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.

A discrete, anomaly-free $\mathbb Z_9$ gauge symmetry may persist to the deep infrared, exactly forbidding proton decay. This $\mathbb Z_9$ can emerge from Higgsing a lepton-flavour non-universal $U(1)_X$ that generates realistic neutrino masses and mixings through a high-scale seesaw and predicts an additional light Goldstone. Adding an anomaly-free chiral heavy-quark sector turns this mode into the QCD axion. The same selection rules that ban proton decay also forbid PQ-violating operators below a suitably high dimension, $d_{\rm PQ}\gtrsim10$, including operators involving the heavy quarks that radiatively match onto the scalar potential. We construct explicit models viable when PQ breaking occurs before or after inflation; in the latter case, avoiding stable heavy relics and eliminating the string-wall network tightly constrain the heavy-quark spectrum. We identify restricted regions of parameter space where thermal leptogenesis remains viable and, for $d_{\rm PQ}\geq13$, can coexist with a high-quality axion constituting all of the dark matter.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SU{\left(2\right)}^{{n}_{2}}\times SU{\left(3\right)}^{{n}_{3}}$$\end{document}. 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 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.