We present a technically natural microscopic realization of apparent phantom dark energy based on an axion coupled to $N$ copies of two-flavor dark QCD related by a $\mathbb{Z}_N$ exchange symmetry. The symmetry exponentially suppresses the axion vacuum potential, naturally generating the dark-energy scale, while reheating into a single dark sector induces a controlled breaking of $\mathbb{Z}_N$ that simultaneously restores the physical axion periodicity, sets the dark-matter abundance, and drives the late-time dark-energy dynamics. The selected sector contains dark-pion dark matter, whose finite density initially traps the axion away from its vacuum minimum. As the Universe expands and the dark-pion density redshifts away, the axion is released and rolls on the reheating-induced vacuum potential, generating an effective phantom crossing without tuned cancellations. We identify a viable parameter region that simultaneously reproduces the observed dark-matter relic abundance and dark-energy scale, satisfies cosmological and astrophysical constraints, and qualitatively reproduces the DESI preference for an evolving dark-energy equation of state.

We develop a framework in which Yukawa hierarchies arise from powers of fully anarchic spurions transforming in higher representations of the flavor symmetry group $SU(2)^{n_2}\times SU(3)^{n_3}$. The core mechanism is the progressive lifting of Yukawa ranks through successive outer products of composite doublets and triplets. We formulate the general construction in detail and build explicit models realizing it. We then investigate whether renormalizable scalar potentials for higher $SU(2)$ representations can dynamically generate anarchic spurions with non-vanishing composites. The framework predicts distinctive patterns in flavor-changing neutral currents and potentially observable stochastic gravitational-wave backgrounds.

We identify a novel next-to-leading order renormalization effect in the dimension-six SMEFT with direct phenomenological impact. The Higgs-Yukawa operator that modifies the top-Higgs coupling $\kappa_t$ induces a shift in the $ W $ mass at two-loop order through a large anomalous dimension, rendering electroweak precision observables a powerful indirect probe of $\kappa_t$. We show that this effect is essential for the consistent interpretation of data from future Tera-$Z$ and Giga-$W$ factories such as FCC-ee. The effect is realized in a simple renormalizable two-Higgs doublet model.

What flavour structure of $t$-channel thermal dark matter remains compatible with current flavour physics and direct detection bounds? We broadly chart the space of hypotheses using the framework of flavour symmetries and their breaking patterns. We then focus on scenarios in which the fermionic dark matter and its scalar mediator are flavour singlets, falling into the class of rank-1 flavour violation. For two representative benchmarks, quarkphilic ($q_L$) and leptophilic ($e_R$), we perform a comprehensive phenomenological analysis, fitting the relic abundance and examining the interplay among flavour observables, direct detection, and collider searches. Our results quantify the allowed deviations from flavour-symmetric limits and assess the discovery prospects in future flavour and direct detection experiments.

We determine how much TeV-scale new physics can deviate from flavor universality, $U(3)^5$, while respecting stringent bounds on flavor-changing neutral currents. The minimal continuous subgroup that must be approximately preserved is identified as $SU(2)_{q} \times U(1)_{X}$. With only a few symmetry-breaking spurions of $\mathcal{O}(10^{-2})$, all observed fermion hierarchies may be reproduced, offering a new perspective on the SM flavor puzzle. Remarkably, this framework provides structural flavor protection for generic TeV-scale new physics within the SMEFT, enlarging the space of collider-accessible scenarios beyond MFV and $U(2)^5$ and allowing for richer patterns of flavor violation.

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.