10 September 2026

The observation of neutrinoless quadruple beta decay (0$ν$4$β$) in the absence of neutrinoless double beta decay (0$ν$2$β$) has been argued to provide a strong indication that neutrinos are Dirac particles. We report a search for 0$ν$4$β$ decay of $^{136}\text{Xe}$ using a total $^{136}\text{Xe}$ exposure of 148.4 kg$\cdot$yr, collected during the commissioning and the first science runs of the PandaX-4T experiment. No significant excess of events over the background is observed. A lower limit on the 0$ν$4$β$ decay half-life of $^{136}\text{Xe}$ is set at 6.01 x $10^{24}$ yr at the 90% confidence level. This result establishes the most stringent constraint on this process in xenon, demonstrating the unique capability of the PandaX-4T detector in probing lepton number violation and shedding light on the fundamental nature of neutrinos.

The mass ratios of the quarks and charged leptons follow a simple pattern. The logarithmic generation steps come in a two to one ratio, a note to its octave, and the ordering is mirrored between the up-down and down-lepton comparisons. The pattern, read as charge counting on a $Z_N$ clock, is realized at level four and at no level that is not a multiple of four, which motivates modular level four and the finite group $S_4$, with the generations in the triplet at $T$ charges $(3,1,0)$ and the mirror in the sign singlet. The charged-lepton mass ratios lie on a theta-dressed lattice at $0.02\%$, which sets the base $\varepsilon=0.18664$, taken as $14/75$, and the harmonic modulus $τ=1.0685i$. Five postulates in the weight one-half theta constants, identified on the same data, reproduce the six quark masses from three lepton masses and the electroweak scale. Two more and one empirical relation for $|V_{td}|$ close the CKM matrix, giving $|V_{us}|=\sqrt{m_d/m_s}=0.2255$, $|V_{cb}|=0.04197$, $|V_{ub}|=0.003721$, and $δ=1.138$ against the measured $1.139\pm0.023$, with no continuous parameter. The unitarity triangle follows, with apex $(0.161,0.348)$ against the measured $(0.161\pm0.010,0.347\pm0.010)$, and $J=3.11\times10^{-5}$ against $(3.09\pm0.07)\times10^{-5}$. The same structure carries the neutrinos. A single theta insertion gives $\sinθ_{13}=θ_2(τ)m_2/m_3$, which holds at $0.7σ$ on the 207-day JUNO data, and the harmonic condition completes a normal-ordered spectrum with $m_1=0.25$~meV, $Σm_ν=0.0589$~eV, a CP-conserving phase $δ_{CP}=π$, and effective Majorana masses quantized at $1.3$ to $3.9$~meV. The ultraviolet completion belongs to the magnetized torus class, with Pati--Salam the natural gauge embedding.

We report a search for neutrino oscillations to sterile neutrinos in the NOvA detectors under a model with three active and one sterile neutrinos. This search simultaneously fits data in the two NOvA detectors and is the first from NOvA to use both neutrino- and antineutrino-mode beams, with exposures of $26.61\times10^{20}$ and $12.50\times10^{20}$ protons on target, respectively. There is no evidence for sterile neutrinos in the data and we are able to exclude regions of parameter space that were allowed by previous experiments, including most of the allowed region reported by IceCube.

We explore a radiative neutrino mass model based on the topology T4-3-i, which is a one-loop completion of the Weinberg operator. We focus on its T4-3-i-C1 realization, containing an inert scalar doublet, a real scalar triplet, a Majorana fermion triplet, and a Dirac singlet fermion. An exact $Z_2$ symmetry forbids the tree-level type-III term and stabilizes the lightest $Z_2$-odd particle, leaving the one-loop topology as the leading source of neutrino mass. The model accomodate a neutral {\it CP}-even scalar dark matter candidate and predicts a rank two neutrino mass matrix, and thus one neutrino is massless. A combined analysis incorporating theoretical and experimental constraints reveals viable solutions to both neutrino mass orderings, with the inverted ordering predicting larger values of $m_{ββ}$, $m_β$, and $\sum_i m_i$, thereby enhancing its testability through future beta-decay, neutrinoless double beta decay, and cosmological probes. Within the same viable parameter region, the observed dark matter relic abundance is accounted for by annihilation and coannihilation processes, while the electroweak triplet sector gives rise to prompt, displaced, or long-lived particle signatures, offering complementary collider probes to dark matter and low-energy searches.

The recent result by the LUX-ZEPLIN (LZ) experiment of a single nuclear-recoil event at $248\,\mathrm{keV}$ suggests an interpretation in terms of inelastic scattering between dark matter (DM) and the xenon target. The widely considered thermal Higgsino DM with $m_χ\sim$~TeV and mass splitting $δ\sim 350$~keV is essentially excluded as it would be captured efficiently by the Sun, with a resulting neutrino flux from its annihilation in excess of the IceCube limit, and expected recoils above the LZ nominal search window, where none were seen. However we argue that although these tensions apply to a Higgsino with constrained cross section, they need not apply to the broader set of inelastic candidates that alternative solutions to the hierarchy problem might suggest. We show that a new massive gauge boson, $Z'$ with a candidate DM sector and Majorana mass splitting of order $\sim 10^{-7}$ of the Dirac mass, evades current constraints. We propose an inelastic dark matter (iDM) candidate that can arise naturally in a Randall-Sundrum warped extra-dimensional model. The DM candidate involves a vector-like fermion confined to the TeV brane and a bulk field. The brane Lagrangian contains Dirac mass terms that are also naturally exponentially suppressed. The left-handed component of the bulk field has a Majorana mass with origin on the UV brane, while the interaction with Standard Model nucleons is mediated by a massive dark Kaluza-Klein (KK) gauge boson whose mass is also automatically in the right range. We propose a concrete model of thermal DM with $m_χ\sim$~TeV in an RS geometry with warp factor $πkR\simeq 31.7$ and the $Z'$ a KK mode with natural TeV-ish scale mass in which the ratio of neutrino to quark coupling is also natural, giving a mass splitting of $δ\sim 300$~keV, and show how it could explain the LZ signal while being consistent with existing constraints.

We investigate three flavor neutrino phenomena in an effective holonomy corrected Schwarzschild geometry. We derive the weak-deflection angle through second post-Minkowskian order, obtain the semiclassical phases along radial and nonradial trajectories, and formulate the two-image flavor probability by including magnifications, Fermat phases, and wave packet overlap. The cross path phase acquires a logarithmic holonomy contribution and can retain information about the absolute neutrino mass scale. We also characterize flavor mode correlations and trajectory-flavor entanglement through the balance among path predictability, interference visibility, and I-concurrence. Neutrino-antineutrino annihilation outside an effective neutrinosphere is examined, with holonomy entering the integrated power through the radial proper volume measure. For a solar mass lens and $10\,\mathrm{MeV}$ neutrinos, the numerical results show displaced oscillation fringes and a geometry dependent redistribution among the electron, muon, and tau channels. The electron-neutrino trajectory-flavor concurrence reaches approximately $0.23$, with an entropy near $0.10$ bit, while remaining weakly sensitive to the mass ordering in the selected configuration. By contrast, the annihilation power increases monotonically, reaching an increase of approximately $39.3\%$ relative to Schwarzschild spacetime (for a particular configuration, i.e., $λ=2$ and $M/R_ν=1/3$). Furthermore, at fixed source parameters and $M/R_ν=1/3$, an assumed maximum excess of $10\%$ in the integrated annihilation power relative to Schwarzschild yields the conditional bounds $a/(2M)\leq0.2879$ and $|λ|\leq0.6358$.

We develop an algebraic framework for the quasi-modularity of symmetric multiple $q$-zeta values. We identify natural classes of symmetric quasi-shuffles whose $q$-zeta values exhaust the algebra of level-one quasi-modular forms, and further classes whose $q$-zeta values are quasi-modular forms of finite level. We also obtain explicit symmetrization formulas and relate symmetric quasi-shuffles to symmetric and quasisymmetric functions.

We discuss orbifold compactifications of the type II string, where the orbifold combines a free action on a base manifold and the $(-1)^{\boldsymbol{F}_{\text{L}}}$ symmetry which acts by -1 on left-moving Ramond sectors. Such backgrounds can preserve minimal supersymmetry and lift to M-theory compactification on smooth unorientable manifolds.

Since neutrinos are quantum systems inherently, the precision with which oscillation parameters can be estimated ultimately depends on how much information about these parameters is encoded in the neutrino state and how efficiently that information can be extracted through measurement. In this work, we quantify how information encoded in reactor antineutrino states flows through the measurement process to the events observed at the detector, using quantum and classical Fisher information. We establish the information ladder for JUNO, revealing that the loss of precision across different information levels is strongly parameter dependent. We demonstrate that the JUNO configuration approaches the optimal statistical limit for the oscillation parameters of the solar sector, while information on $θ_{13}$ and $Δm_{31}^{2}$ is significantly degraded by the measurement strategy and detector effects. Despite this information loss, the remaining information is sufficient for JUNO to achieve sub-percent precision on $Δm_{31}^{2}$ within six years.

Recently, the LUX-ZEPLIN (LZ) Collaboration reported an isolated nuclear-recoil event at $248\pm 23_\mathrm{stat}\pm 23_\mathrm{syst}~\mathrm{keV_{nr}}$, in a region where the expected background is very small and conventional elastic dark matter (DM)-nucleus scattering cannot readily account for such a localized feature. We investigate whether LZ230616 could instead originate from coherent elastic neutrino-nucleus scattering (CE$ν$NS). We consider neutrino-nucleus interactions within and beyond the Standard Model, together with exotic neutrino fluxes from DM annihilation ($χχ\to ν\barν$) or decay ($χ\to ν\barν$) into neutrino pairs and from primordial black hole (PBH) evaporation. We show that kinematic considerations, the accompanying low energy recoil spectrum, and existing constraints exclude a viable interpretation of LZ230616 in terms of elastic neutrino-nucleus scattering for all scenarios considered.

We investigate whether cosmogenic gamma rays and neutrinos from ultra-high-energy cosmic rays (UHECRs) produced in hadronically active blazars can significantly contribute to the observed spectral energy distribution (SED), and examine the potential of the Cherenkov Telescope Array Observatory (CTAO) to detect and discriminate this component. For four nearest neutrino bright blazars modeled by Rodrigues (2024), specifically AP Librae, TXS 1700+685, PKS 2326$-$502, and PKS 2345$-$16, we constrain the UHECR luminosity by requiring that the total emission does not overshoot available multi-wavelength data, assuming acceleration in the optically thin large scale jet, propagate UHECRs through realistic Galactic and extragalactic magnetic fields, and forecast CTAO performance. We find that cosmogenic gamma rays contribute up to about 7.5% of the total gamma-ray emission at the highest energies ($10^{20}$ eV), and thus remain subdominant in the SED. In contrast, the associated neutrino emission, at approximately $10^{44}$ to $10^{46}$ erg s$^{-1}$, offers a robust propagation signature of hadronic acceleration. Our simulations of 50 hour CTAO exposures show that the observatory can accurately reconstruct the intrinsic gamma ray spectrum, enabling strong constraints on the hadronic origin and propagation of UHECRs. These results demonstrate the power of combining CTAO gamma-ray measurements with neutrino observations to probe blazar hadronic processes.

The spatial distribution of anomalies in extra dimensional theories on a slice of AdS leads to a puzzle where anomalies may not match across different geometries that are dual to various states of the same CFT. We argue that consistency of the anomaly across such geometries necessitates the addition of topological terms or other bulk fermions to the theory that flow any IR localized consistent anomaly into the ``UV" region of these geometries if one wishes to have such a dual interpretation.