08 September 2026

Much of the literature on neutrinoless double beta ($0νββ$) decay with light new-physics mediators focuses on invisible missing energy. We investigate the scenario in which a massive Majoron-like particle $φ$ is produced on-shell during $0νββ$ decay and subsequently decays into visible final states after travelling a macroscopic distance. Specifically, we analyze the displaced energy deposition from $φ$ decays into a photon pair ($γγ$), a photon and a dark photon ($γγ_D$) and an electron-positron pair ($e^+e^-$). We demonstrate that the displaced decays modify the expected visible energy spectra and provide novel, distinct experimental signatures at current and upcoming $0νββ$ experiments, with the promise of improving the sensitivity of the standard invisible Majoron searches in $0νββ$ decay by more than two orders of magnitude. The relevant effective couplings can naturally arise in well-motivated ultraviolet-complete scenarios that conventional $0νββ$ decay searches cannot probe.

The neutrino mass ordering remains unresolved because long-baseline oscillation measurements are entangled with the unknown CP phase $δ_{CP}$; a collider probe free of this degeneracy would provide a qualitatively different, complementary test. We show that when the long-lived charged particle producing a displaced-lepton signal at the High-Luminosity LHC is also the mediator responsible for Majorana neutrino masses---the \textit{shared-coupling condition}---the Casas--Ibarra parametrization determines the lepton flavor ratio $N_e/N_μ$ of time-delayed leptons in terms of Pontecorvo--Maki--Nakagawa--Sakata (PMNS) mixing parameters alone. Within the resulting \textit{shared-coupling class} of models the ratio is fixed by oscillation data, independent of all beyond-Standard-Model mass and coupling parameters up to calculable corrections bounded by charged-lepton-flavor-violation data, yielding $N_e/N_μ= 0.140$ for the Normal and $2.11$ for the Inverted Hierarchy---a separation of more than an order of magnitude between the two predictions. This prediction holds identically across the Scotogenic model, the Type-III seesaw, the inverse and linear seesaw, and lepton-portal dark matter, and is stable against oscillation-parameter uncertainties and detector-efficiency variations, which cancel in the ratio. A single efficiency-corrected decision criterion identifies the hierarchy, and explicit signal-yield estimates combined with an exact Poisson test show that $\mathcal{O}(25)$ displaced-lepton events suffice for a $3σ$ discrimination with the timing infrastructure already under construction at CMS and ATLAS---so that a positive long-lived-particle signal would simultaneously resolve the mass ordering, with no dependence on $δ_{CP}$.

The existence of right-handed (RH) neutrinos is strongly motivated by the observation of small neutrino masses and as a means to shed light on the origin of parity violation in the Standard Model (SM). Experimental searches for the corresponding mass eigenstates, referred to as heavy neutral leptons (HNLs), have been carried out in a variety of experiments and within different HNL models. In the current work we use the SM effective field theory with added RH neutrinos, known as $ν$SMEFT, to study GeV-scale HNL production in $e^+e^-$ collisions at the Belle~II experiment. We focus on leptonic decays of long-lived HNLs that produce a displaced vertex in the Belle~II detector. Accounting for detection efficiency and backgrounds, we estimate the sensitivity of Belle~II to the new-physics scale of four-fermion, Higgs-current, and dipole operators in $ν$SMEFT. We find that for most operators, the search we propose probes large regions of parameter space that are not excluded by other searches.

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.

We determine the gauge-invariant identity, mass scale and ultraviolet stability of the dark matter candidate arising from \(G(2)\to SU(3)_C\) in the exceptional \(G(2)\!-\!E_6\!-\!E_7\) construction. The broken \(G(2)\) sector contains odd \(1^{+-}\) and \(0^{--}\) channels, whereas the scalar \(0^{++}\sim X\bar X\) state is even and unprotected. For \(m_X\simeq5.7\times10^{13}\,\mathrm{GeV}\), weak-binding reference masses are \(M_{2X}\simeq1.14\times10^{14}\,\mathrm{GeV}\) and \(M_{3X}\simeq1.71\times10^{14}\,\mathrm{GeV}\), while the exact pole masses remain nonperturbative. Gauge-invariant Fröhlich--Morchio--Strocchi (FMS) operators, Hall--Post bounds, \(Y\)-junction arguments and the pure-\(SU(3)\) glue spectrum favor \(1^{+-}\) in their controlled regimes without excluding a deeply bound \(0^{--}\) state. We then test whether this dark grading survives the full chiral exceptional embedding. An on-shell analysis finds no independent purely dark odd operator through dimension seven: the first nonvanishing basis appears at dimension nine. So the minimal one-copy exceptional embedding does not provide an exact ultraviolet dark \(G\)-parity. Moving the dark Higgs from the common \(\mathbf{1463}_H\) parent to a separated \(\mathbf{1539}_H\) removes the scalar-parent obstruction and the relevant dimension-nine exceptional parents vanish on the selected pure-dark component in the undressed limit. A genuinely gauged or geometric \(\mathbb Z_{2,D}\) would therefore leave a bosonic parity after dark Higgsing. Its extension to the mirror-free theory nevertheless fails because the required \(G(2)\) conjugation also conjugates color, \(\mathbf3_C\leftrightarrow\bar{\mathbf3}_C\). The remaining obstruction to exact dark matter stability is therefore ultraviolet and chiral, rather than low-energy or purely scalar.

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 introduce a new method for studying mod-$\ell$ congruences between eigenforms through the modular representation theory of $\mathrm{PGL}_2(\mathbb{F}_p)$. When $p\equiv \pm 1 \pmod{\ell}$, we use this theory to construct and describe extra structures on spaces of modular forms with $Γ_0(p^2)$-level at $p$ and a fixed mod-$\ell$ Galois representation. The structural results we obtain can be viewed as a refinement of classical level-raising theorems since they not only allow us to prove the existence of congruences, but also to count the number of such congruences. Our methods work equally well in the residually irreducible and residually reducible cases, allowing us to prove several new instances of congruences between Eisenstein series and cuspforms (as well as independently rederiving classical results of Mazur and more recent results of Lang--Wake). Notably, our approach proves these results without computing constant terms of Eisenstein series, without Galois deformation theory and $R=\mathbb{T}$ theorems, and without the Jacquet--Langlands correspondence.

Sterile neutrinos are well-motivated dark matter candidates, but their conventional production through active-sterile mixing is tightly constrained by X-ray searches and structure-formation observations. We propose a distinct production mechanism operating entirely within a sterile sector: two sterile neutrinos, $N_1$ and $N_2$, coupled to a singlet scalar $φ$, with $N_1$ the dark matter candidate and $N_2$ held in equilibrium through frequent scattering induced by its scalar interaction. Thermal self-energies induced by the $N_2$ and $φ$ backgrounds generate both a temperature-dependent mass splitting and an off-diagonal mixing between $N_1$ and $N_2$. As the Universe cools, the in-medium levels can undergo a level crossing, leading to resonantly enhanced conversion of the thermal $N_2$ population into $N_1$. We formulate the conversion using a density-matrix kinetic equation that consistently incorporates coherent $N_1$-$N_2$ conversion, collisional decoherence, and thermal repopulation of $N_2$. For a narrow resonance, the integrated conversion probability admits a simple analytic form that coincides with the Landau-Zener result, despite the underlying collisionally damped dynamics. In the weak-conversion regime relevant for freeze-in, this correspondence provides a robust analytic description of the resonant production. We derive the resulting dark matter abundance and identify the conditions for cosmological stability of $N_1$ and for resonant conversion to dominate over direct scattering and decay production. The resulting relic abundance scales as $Y_1\propto g_{12}^2 g_{22}M_{\rm Pl}/m_1$, making the dark matter energy density approximately independent of $m_1$. This mechanism provides a new route to sterile-neutrino dark matter that does not require appreciable active-sterile mixing.

We study the stability of collective neutrino oscillations using a distributional approach motivated by the statistical mechanics of Kuramoto synchronization. Treating the ensemble of neutrino flavor polarization vectors in the thermodynamic limit $N\to\infty$, we derive an exact nonlinear Fokker--Planck (continuity) equation for the one-body distribution $F(\vec{\mathbf{S}},ω,t)$ on the flavor sphere. This equation admits a two-parameter family of azimuthally symmetric stationary solutions, whose stability we analyze by linearizing around them. The resulting eigenvalue condition determines the growth or decay rate of small perturbations from \emph{any} initial distribution -- not merely from a state close to full flavor coherence -- thereby going significantly beyond the conventional linear stability analysis of collective modes. In special limits the condition reproduces known synchronization thresholds in the two-beam model, providing a non-trivial check of the framework. We present analytical results for the eigenvalue equation and explore stability phase diagrams for physically relevant frequency distributions.

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.

Large-volume neutrino telescopes infer neutrino properties from Cherenkov light, but simulating the transport of billions of photons through highly scattering ice or water is computationally costly. We introduce candela, a differentiable SIREN neural field that learns the photon Green's function of the IceCube Neutrino Observatory, a cubic-kilometer detector embedded in Antarctic glacial ice. Given a point-like energy deposit and sensor, it predicts the expected photon yield and full arrival-time distribution at the sensor. Complete events are simulated by decomposing charged-particle energy deposits into point-like sources and superposing their predicted sensor responses. Trained on Monte-Carlo simulations, candela generates events $50$--$100\times$ faster than existing methods, with cost scaling only weakly with neutrino energy. It keeps median yields within $2\%$ of the MC expectation and timing distributions at the MC statistical floor across six photon-count decades. The model also provides end-to-end gradients with respect to event parameters and opens a path toward optimizing scattering-medium properties, which often dominate systematic uncertainties in neutrino telescopes.

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.

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. [...]