-proton collider at 100 TeV (FCC-hh) and a multi-TeV muon collider (MuC). In this work, we compare the discovery prospects at these colliders on benchmark new physics models indirectly detectable in b → sμ+μ− decays but beyond the reach of the high-pT searches at the HL-LHC. We consider a comprehensive set of scenarios: semileptonic contact interactions, Z′ from a gauged U1B3−Lμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{U}{(1)}_{B_3-{L}_{\mu }} $$\end{document} and U1Lμ−Lτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$\end{document}, the scalar leptoquark S3, and the vector leptoquark U1. We find that a 3 TeV MuC has a sensitivity reach comparable to the one of the FCC-hh. However, for a heavy enough mediator, the new physics effects at a 3 TeV MuC are only observed indirectly via deviations in the highest energy bin, while the FCC-hh has a greater potential for the discovery of a resonance. Finally, to completely cover the parameter space suggested by the bsμμ anomalies, among the proposed future colliders, only a MuC of 10 TeV (or higher) can meet the challenge.

We investigate an economical explanation for the (g − 2)μ anomaly with a neutral vector boson from a spontaneously broken U(1)X gauge symmetry. The Standard Model fermion content is minimally extended by 3 right-handed neutrinos. Using a battery of complementary constraints, we perform a thorough investigation of the renormalizable, quark flavor-universal, vector-like U(1)X models, allowing for arbitrary kinetic mixing. Out of 419 models with integer charges not greater than ten, only 7 models are viable solutions, describing a narrow region in model space. These are either Lμ− Lτ or models with a ratio of electron to baryon number close to −2. The key complementary constraints are from the searches for nonstandard neutrino interactions. Furthermore, we comment on the severe challenges to chiral U(1)X solutions and show the severe constraints on a particularly promising such candidate.

We study the flavor structure of the lepton and baryon number-conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [1], we define several well-motivated flavor symmetries and symmetry-breaking patterns that serve as competing hypotheses about the ultraviolet (UV) dynamics beyond the SM, not far above the TeV scale. In particular, we consider four different structures in the quark sector and seven in the charged lepton sector. The set of flavor-breaking spurions is (almost) always taken to be the minimal one needed to reproduce the observed charged fermion masses and mixings. For each case, we explicitly construct and count the operators to the first few orders in the spurion expansion, providing ready-for-use setups for phenomenological studies and global fits. We provide a Mathematica package SMEFTflavor (https://github.com/aethomsen/SMEFTflavor) to facilitate similar analyses for flavor symmetries not covered in this work.

Muon colliders provide a unique route to deliver high energy collisions that enable discovery searches and precision measurements to extend our under-standing of the fundamental laws of physics. The muon collider design aims to deliver physics reach at the highest energies with costs, power consumption and on a time scale that may prove favorable relative to other proposed facilities. In this context, a new international collaboration has formed to further extend the design concepts and performance studies of such a machine. This effort is focused on delivering the elements of a ∼ 10 TeV center of mass (CM) energy design to explore the physics energy frontier. The path to such a machine may pass through lower energy options. Currently a 3 TeV CM stage is considered. Other energy stages could also be explored, e.g. an s-channel Higgs Factory operating at 125 GeV CM. We describe the status of the R&D and design effort towards such a machine and lay out a plan to bring these concepts to maturity as a tool for the high energy physics community.

Muon colliders provide a unique route to deliver high energy collisions that enable discovery searches and precision measurements to extend our understanding of the fundamental laws of physics. The muon collider design aims to deliver physics reach at the highest energies with costs, power consumption and on a time scale that may prove favorable relative to other proposed facilities. In this context, a new international collaboration has formed to further extend the design concepts and performance studies of such a machine. This effort is focused on delivering the elements of a $\sim$10 TeV center of mass (CM) energy design to explore the physics energy frontier. The path to such a machine may pass through lower energy options. Currently a 3 TeV CM stage is considered. Other energy stages could also be explored, e.g. an s-channel Higgs Factory operating at 125 GeV CM. We describe the status of the R&D and design effort towards such a machine and lay out a plan to bring these concepts to maturity as a tool for the high energy physics community.

In the path towards a muon collider with center of mass energy of 10 TeV or more, a stage at 3 TeV emerges as an appealing option. Reviewing the physics potential of such muon collider is the main purpose of this document. In order to outline the progression of the physics performances across the stages, a few sensitivity projections for higher energy are also presented. There are many opportunities for probing new physics at a 3 TeV muon collider. Some of them are in common with the extensively documented physics case of the CLIC 3 TeV energy stage, and include measuring the Higgs trilinear coupling and testing the possible composite nature of the Higgs boson and of the top quark at the 20 TeV scale. Other opportunities are unique of a 3 TeV muon collider, and stem from the fact that muons are collided rather than electrons. This is exemplified by studying the potential to explore the microscopic origin of the current $g$-2 and $B$-physics anomalies, which are both related with muons.

The perspective of designing muon colliders with high energy and luminosity, which is being investigated by the International Muon Collider Collaboration, has triggered a growing interest in their physics reach. We present a concise summary of the muon colliders potential to explore new physics, leveraging on the unique possibility of combining high available energy with very precise measurements.

We explore a novel mechanism to restrict TeV-scale leptoquark interactions and render the proton exactly stable to all orders in the effective field theory expansion. A scalar condensate breaks a lepton-flavored U(1) X gauge symmetry in the ultraviolet and generates neutrino masses, leaving a discrete Z 9 or Z 18 gauge symmetry in the infrared, forbidding ∆ B = 1 processes. This provides an elegant framework to address the flavour anomalies and can be adapted to many other new-physics models. The U(1) X can emerge from a gauge–flavour unified SU(12) × SU(2) × SU(2) theory at even higher energies.

Significant deviations from Standard Model (SM) predictions have been observed in $ b \to s \mu^+ \mu^-$ decays and in the muon $g-2$. Scalar leptoquark extensions of the SM are known to be able to address these anomalies, but generically give rise to lepton flavor violation (LFV) or even proton decay. We propose new muon flavored gauge symmetries as a guiding principle for leptoquark models that preserve the global symmetries of the SM and explain the non-observation of LFV. A minimal model is shown to easily accommodate the anomalies without encountering other experimental constraints. This talk is mainly based on Ref. [1].

We develop an economical theoretical framework for combined explanations of the flavor physics anomalies involving muons: (g − 2)μ, RK∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_{K^{\left(\ast \right)}} $$\end{document}, and b → sμ+μ− angular distributions and branching ratios, that was first initiated by some of us in ref. [1]. The Standard Model (SM) is supplemented with a lepton-flavored U(1)X gauge group. The U(1)X gauge boson with the mass of O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(0.1) GeV resolves the (g − 2)μ tension. A TeV-scale leptoquark, charged under the U(1)X, carries a muon number and mediates B-decays without prompting charged lepton flavor violation or inducing proton decay. We explore the theory space of the chiral, anomaly-free U(1)X gauge extensions featuring the above scenario, and identify many suitable charge assignments for the SM+3νR fermion content with the integer charges in the range XFi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {X}_{F_i} $$\end{document} ∈ [−10, 10]. We then carry out a comprehensive phenomenological study of the muonic force in representative benchmark models. Interestingly, we found models which can resolve the tension without conflicting the complementary constraints, and all of the viable parameter space will be tested in future muonic resonance searches. Finally, the catalog of the anomaly-free lepton-non-universal charge assignments motivated us to explore different directions in model building. We present a model in which the muon mass and the (g − 2)μ are generated radiatively from a common short-distance dynamics after the U(1)X breaking. We also show how to charge a vector leptoquark under U(1)μ−τ in a complete gauge model.

We discuss neutrino magnetic moments as a way of constraining physics beyond the Standard Model. In fact, new physics at the TeV scale can easily generate observable neutrino magnetic moments, and there exists a multitude of ways of probing them. We highlight in particular direct dark matter detection experiments (which are sensitive to neutrino magnetic moments because of the predicted modifications to the solar neutrino scattering rate), stellar cooling, and cosmological constraints.