Experimental searches for fifth forces coupled to muons are fundamentally limited by the scarcity of muons in ordinary matter, whereas neutron stars contain abundant muon populations. We show that these compact objects therefore provide superior sensitivity across a broad range of mediator masses. Neutron-star cooling implies limits of $g_{\phi\mu}\lesssim10^{-12}$ and $g_{V\!\mu}\lesssim3\times10^{-13}$ on scalar and vector bosons with masses $m_X\lesssim100$ keV, whereas SN 1987A cooling implies only $g\lesssim3\times10^{-9}$. Moreover, hydrostatic equilibrium requires any long-range muonic force to be sufficiently weak, surpassing cooling bounds for $m_X\lesssim10^{-5}$ eV. Together, these observables provide the most stringent probes of muonic interactions over distance scales ranging from picometers to kilometers.

Neutron stars (NSs) are powerful factories for new particles with masses up to the 100 keV range. These compact stars contain significant populations of charged particles, notably protons, electrons and muons. We calculate the emission rates for new scalar, vector, and pseudoscalar bosons that predominantly couple to electrons and muons. For vector bosons, the in-medium renormalization of the effective couplings strongly modifies the emission rates, e.g., purely muon-philic vectors are predominantly emitted by ultra-relativistic electrons. We focus on bremsstrahlung in electromagnetic lepton-lepton or lepton-proton collisions in the ultradegenerate limit. When protons are superconducting, the scalar and vector energy loss rates scale as $T^4$, the pseudoscalar one as $T^6$, to be compared with $T^8$ for neutrino losses by the modified Urca process. For normal-conducting protons, the screening of transverse photons implies instead scalings with a power reduced by $1/3$ and thus $T^{11/3}$ for scalars and vectors, and $T^{17/3}$ for pseudoscalars. As the NS cools, such new particle losses would become important at late times, when surface photon emission begins to take over, which itself scales roughly as $T^2$ in terms of the internal temperature. Our results can be used to constrain the leptophilic coupling strengths through observed NS cooling ages.

The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the complete set of leading order Renormalization Group Equations (RGEs) in arbitrary gauge EFTs containing scalar and fermion fields. Renormalization effects are consistently taken into account at the order $1/\Lambda^2$ in the new physics scale $\Lambda$ for all renormalizable and non-renormalizable couplings. The obtained template RGEs include operator mixing across different dimensions and are valid for arbitrary gauge groups.

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. The content and structure of this report are guided by the scope and priorities defined in the mandate of the FCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics potential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated here or are addressed only briefly, in alignment with the study’s focus. 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.

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. The FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW pair production threshold, the ZH production peak, and the top/anti-top production threshold—each 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 between the Z, WW, and ZH substages remains flexible. The 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 upcoming High-Luminosity LHC. Its mass reach for direct discovery extends to several tens of TeV. In addition to proton-proton collisions, the 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.

We investigate the neutrino sector in the framework of flavor deconstruction with an inverse-seesaw realization. This setup naturally links the hierarchical charged-fermion masses to the anarchic pattern of light-neutrino mixing. We determine the viable parameter space consistent with oscillation data and study the phenomenology of heavy neutral leptons (HNL) and lepton-flavor-violating (LFV) processes. Current bounds from direct HNL searches and LFV decays constrain the right-handed neutrino scale to a few TeV, while future μ → e experiments will probe most of the region with Λ ≲ 10 TeV. Among possible realizations, models deconstructing SU(2)L × U(1)B−L or SU(2)L × U(1)R × U(1)B−L are those allowing the lowest deconstruction scale.

The future circular e+e− collider (FCC-ee or CEPC) will provide unprecedented sensitivity to indirect new physics signals emerging as small deviations from the Standard Model predictions in electroweak precision tests. Assuming new physics scenarios containing a dark matter candidate and a t-channel mediator, we analyse the synergy and interplay of future Tera-Z factories and non-collider tests conducted through direct and indirect searches of dark matter. Our results highlight the excellent prospect for a Tera-Z run to indirectly probe the presence and nature of dark matter.

We point out that a QCD-like dark sector can be coupled to the Standard Model by gauging the topological Skyrme current, which measures the dark baryon number in the infrared, to give a technically natural model for dark matter. This coupling allows for a semi-annihilation process χχ → χXμ, where Xμ is the gauge boson mediator and χ a dark pion field, which plays the dominant role in setting the dark matter relic abundance. The topological interaction is purely p-wave and so free from indirect detection constraints. We show that the dark matter pion mass needs to be in the range 10 MeV ≲ mχ ≲ 1 TeV; towards the lighter end of this range, there can moreover be significant self-interactions. We discuss prospects for probing this scenario at collider experiments, ranging from the LHC to low-energy e+e− colliders, future Higgs factories, and beam-dump experiments.

We discuss a set of precision observables that can probe the existence of a light particle $X$ coupled to electrons in the mass range of 1-100 MeV. As a case study, we consider the recent excess of $e^+e^-$ final-state events at $\sqrt{s} = 16.9$ MeV reported by the PADME collaboration. Interestingly, this mass is tantalizingly close to the invariant mass at which anomalous $e^+e^-$ pair production has previously been observed in nuclear transitions from excited to ground states by the ATOMKI collaboration. For the scenario in which the new particle has a vector coupling to electrons, we show that the PADME excess is already in tension with constraints from the anomalous magnetic moment of the electron. Further improvements in the measurement of the electron $g$-2, together with upcoming results from PIONEER (searching for $\pi^+\to e^+ \nu X$) and Mu3e (searching for $\mu^+ \to e^+ \bar\nu_\mu\nu_e X$), are expected to definitively probe this scenario in the near future. We also explore alternative possibilities where the new particle has scalar, pseudoscalar, or axial-vector couplings.

We classify the physical operators of the most general bosonic effective gauge theory up to dimension six using on-shell methods. Based on this classification, we compute the complete one-loop anomalous dimension employing both on-shell unitarity-based and geometric techniques. Our analysis fully accounts for the mixing of operators with different dimensions. The results broadly apply to any Effective Field Theory with arbitrary gauge symmetry and bosonic degrees of freedom. To illustrate their utility, we perform a complete cross-check of results on the renormalization of the Standard Model Effective Field Theory (SMEFT), O(n) scalar theory, and the SMEFT extended with an axion-like particle. Additionally, we present new results for axion-like particles with CP-violating interactions.

We classify the physical operators of the most general bosonic effective gauge theory up to dimension six using on-shell methods. Based on this classification, we compute the complete one-loop anomalous dimension employing both on-shell unitarity-based and geometric techniques. Our analysis fully accounts for the mixing of operators with different dimensions. The results broadly apply to any Effective Field Theory with arbitrary gauge symmetry and bosonic degrees of freedom. To illustrate their utility, we perform a complete cross-check of results on the renormalization of the Standard Model Effective Field Theory (SMEFT), $O(n)$ scalar theory, and the SMEFT extended with an axion-like particle. Additionally, we present new results for axion-like particles with CP-violating interactions.

A dedicated run of a future electron-positron collider (FCC-ee) at a center-of-mass energy equal to the Higgs boson mass would enable a direct measurement of the electron Yukawa coupling. However, it poses substantial experimental difficulties due to large backgrounds, the requirement for monochromatised e+e− beams, and the potential extension of the FCC-ee timeline. Given this, we explore the extent to which the electron Yukawa coupling can be enhanced in simplified UV models and examine whether such scenarios can be constrained by other FCC-ee runs or upcoming experiments at the intensity frontier. Our results indicate that in certain classes of models, the (g − 2)e provides a probe of the electron Yukawa coupling that is as effective or better than the FCC-ee. Nevertheless, there exist models that can lead to sizeable deviations in the electron Yukawa coupling which can only be probed in a dedicated run at the Higgs pole mass.

We investigate models that can induce significant modifications to the couplings of first- and second-generation quarks with Higgs bosons. Specifically, we identify all simplified models featuring two vector-like quark states which can lead to substantial enhancements in these couplings. In addition, these models generate operators in Standard Model Effective Field Theory, both at tree-level and one-loop, that are constrained by electroweak precision and Higgs data. We show how to evade constraints from flavour physics and consider direct searches for vector-like quarks. Ultimately, we demonstrate that viable ultraviolet models can be found with first-generation quark Yukawa couplings enhanced by several hundred times their Standard Model value, while the Higgs couplings to charm (strange) quarks can be increased by factors of a few (few tens). Given the importance of electroweak precision data in constraining these models, we also discuss projections for future measurements at the Tera-Z FCC-ee machine.