We chart new-physics models that produce exotic, high-multiplicity muon decays featuring prompt or displaced $e^+e^-$ pairs and/or photons, with or without missing energy, such as $\mu \to 5e$, $\mu \to 7e$, etc. Starting from an effective-field-theory perspective, we estimate the reach on the ultraviolet scale and identify conditions under which lower-multiplicity modes are suppressed or occur at comparable rates. We then construct explicit realizations in minimal dark-sector models with light, feebly interacting particles, such as flavor-protected scalars, dark photons, inelastic dark matter, and axion-like particles. The predicted novel signatures can be probed at MEG II and Mu3e, as well as during calibration runs of COMET and Mu2e. A future discovery would provide valuable insights into short-distance dynamics and the mechanism of lepton-flavor symmetry breaking.

The future circular $e^+ e^-$ collider (FCC-ee) stands out as the next flagship project in particle physics, dedicated to uncovering the microscopic origin of the Higgs boson. In this context, we assess indirect probes of the Minimal Supersymmetric Standard Model (MSSM), a well-established benchmark hypothesis, exploring the complementarity between Higgs measurements and electroweak precision tests at the $Z$-pole. We study three key sectors: the heavy Higgs doublet, scalar top partners, and light gauginos and higgsinos, focusing on the parameter space favored by naturalness. Remarkably, the Tera-$Z$ program consistently offers significantly greater indirect sensitivity than the Mega-$h$ run. While promising, these prospects hinge on reducing SM uncertainties. Accordingly, we highlight key precision observables for targeted theoretical work.

The ECFA Higgs, electroweak, and top Factory Study ran between 2021 and 2025 as a broad effort across the experimental and theoretical particle physics communities, bringing together participants from many different proposed future collider projects. Activities across three main working groups advanced the joint development of tools and analysis techniques, fostered new considerations of detector design and optimisation, and led to a new set of studies resulting in improved projected sensitivities across a wide physics programme. This report demonstrates the significant expansion in the state-of-the-art understanding of the physics potential of future e+e- Higgs, electroweak, and top factories, and has been submitted as input to the 2025 European Strategy for Particle Physics Update.

The ECFA Higgs, electroweak, and top Factory Study ran between 2021 and 2025 as a broad effort across the experimental and theoretical particle physics communities, bringing together participants from many different proposed future collider projects. Activities across three main working groups advanced the joint development of tools and analysis techniques, fostered new considerations of detector design and optimisation, and led to a new set of studies resulting in improved projected sensitivities across a wide physics programme. This report demonstrates the significant expansion in the state-of-the-art understanding of the physics potential of future e+e- Higgs, electroweak, and top factories, and has been submitted as input to the 2025 European Strategy for Particle Physics Update.

We investigate the phenomenology of a model [1] in which the proton is rendered absolutely stable by an IR mechanism that remains robust against unknown quantum gravity effects. A linear combination of baryon number and lepton flavors is gauged and spontaneously broken to a residual ℤ9 discrete gauge symmetry enforcing a strict selection rule: ΔB = 0 (mod 3). Despite its minimal field content, the model successfully accounts for established empirical evidence of physics beyond the SM. High-scale symmetry breaking simultaneously provides a seesaw mechanism explaining the smallness of neutrino masses, minimal thermal leptogenesis, and a viable phenomenology of the majoron as dark matter. Any cosmic string-wall network remaining after inflation is unstable for numerous charge assignments. Lepton flavor non-universality, central to the construction, leads to predictive neutrino textures testable via oscillation experiments, neutrinoless double beta decay, and cosmology. The model motivates searches in X- and γ-ray lines, neutrino telescopes, and predicts CMB imprints.

We investigate the phenomenology of a model in which the proton is rendered absolutely stable by an IR mechanism that remains robust against unknown quantum gravity effects. A linear combination of baryon number and lepton flavors is gauged and spontaneously broken to a residual $\mathbb{Z}_9$ discrete gauge symmetry enforcing a strict selection rule: $\Delta B = 0\,(\mathrm{mod}\,3)$. Despite its minimal field content, the model successfully accounts for established empirical evidence of physics beyond the SM. High-scale symmetry breaking simultaneously provides a seesaw mechanism explaining the smallness of neutrino masses, minimal thermal leptogenesis, and a viable phenomenology of the majoron as dark matter. Any cosmic string-wall network remaining after inflation is unstable for numerous charge assignments. Lepton flavor non-universality, central to the construction, leads to predictive neutrino textures testable via oscillation experiments, neutrinoless double beta decay, and cosmology. The model motivates searches in $X$- and $\gamma$-ray lines, neutrino telescopes, and predicts CMB imprints.

In response to the 2020 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) Feasibility Study was launched as an international collaboration hosted by CERN. This report describes the FCC integrated programme, which consists of two stages: an electron-positron collider (FCC-ee) in the first phase, serving as a high-luminosity Higgs, top, and electroweak factory; followed by a proton-proton collider (FCC-hh) at the energy frontier in the second phase. FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW production threshold, the ZH production peak, and the top/anti-top production threshold - delivering the highest possible luminosities to four experiments. Over 15 years of operation, FCC-ee will produce more than 6 trillion Z bosons, 200 million WW pairs, nearly 3 million Higgs bosons, and 2 million top anti-top pairs. Precise energy calibration at the Z pole and WW threshold will be achieved through frequent resonant depolarisation of pilot bunches. The sequence of operation modes remains flexible. FCC-hh will operate at a centre-of-mass energy of approximately 85 TeV - nearly an order of magnitude higher than the LHC - and is designed to deliver 5 to 10 times the integrated luminosity of the HL-LHC. Its mass reach for direct discovery extends to several tens of TeV. In addition to proton-proton collisions, FCC-hh is capable of supporting ion-ion, ion-proton, and lepton-hadron collision modes. This second volume of the Feasibility Study Report presents the complete design of the FCC-ee collider, its operation and staging strategy, the full-energy booster and injector complex, required accelerator technologies, safety concepts, and technical infrastructure. It also includes the design of the FCC-hh hadron collider, development of high-field magnets, hadron injector options, and key technical systems for FCC-hh.

Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools /reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

Volume 3 of the FCC Feasibility Report presents studies related to civil engineering, the development of a project implementation scenario, and environmental and sustainability aspects. The report details the iterative improvements made to the civil engineering concepts since 2018, taking into account subsurface conditions, accelerator and experiment requirements, and territorial considerations. It outlines a technically feasible and economically viable civil engineering configuration that serves as the baseline for detailed subsurface investigations, construction design, cost estimation, and project implementation planning. Additionally, the report highlights ongoing subsurface investigations in key areas to support the development of an improved 3D subsurface model of the region. The report describes development of the project scenario based on the 'avoid-reduce-compensate' iterative optimisation approach. The reference scenario balances optimal physics performance with territorial compatibility, implementation risks, and costs. Environmental field investigations covering almost 600 hectares of terrain - including numerous urban, economic, social, and technical aspects - confirmed the project's technical feasibility and contributed to the preparation of essential input documents for the formal project authorisation phase. The summary also highlights the initiation of public dialogue as part of the authorisation process. The results of a comprehensive socio-economic impact assessment, which included significant environmental effects, are presented. Even under the most conservative and stringent conditions, a positive benefit-cost ratio for the FCC-ee is obtained. Finally, the report provides a concise summary of the studies conducted to document the current state of the environment.

In this paper, we analyze examples of research institutes that stand out in scientific excellence and social impact. We define key practices for evaluating research results, economic conditions, and the selection of specific research topics. Special focus is placed on small countries and the field of artificial intelligence. The aim is to identify components that enable institutes to achieve a high level of innovation, self-sustainability, and social benefits.

The flavor puzzles remain among the most compelling open questions in particle physics. The striking hierarchies observed in the masses and mixing of charged fermions define the Standard Model (SM) flavor puzzle, a profound structural enigma pointing to physics beyond the SM. Simultaneously, the absence of deviations from SM predictions in precision measurements of flavor-changing neutral currents imposes severe constraints on new physics at the TeV scale, giving rise to the new physics flavor puzzle. This review provides an overview of a selection of recent advancements in flavor model building, with a particular focus on attempts to address one or both of these puzzles within the quark sector.

The flavor puzzles remain among the most compelling open questions in particle physics. The striking hierarchies observed in the masses and mixing of charged fermions define the Standard Model (SM) flavor puzzle, a profound structural enigma pointing to physics beyond the SM. Simultaneously, the absence of deviations from SM predictions in precision measurements of flavor-changing neutral currents imposes severe constraints on new physics at the TeV scale, giving rise to the new physics flavor puzzle. This review provides an overview of a selection of recent advancements in flavor model building, with a particular focus on attempts to address one or both of these puzzles within the quark sector.

Leveraging recent advancements in machine learning-based flavor tagging, we develop an optimal analysis for measuring the hadronic cross-section ratios R_bRb, R_cRc, and R_sRs at the FCC-ee during its WWWW, ZhZh, and t\bar{t}tt‾ runs. Our results indicate up to a two-order-of-magnitude improvement in precision, providing an unprecedented test of the SM. Using these observables, along with R_\ellRℓ and R_tRt, we project sensitivity to flavor non-universal four-fermion (4F) interactions within the SMEFT, contributing both at the tree-level and through the renormalization group (RG). We highlight a subtle complementarity with RG-induced effects at the FCC-ee’s ZZ-pole. Our analysis demonstrates significant improvements over the current LEP-II and LHC bounds in probing flavor-conserving 4F operators involving heavy quark flavors and all lepton flavors. As an application, we explore simplified models addressing current BB-meson anomalies, demonstrating that FCC-ee can effectively probe the relevant parameter space. Finally, we design optimized search strategies for quark flavor-violating 4F interactions.