arXiv highlights

We propose a low-scale spontaneous leptogenesis scenario within the dynamical minimal scotogenic model for accommodating neutrino masses and inert scalar dark matter simultaneously. Thus, we dub the mechanism Spontaneous Scoto-leptogenesis. In this setup, a rolling Majoron arising from the global $U(1)_{B-L}$ symmetry breaking induces an effective chemical potential for the $B-L$ charge in the presence of $B-L$ violating interactions that allow for the efficient decays and inverse decays of right handed neutrinos (RHN), so it gives rise to the observed baryon asymmetry of the Universe through the electroweak sphaleron conversion. The mechanism becomes effective in the strong washout regime and successfully lowers the viable mass scale of the lightest RHN to the range of TeV scales, thereby making the thermal scotogenic leptogenesis with two hierarchical RHNs accessible to direct tests. We identify the roles of the $λ_5$ coupling for spontaneous leptogenesis and inert scalar dark matter through the efficient erasure of the inert scalar asymmetry. We also explore the regime for Majoron dark matter from the kinetic misalignment, showing that a multicomponent dark sector comprising the inert scalar and the Majoron can be realized in the model. The resulting framework provides a unified origin for low-scale baryogenesis, neutrino masses, and multicomponent dark sector, so it can be tested by complementary experimental probes through direct detection experiments, collider searches for inert scalars, and future detection of Majoron dark matter or dark radiation.

We present the first complete field-theoretic realization of the finite one-loop T4-3-i topology for Majorana neutrino mass. Here, T4-3-i denotes a one-loop realization of the Weinberg operator in which a fermion links the two external lepton--Higgs pairs. If this fermion is a Majorana singlet or triplet, the same interactions generate a tree-level type-I or type-III seesaw contribution, respectively, so that the loop is not the leading source of neutrino mass. This lower-order contribution is removed by taking the mediator to be a Dirac fermion $N$, placing lepton-number violation in a separate Majorana fermion $ψ$ inside the loop, and imposing an exact $Z_2$ symmetry that keeps the new scalars inert and stabilizes the lightest odd state. We classify the allowed electroweak charge assignments and study the minimal singlet-doublet realization, denoted T4-3-i-B1, which contains one Dirac fermion, one Majorana fermion, an inert scalar doublet, and an inert scalar singlet. The resulting rank-two neutrino mass matrix predicts one massless neutrino. We confront both normal and inverted neutrino-mass orderings with neutrino-oscillation and cosmological data, charged-lepton flavor violation, including $μ-e$ conversion, electroweak precision observables, $h\toγγ$, theoretical consistency conditions, the relic abundance, and direct-detection limits. Both fermionic and scalar dark matter are viable. The fermionic candidate has only a loop-induced Higgs coupling and consequently a strongly suppressed spin-independent scattering rate, whereas the scalar candidate couples through a tree-level Higgs portal and can lie above the neutrino floor while remaining compatible with current limits. In both cases, coannihilation with inert scalars is essential for reproducing the observed relic abundance.

We study the possibility of an inverse first-order electroweak phase transition (IFOEWPT) and observable gravitational waves (GW) in a radiative neutrino mass model of scotogenic type where singlet-doublet (SD) fermions, the lightest of whom is the dark matter (DM) candidate, generate the necessary seesaw at one-loop level. Considering the possibility of light neutrinos being Dirac for simplicity and additional detection prospects, we extend the standard model (SM) with two generations of $SU(2)_L$ singlet and doublet fermions, one singlet scalar, and three right-handed neutrinos (RHNs). While RHNs provide the right chiral parts of light Dirac neutrinos, the SD fermions and the scalar singlet facilitate the one-loop neutrino mass diagram. The neutral component of the lighter SD fermion, stabilized under a residual $Z_2$ symmetry plays the role of DM while the heavier SD fermions strongly couple to the Higgs leading to an IFOEWPT where the Universe undergoes two different first-order phase transition as it goes from the symmetric to the final broken Higgs phase. We constrain the parameter space from the requirements of generating the correct neutrino mass, DM relic as well as IFOEWPT while incorporating the existing constraints from different experiments. The final allowed parameter space of the model can be probed at collider, direct-detection, GW and cosmic microwave background (CMB) experiments in near future.

Newtrinos.jl is an open-source Julia package for performing global analyses of neutrino data. It provides a modular, three-layer architecture that separates physics models, experiment descriptions, and statistical inference into independent modules. This allows researchers to freely combine experiments and test them against a variety of theoretical models. New experiments and physics models can be added without modifying core code. Full statistical forward models including all relevant systematic uncertainties are implemented for each experimental dataset, defining both the likelihood and the data-generating process and enabling modern statistical inference workflows. The framework is composable, making it straightforward to construct joint likelihoods over multiple datasets. Physics and nuisance parameters can be merged, correlated, or decorrelated across experiments to ensure consistency in the joint fit. The package supports Frequentist and Bayesian inference and is parallelizable across CPU threads or distributed workers. Written entirely in Julia, all models are automatically differentiable, enabling exact gradient computation.

Convolution identities and recursive formulas have long played a role in the theory of holomorphic modular forms and their applications. These have served both as striking formulas and as fundamentally useful tools for applications to combinatorics. Recently, there has been renewed interest in examples arising from non-holomorphic modular forms. These include the famous Hurwitz-Kronecker class number relations dating to 1885, and groundbreaking work of Imamoğlu, Raum, and Richter from 2014. Imamoğlu, Raum, and Richter developed a theory of holomorphic projection for products of (vector-valued) harmonic Maass forms and holomorphic modular forms to produce many such formulas. This was related shortly thereafter by Duncan, Griffin, and Ono to replicable-type functions in the sense of Conway and Norton, and such recursions played a key role in their proof of the Umbral Moonshine Conjecture. Here, we develop new results on holomorphic projections of such functions which is more convenient for many natural cases. Imamoğlu, Raum, and Richter's choice corresponds to the case in which the generalized Pell equation $m^2 - Dn^2 = N$ has a square value for $D$, which has only finitely many solutions for a given value of $N$. Our main results cover the cases of general $D$, in particular those for which the Pell equation has infinitely many solutions. As an application, we resolve a recent conjecture of the second author. More generally, our approach yields 18 convolution identities for mock theta functions, which we boil down to 5 identities that can directly be used to prove the others. In the appendices, we also show how these identities can be proven by more direct $q$-series methods; however, the key utility of the holomorphic projection formulas is that they give a tool to automatically discover and verify such formulas.

In 1972, M. Sato proposed an approach to proving modularity of forms like Thetanullwerte by characterizing them via certain differential operators of infinite order (DOI) in the modular variable(s) alone. A DOI is an infinite series in derivatives decreasing so fast that it acts on holomorphic functions by a sheaf morphism. This approach was developed by several authors including Kashiwara, Kawai, Takei and Yoshida. We give an interpretation of this approach using supersymmetry which provides a natural source of DOIs: the naive exponential of any odd supersymmetry generator is a DOI. The case of the Riemann theta function of genus n is governed by the supergroup OSp(1|2n) (and its metaplectic cover) acting on a natural super-thickening of the Siegel plane. For n=2 this is the 3-dimensional N=1 superconformal group and the structure at hand is precisely the free massless scalar supermultiplet (combining the Laplace and Dirac equations). For n>2 we get a super-extension of the generalized conformal structure existing on the Lagrangian Grassmannian as on any Hermitian symmetric space. An additional interesting feature here is that the odd supersymmetry generators acting ``on-shell'' (i.e., in the space of solutions of the equations of motion) satisfy even-style Heisenberg commutation relations. These equations of motion upgrade to a complex of differential operators corresponding to a natural BGG-type resolution of the super-Weil representation of osp(1|2n).

Computing neutrino oscillation probabilities is a solved problem; computing their derivatives is not. We present MANGO (MANGO: A Neutrino Gradient Oscillator), a composable oscillation engine in which every computed quantity is differentiable with respect to all inputs, including propagation geometry, detector depth, and individual Earth-shell densities. None of these quantities appear in traditional analytic probability formulas. The engine supports vacuum, constant-density, layered-PREM, arbitrary-profile, and adiabatic solar propagation, alongside front-ends for non-standard interactions, 3+N sterile states, decoherence, and non-unitary mixing. Because reverse-mode cost depends on output rather than input dimension, evaluating sensitivities incurs a constant 2.5-3x forward-pass overhead. As a result, calculating sensitivities for all 369 density, electron-fraction, and shell-radius parameters of a layered Earth costs no more than the 6 standard oscillation parameters. By maintaining exact sensitivity signals, MANGO allows gradients to flow continuously past the probability stage and through detector response, event weighting, binning, and likelihoods. We demonstrate this on a stylized Earth-tomography analysis. In a single pass, MANGO computes the marginalized uncertainty on a six-zone radial density model and, by differentiating through the inverse Fisher matrix, evaluates its sensitivity with respect to detector angular resolution. This provides an experimental-design metric unreachable using traditional analytic probability formulas. Three-flavor and layered-Earth probabilities match external benchmarks (OscProb, NuFast-Earth) to within 10^-9 to 10^-5, while all forward models, BSM limits, and differentiation paths are verified against exact analytic solutions and finite differences.

The jets of blazar active galactic nuclei (AGN) are promising sites of hadron acceleration and subsequent neutrino production, owing to their extreme intrinsic power and high radiation density. Potential associations of IceCube neutrinos with blazars displaying delayed radio flares, such as TXS~0506+056 and PKS~1424+240, may support this scenario. However, the mechanisms and location of particle acceleration in the jet remain unclear. The 2017 IceCube event associated with TXS 0506+056 was concurrent with the initial peak of a flare in gamma rays, followed by a longer flare at radio frequencies peaking three years later. State-of-the-art single-zone radiative source models focus on the compact high-energy-emitting region, and thus fail to describe this subsequent radio enhancement. In this work, we model the time-domain multi-frequency evolution of TXS 0506+056 by considering electron emission along the physically extended jet. We couple a numerical particle interaction framework with a dynamic description of the temporal and spatial jet evolution down to the parsec scale. We fit the model to multi-wavelength data, including multi-frequency radio light curves. The results suggest that the parsec-scale jet meets a population of older, cooled electrons near the edge of the observable radio core, establishing a causal relation between the initial high-energy emission and trailing radio activity. This spatially and temporally resolved modeling approach can offer new insights into the physical conditions along the jet of flaring neutrino candidate blazars.