04 September 2026

We investigate the dark matter (DM) phenomenology and subsequent collider signatures of a dark leptoquark (LQ) model containing dark vector-like quarks (VLQs) and a scalar singlet. The dark LQs and VLQs participate in the radiative generation of Majorana neutrino masses at one loop. Since the coloured LQs and VLQs cannot serve as viable DM candidates, a $\mathbb{Z}_2$-odd singlet scalar is introduced as the DM candidate. The $\mathbb{Z}_2$-odd nature of the LQs forbids their conventional decays into a quark and a lepton, allowing them to evade the standard LHC constraints that apply to visible LQ signatures. This framework therefore offers the distinctive possibility of sub-TeV dark LQs coexisting with TeV-scale dark VLQs. These sub-TeV dark LQs help in achieving the observed relic abundance of the singlet through co-annihilation. We analyse the resulting DM phenomenology and assess the prospects for probing this scenario at a future muon collider.

The LUX-ZEPLIN (LZ) experiment has reported one nuclear recoil event reconstructed at $E_R=248\pm23_{\rm stat}\pm23_{\rm sys}$\,keV in a search extending to $E_R\simeq270$\,keV. We investigate an inelastic electroweak (EW) doublet interpretation in which spontaneous Peccei--Quinn (PQ) breaking leaves a residual parity that stabilizes the lighter neutral state and generates the Majorana splitting. A PQ-charged singlet fermion acquires its Majorana mass from the PQ-breaking vacuum expectation value and, after being integrated out, induces the dimension-five operator that splits a vectorlike EW doublet. A minimal KSVZ colored sector supplies the QCD anomaly. For a representative PQ-breaking scale $v_S=4.4\times10^{11}$\,GeV and Majorana mass $M_N\simeq50$\,TeV, the relation $M_N=y_Sv_S/\sqrt{2}$ gives $y_S\simeq1.6\times10^{-7}$, while the splitting relevant for LZ requires a Higgs--doublet Yukawa coupling $y\simeq0.023$. In a standard thermal history, the EW doublet constitutes only a subcomponent of the dark matter. A rate estimate probing the high velocity tail gives representative benchmarks with $M_D\simeq380$--$420$\,GeV, $\dchi\simeq323$--$330$\,keV, and $ξ_χ\simeq0.12$--$0.15$ yielding an order-one LZ event count. The remaining abundance is supplied by the QCD axion through vacuum misalignment for suitable $v_S$ and initial angle. The excited state has a radiative lifetime of order $3\times10^{-2}$\,s and a decay length of order $20$\,km, leaving the LZ topology as a single nuclear recoil while enabling a complementary luminous signal after terrestrial upscattering.

We study the quark sector of a model with three Higgs electroweak doublets, complemented with a modular $S_3$ symmetry. We show that a proper assignment of the quark and Higgs fields in $S_3$ and their modular weights allows to write a mass matrix with a phenomenologically viable texture. Moreover, by considering the conditions on the Higgs VEVs derived from the minimization of the scalar potential together with evaluation of the Yukawa couplings at the fixed point $τ=i$, leads to a significant reduction of the free parameters. We present two setups, one with three effective parameters, which is overly constrained, and one with four effective parameters, where the $V_{CKM}$ matrix can be fitted precisely.

We investigate the geometry of viable Froggatt--Nielsen-like flavor textures in a controlled toy landscape. In this first texture-level analysis, each point is represented by the eighteen integer exponents entering the up- and down-type Yukawa matrices, without imposing the additional charge-factorization constraints of specific Froggatt--Nielsen models. Viability is imposed through cuts on quark mass ratios and selected CKM observables. We construct four benchmark ensembles, ranging from masses-only constraints to the inclusion of the full set of CKM observables considered in this work, and study the resulting point clouds in the raw exponent space. Principal-component analysis shows no evidence for strong linear compression: in all benchmarks, fifteen principal components are required to account for 90% of the variance. Nearest-neighbour intrinsic-dimensionality diagnostics, including TwoNN and Levina--Bickel estimators, support the same qualitative conclusion, yielding high effective dimensions of order 10-12. These results do not rule out hidden flavor-theory geometry in other coordinates; rather, they suggest that raw Froggatt--Nielsen exponents may not provide natural coordinates for revealing such a geometry.

In this paper, we show that $\operatorname{SL}_2(\mathbb{F}_{13})$ and $\operatorname{SL}_2(\mathbb{F}_{19})$ are Galois groups of totally real extensions of $\mathbb{Q}$. For each of these primes $\ell$, we find a polynomial of degree $\ell+1$ whose splitting field has Galois group $\operatorname{PSL}_2(\mathbb{F}_\ell)$. These fields satisfy Böge's criterion and the associated central embedding problem has a proper solution with Galois group $\operatorname{SL}_2(\mathbb{F}_\ell)$. One can choose the resulting fields totally real via a quadratic twist. The degree $14$ polynomial is found through a genus one Hurwitz family of degree 14 covers. The degree 20 polynomial is found using Yang's modular equations for the Shimura curve $X_6^*(1)$.

We study the 2-division of the Klein-Vélu elliptic normal septic. Its three non-zero 2-torsion points give rise to an explicit cubic equation over the function field of $X(7)$. We identify the three roots of this cubic with modular functions expressed in terms of septic theta functions at $τ/2,τ$, and $2τ$, and show that its splitting field is precisely the function field of $X(14)$. This gives an explicit link between the 2-division geometry of the Klein-Vélu septic and the passage from full level 7 to full level $14$. Several intermediate modular function fields in the resulting $S_3$-extension are also described.

The structure of non-invertible symmetries in 2D CFT is closely tied to the algebra of preserved holomorphic fields, its representation theory, and its embedding in the full chiral algebra of the CFT. Unfortunately, finding new embeddings of a chiral algebra into another is a difficult mathematical problem, and one of the major obstacles in the pursue of new and exotic categories of non-invertible symmetries. In this work, we describe a simple general technique that leads to a number of new non-trivial results in this direction: (1) For the holomorphic Monster CFT $V^\natural$, we show that for every `Fricke' non-anomalous Monster element of order $N$, there is an embedding of the parafermion algebra $\frac{su(2)_N}{u(1)}$ in $V^\natural$, we compute the characters of its commutant, and describe the topological defects preserving these subalgebras. (2) We provide an easy-to-check sufficient condition for a holomorphic VOA $V$ to be self-orbifold under a cyclic group of (invertible) symmetries, and determine the associated duality defect. (3) We find several new topological defects in CFTs arising from heterotic strings on $T^4$. (4) We prove a number of VOA embeddings and topological defects in the Leech lattice CFT, in Schellekens theories, and other CFTs of various central charges, and suggest several generalizations of our methods.

New physics generating four-quark interactions can be difficult to detect at the LHC, especially if it does not couple to first generation quarks. We investigate the possible role of such interactions in generating measurable deviations in Higgs-quark couplings. We find important constraints from flavour physics and top-pair production, but show that Higgs-charm and Higgs-bottom couplings remain the most sensitive LHC observables to some four-quark operators involving scalar currents. At FCC-ee, more operators and flavour structures can be tested. We further investigate simple single-particle models that can generate these interactions, including a second Higgs doublet, and scalar and vector diquarks. We find that in some cases, including new scalars most strongly coupled to the third generation of quarks, deviations in Yukawa couplings could offer the first signs of new physics generating four-quark interactions.

The recent observation of an isolated nuclear recoil at $248\pm 23\pm 23$ keV energy by LUX-ZEPLIN (LZ) experiment has motivated the community to look for a new physics explanation, as the Standard model background estimation fails to accomodate that. Most of the existing literature hitherto considers a galactic halo dark matter with a heavier partner. In this work, we traverse the alternate route of atmospheric neutrino ($ν$) up-scattering, thus producing a massive beyond standard model (BSM) particle $χ$. The kinematic requirement of such a scattering poses a cut off in the lower recoil energies providing an explanation of the unique isolated event at such a higher recoil energy. Such up-scattering with the nucleons ($\nuc$), $ν\nuc\to χ\nuc$ can be naturally realized in sterile neutrino models, though we keep our analysis generic without specifying $χ$. We identify the region of parameter space that can produce such an isolated event assuming a scalar mediator with mass $m_φ$ and coupling $y_{χ,q}$. For example, with $m_χ\sim1$ GeV, and $\sqrt{y_χy_q}/m_φ=2 \times 10^{-2}$ GeV$^{-1}$ can satisfy such an excess of events while remaining allowed by other existing constraints as well.

The high-recoil event reported by LUX--ZEPLIN motivates a TeV Higgsino with a sub-MeV neutral-state splitting. Away from cancellations, such a small gap in the MSSM points to electroweak-gaugino masses of order $10^7\,\mathrm{GeV}$, far above the Higgsino mass. We show that the non-universal boundary condition $M_1^G/M_2^G=-3/5$ at the $\mathrm{SU}(5)$ GUT scale cancels the leading bino and wino contributions and is preserved by homogeneous one-loop evolution down to the Higgsino scale. The remaining finite-gaugino terms admit a controlled tree-level solution with a wino mass near $120\TeV$ for a $350\keV$ gap, a $1.091\TeV$ Higgsino and $\tanβ=10$. We identify mixed $\mathrm{SU}(5)$ representations that realize the required gaugino ratio and examine the radiative sensitivity and spectrum consistency of this construction. Because the inelastic $Z$ coupling remains essentially unsuppressed, a full-density thermal Higgsino is still subject to the published solar-capture bounds under their astrophysical and transport assumptions.

The magnetic Penrose process (MPP) is one of the most efficient mechanisms for extracting rotational energy from a magnetized Kerr black hole (BH), enabling charged particles to reach very-high energies. We investigate this process in Sagittarius A* (Sgr A*), the supermassive BH at the Galactic center (GC), focusing on its ultra-high-efficiency regime, in which neutrons undergo beta decay inside the BH ergosphere. As a key novelty, we compute the neutron production spectrum in the accretion flow directly from the nuclear reaction kinematics and follow neutron trajectories in the Kerr spacetime to determine the population that reaches the ergosphere and undergoes the MPP. From this population, we derive the spectrum of accelerated protons and show that Sgr A* can accelerate them up to PeV energies, strengthening its interpretation as a candidate Galactic PeVatron. We further compute the gamma-ray and neutrino emission produced through hadronic interactions of the escaping protons in the Central Molecular Zone. The predicted gamma-ray fluxes exhibit distinctive spectral features that could provide an observational signature of the MPP and may constitute a non-negligible contribution to the very-high-energy emission detected by H.E.S.S. and HAWC. The associated neutrino fluxes remain below the diffuse Galactic component inferred by IceCube, but may still contribute to the high-energy emission from the GC. Remarkably, the predicted signals lie within the projected sensitivity of SWGO for all scenarios considered here and, for some models, only a factor of a few below the nominal CTAO sensitivity, while KM3NeT/ARCA and IceCube-Gen2 will provide complementary tests. Our results establish the MPP as an observable mechanism for extracting BH rotational energy, providing a direct connection between horizon-scale physics and multimessenger observations that can be extended to other magnetized BHs.

A stacking search for high-energy astrophysical neutrino emission is presented using three candidate source populations: ultra-luminous infrared galaxies and two categories of blazars, specifically high-synchrotron-peaked BL Lacs and extreme blazars. The analysis is based on 336 days of data from the Astroparticle Research with Cosmics in the Abyss component of the KM3NeT research infrastructure (KM3NeT/ARCA), collected with detector configurations comprising 19-21 detection units, yielding 1544 selected track-like neutrino candidates. The sample of ultra-luminous infrared galaxies consists of 75 sources, for which conventional power-law spectra are assumed in modelling their signal emission. The blazar samples comprise 232 high-synchrotron-peaked BL Lac objects and 88 extreme synchrotron-peaked emitters, respectively. Their expected neutrino fluxes are obtained from numerical tools constrained by multi-wavelength observational data. No statistically significant excess above the atmospheric background is found for the three catalogues and 90% confidence level upper limits are set.

The Neutrino Observatory in the Nanhai (NEON) is a proposed deep-sea neutrino telescope deployed in the South China Sea. Accurate reconstruction of shower-like events is crucial for neutrino energy measurements and multi-messenger astronomy, yet it poses significant challenges due to seawater optical attenuation, irregular detector geometry, and substantial $^{40}\mathrm{K}$ ambient background. In this work, we present the first comprehensive reconstruction framework for shower-like events in NEON, encompassing both a physics-driven maximum likelihood estimation (MLE) method and a data-driven Graph Neural Network (GNN). The traditional MLE framework integrates spatial-isochronic hit selection, vertex reconstruction via time-residual M-estimator minimization, and decoupled directional and energy estimation based on pre-computed photon distribution tables. Physical calibrations, including PMT angular acceptance, hit-level time slewing corrections, and an effective line-source shower extension, are incorporated into the likelihood formulation. In parallel, a two-stage GNN is developed to capture intra-DOM PMT correlations and distance-weighted inter-DOM topological patterns. Simulation studies show that the MLE method achieves an overall median angular resolution of $4.19^\circ$ and an energy resolution of 25\%-37\% over 1 TeV to 1 PeV with negligible systematic bias. The GNN further improves reconstruction fidelity in the low-to-intermediate energy regime, achieving a median angular resolution of $1.8^\circ$ at 30 TeV and an energy resolution of $\sim$ 20\% between 40 and 300 TeV. Based on these reconstruction performances, the effective area and point-source discovery potential of NEON are evaluated. This framework establishes an essential reconstruction benchmark for NEON and provides practical methodologies for future next-generation deep-sea neutrino telescopes.

We study the shape of three-dimensional and projected dark-matter halo profiles extracted from cosmological $N$-body simulations in $Λ$CDM and non-standard cosmologies, using the \texttt{DUSTGRAIN-PF} and \texttt{DEMNUni} suites. The models considered include massive neutrinos, $f(\mathcal{R})$ gravity, and dynamical dark energy. By comparing density, mass, velocity-dispersion, and excess-surface-density profiles up to $5\,r_{500{\rm c}}$, we quantify the differential imprint of non-standard physics on halo structure in view of \textit{Euclid} cluster WL studies. Our main analysis is performed at $z=1.1$, a high-redshift regime where the weak-lensing signal-to-noise starts to degrade, providing a conservative stress test for detectability; for \texttt{DUSTGRAIN-PF} we additionally analyse $z=0.5$ and $z=0.3$ snapshots. In low-mass haloes ($M_{\rm 200c}<7\times10^{13}\,M_\odot$), $f(\mathcal{R})$ gravity produces deviations of order $10\,\%$ in projected and three-dimensional profiles, especially in the outskirts where screening is less efficient. Massive neutrinos partially reduce this signal, reflecting the competition between free streaming and fifth-force-enhanced growth. Dynamical dark energy and massive-neutrino cosmologies generally induce smaller, few-percent deviations, with the largest effects again found in low-mass haloes and at large radii. Under simplified assumptions for \Euclid WL, detecting such profile differences at $z=1.1$ requires stacks of $\sim10^5$ haloes, while a few thousands haloes may be sufficient at $z\lesssim0.5$. This further calls for the need of integrating such precise modelling of non-standard effects -- along with other observational effects -- in any likelihood involving \textit{Euclid} WL masses to avoid non-negligible systematic biases. Concentration--mass relations show weaker cosmology dependence, typically at the $\sim5\,\%$ level. [...]

Motivated by the question of whether the internal scales of a compactification can be parametrically decoupled from the external curvature scale, and by the possibility of probing such vacua holographically, we construct the first AdS$_2$ flux vacua with parametric scale separation. We compactify type II string theory on a $G_2$ structure orbifold times a circle in the presence of smeared spacetime-filling O1/O5-planes or O4/O8-planes, together with NSNS and RR fluxes. We derive the two-dimensional dilaton-gravity effective theory and exhibit families of vacua in which unbounded $F_5$ and $H_7$ fluxes provide parametric control in type IIB, while unbounded $F_4$, $F_8$, and $H_7$ fluxes provide parametric control in type IIA. For large flux quanta, the string coupling becomes parametrically weak, all internal bulk radii become parametrically large in string units, and the Kaluza--Klein scale separates from the $\mathrm{AdS}_2$ curvature scale. We analyze the ten-dimensional Killing-spinor equations and identify parametric branches preserving $\mathcal N=(1,1)$ supersymmetry in two dimensions. We explain how our geometrically scale-separated AdS$_2$ vacua are compatible with a recent no-go theorem for scale separation in theories with extended supersymmetry. Finally, we discuss various T-dualities leading to other type IIB and type IIA compactifications on $G_2$ structure spaces times a circle and $SU(3)$ structure spaces times a two-torus.