Using on-shell methods, we derive an all-order non-renormalization theorem for general four-dimensional effective field theories, relying on Poincar\'e invariance and unitarity. Each operator $\mathcal O$ is assigned the weights $(w,\bar w)=(\ell-h,\ell+h)$, where $\ell$ and $h$ are the number of particles and total helicity of its minimal configuration. At $L$ loops, the mixing $\mathcal O_j\to\mathcal O_i$ vanishes when $\ell_j-\ell_i=L-1$ and either $w_i<w_j-2(L-1)$ or $\bar w_i<\bar w_j-2(L-1)$, in the absence of non-holomorphic Yukawa couplings. These zeros follow entirely from tree-level data and are scheme independent under finite renormalizations that preserve the operator-length selection rule. For operators of dimensions five through eight, we identify broad classes of previously unknown zeros at higher loop orders, with particular emphasis on two loops, where the theorem provides direct checks on current calculations, as in the Standard Model Effective Field Theory.

We study the phenomenology of the topological portal between QCD and pseudo-Nambu--Goldstone dark matter proposed in~\cite{Davighi:2024zip}. We construct a weakly coupled ultraviolet completion in which a vector mediator gauges a baryonic current of QCD for the light quark flavours, linking it to dark pions parametrizing the coset $SU(2)_D/U(1)_D$. As a concrete anomaly-free realisation, we gauge the leptophobic combination $B_1+B_2-2B_3$. This completion allows us to calculate thermal coannihilation beyond the regime of validity of the pion effective theory, including resonant mediator effects, and to test the resulting thermal target with boosted-dijet and monojet searches at the LHC, with LEP and bottomonium data, and with flavour observables. These collider signatures follow directly from the symmetry structure required by matching onto the topological portal. At low momentum transfer, the topological operator instead controls the decay of the heavier dark pion, which is long-lived. A future high-statistics $Z$ factory, such as FCC-ee, can probe the low-mass region where hadron-collider sensitivity deteriorates, providing complementary tests of the topological portal.

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.

Testing muonic fifth forces is difficult because muons are scarce in ordinary matter. However, they are abundant in neutron stars. We show that this population responds coherently to electromagnetic fluctuations induced by proton and electron collisions, emitting the fifth-force mediator and cooling the star. This energy loss constrains $g_{X\mu}\lesssim 10^{-13}$ for scalars with $m_\phi\lesssim 100$ keV and vectors with $10^{-5}\,\mathrm{eV}\lesssim m_V\lesssim 100$ keV, far more strongly than SN 1987A cooling. Vector forces at smaller $m_V$ deplete muons, suppressing the coherent response. Cooling from incoherent muon scattering still constrains $g_{V \mu}\lesssim 2.5\times 10^{-12}$ for $1.3\times 10^{-7}\,\mathrm{eV}\lesssim m_V\lesssim 10^{-5}$ eV. Together, these bounds provide the most sensitive probes of muonic interactions across a broad range of parameters.

Neutron stars (NSs) are powerful factories for new particles with masses up to the 100~keV range. These compact stars contain significant amounts of protons, electrons, and muons. We deduce the emission rates for new scalar, vector, and pseudoscalar bosons coupling to electrons and muons. For muonic vector bosons, in addition to direct emission from leptons in incoherent scatterings with the medium, a competing channel is the coherent excitation of the lepton population electromagnetically induced by incoherent hadronic scatterings - an effective in-medium coupling. For muonic scalar bosons, emission from the effective in-medium coupling to electrons is always dominant due to their relativistically boosted emission. Pseudoscalars can only be emitted through incoherent leptonic scatterings. If protons are superconducting, the scalar and vector energy loss rates scale as $T^4$, the pseudoscalar ones as $T^6$, to be compared with $T^8$ for neutrino losses by the modified Urca (MUrca) process. For normal-conducting protons, the damping of transverse photons implies instead scalings with a power $T^{11/3}$ for scalars, and $T^{17/3}$ for pseudoscalars; vectors, emitted by nonrelativistic protons in the nonsuperconducting regime, still scale as $T^4$. 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/Λ2 in the new physics scale Λ 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.