31 August 2026

We utilize renormalization group equations (RGEs) for neutrino oscillations in matter to decipher the structure of exact matter invariants. By combining the RGEs with the $S^{}_3$ permutation covariance under relabeling of the neutrino mass eigenstates, we recast all five algebraically independent matter invariants in the three-flavor framework as exact first integrals. Treating the matter potential as a matter spurion and imposing the cancellation conditions for the $1/\widetildeΔ_{ij}^{}$ poles in the RGEs, we further prove that the three-flavor framework contains only two independent monomial invariants, which can be related to the Naumov and Toshev relations. We then extend the analysis to the four-flavor framework, where we uncover a complete set of eleven algebraically independent matter invariants and prove that the rank-two electron--sterile spurion obstructs the common pole cancellation required for any nontrivial multiplicative monomial invariant.

We propose an anomaly-free and renormalizable axial $U_A(1)_{L_μ-L_τ}$ model and study its experimental signatures for $A'$ masses from the MeV scale to the TeV scale. The opposite charges of the left- and right-handed charged leptons forbid the usual muon and tau Yukawa interactions. Their masses are instead generated by a singlet scalar and heavy vector-like leptons through a universal-seesaw mechanism. We focus on heavy vector-like leptons, small light--heavy mixing, and $m_s\gtrsim10~\mathrm{GeV}$. In this limit, the observables considered here depend mainly on $(m_{A'},g_X)$, while the other model parameters are restricted by mixing and perturbativity. We confront this benchmark with current experimental searches. For neutrino trident production, our finite-$m_μ$ calculation shows that $A'$ modifies the axial weak coefficient, rather than the vector coefficient relevant to the usual $L_μ-L_τ$ model. The longitudinal mode enhances muon bremsstrahlung and gives a negative contribution to $(g-2)_μ$; the latter dominates over the scalar contribution in our benchmark. Combining these results with invisible meson decays and four-muon resonance searches, we summarize the phenomenological constraints in the $(m_{A'},g_X)$ plane. For $m_{A'}\gg m_μ$, vector and axial final-state-radiation rates become nearly identical, so the corresponding collider limits can be obtained by rate matching. At a future muon collider, the total rate alone does not fully resolve the interaction structure, whereas angular distributions, especially the forward--backward asymmetry in $μ^+μ^-\toτ^+τ^-$, retain direct sensitivity to chirality.

A proof is given that the six fixed points of the massless 1-loop renormalization group running of the CKM matrix in the Standard Model found previously at 1-loop are fixed points to all orders in perturbation theory. A previous proof required an extra assumption on the running which is eliminated in the proof presented here.

A space $\mathcal{L}_N^r$ of Drinfeld modules of rank $r \geq 1$ with level structure, or equivalently lattices of rank $r$ with level structure, is introduced, and its irreducible components and group actions on it are investigated. A metric is defined on this space, its completion $\overleftarrow{\mathcal{L}_{N}^{r}}$ is established and the aforementioned group actions are extended to the completion. A decomposition of the completion into multiple smaller spaces $\mathcal{L}_N^s$ is proven. Drinfeld modular forms are defined as homogeneous holomorphic functions on $\mathcal{L}_{N}^{r}$ which are continuous on the completion $\overleftarrow{\mathcal{L}_{N}^{r}}$, and the group actions above are extended to actions on the spaces of modular forms. Finally, the modular forms defined here are compared with those of Basson, Breuer, and Pink and with those of Gekeler, and it is shown that the cusp forms (those which are zero on the boundary) coincide.

The flavor structure of the Standard Model (SM) remains one of the most compelling questions in particle physics, with the third generation being particularly intriguing due to its significantly larger masses and comparatively less precisely measured properties. These features make third-generation flavor transitions particularly interesting in context of search for physics beyond the SM. In this work, we investigate flavor-violating transitions between the third and the first two generations, mediated by the neutral gauge bosons ($Z/γ$), within the framework of the SM Effective Field Theory (SMEFT), using dipole and Higgs-current operators. We determine the optimal sensitivities using the optimal observable technique (OOT) at different center-of-mass energies of the upcoming Future Circular Collider in the $e^+e^-$ mode (FCC-ee). We further derive complementary constraints on the relevant SMEFT operators from low-energy flavor-violating observables and heavy fermion decay channels. Our analysis also reveals characteristic interference patterns among the dipole contributions, which depend on the underlying flavor transition and exhibit distinct behavior between the $Z$ pole and higher-energy FCC-ee stages. The FCC-ee provides a complementary and direct probe of flavor-violating interactions at the electroweak scale, with the projections showing improved sensitivity for several interactions and comparable sensitivity to existing flavor constraints for several others. This highlights the importance of a systematic assessment across the different FCC-ee energy stages, which provides a comprehensive picture of its potential to explore flavor-violating phenomena and its complementarity with low-energy flavor experiments.

Embedded in the South Pole's glacial ice, IceCube detects neutrino-induced Cherenkov light using an array of digital optical modules equipped with single photomultiplier tubes (PMTs). The new extension installed in 2025/2026, the IceCube Upgrade, introduces densely instrumented multi-PMT optical modules within the existing infill array known as IceCube DeepCore. It is expected to enhance sensitivity in the GeV regime, with commissioning of the detector expected to be complete by the end of 2026. We present the projected sensitivities of the IceCube Upgrade for three key analyses: neutrino transient searches, steady emission from point sources such as NGC 1068, and diffuse emission from the Milky Way. These case studies represent direct extensions of current IceCube analyses. Using new Monte Carlo datasets, we demonstrate that the IceCube Upgrade achieves order-of-magnitude improvement in sensitivity at low energies ($\lesssim 10$ GeV) for time-dependent sources across short timescales. Conversely, for time-independent searches, the relative impact of the IceCube Upgrade's low-energy data is diluted by the decade-long accumulation of high-energy archival data. Nevertheless, we project significant improvements for soft-spectrum sources especially across the southern sky, driven by the IceCube Upgrade's superior background rejection capabilities. The improved sensitivity at low energies for both transient and steady sources will open up an expanded discovery window for IceCube in the GeV band over the next decade.

Neutral-current interactions of atmospheric neutrinos in large liquid scintillator detectors offer a new opportunity to study single-signal events (hereafter singles), characterized by a prompt energy deposition on the MeV-to-GeV scale and no identified delayed signal. In this work, we systematically investigate the model dependence of atmospheric-neutrino singles due to the primary neutrino-nucleus interaction, residual-nucleus de-excitation, and secondary interactions in the scintillator. Our results show that the dominant model dependence originates from the primary neutrino-nucleus interaction, especially for neutral-current processes on carbon, whereas de-excitation is essential for the singles selection yet leads to relatively small spectral variations among realistic models. Secondary-interaction effects are also subdominant overall. We further present the predicted event rates and prompt-energy spectra for neutral-current singles, along with the charged-current contribution. Separately, we estimate the low-energy contribution from elastic scattering of sub-\SI{100}{\MeV} atmospheric neutrinos on free protons. These results highlight the physics potential of current and future large liquid scintillator detectors, such as the Jiangmen Underground Neutrino Observatory, to study atmospheric-neutrino singles, probe neutrino-nucleus interaction models, and improve background estimates for rare-event searches.

The rare decays $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ are among the most precisely predicted flavor observables, enabling determinations of the CKM matrix and its CP-violating phase, as well as providing sensitivity to new physics at scales far beyond the reach of colliders. We propose a dedicated rare-kaon program at Fermilab, exploiting the high-intensity proton complex currently under construction for its neutrino programs and potential collider R&D. In this letter, we estimate the achievable kaon flux and project the sensitivity to the aforementioned kaon golden modes, as well as the reach on new dynamics in the UV with an EFT framework. Such a program could measure both modes with unprecedented precision, probe new physics up to $\mathcal{O}(100)$ TeV, and determine the unitarity triangle from kaon processes alone. All this can be achieved while sharing infrastructure with other frontier programs.

We investigate the neutrino flux from the Sun and Earth, as well as the heating of Jupiter and white dwarfs, induced by the annihilation of spin-$1/2$ dark matter particles captured through their electromagnetic interactions with nuclei. Using current data, we derive constraints on the electromagnetic moments and compare them with existing bounds from direct dark matter searches, laboratory experiments, and astrophysical observations. We find that celestial bodies provide leading constraints in several regions of parameter space: the Earth is particularly sensitive to millicharged dark matter, while massive white dwarfs provide powerful probes of the magnetic dipole moment, charge radius, and anapole moment in regions where direct searches lose sensitivity. We illustrate the implications of these constraints in simplified models of Dirac and Majorana dark matter with radiatively generated electromagnetic moments, as we discuss the complementarity between capture in celestial bodies and other dark matter searches.

Massive cryogenic calorimeters read out by transition-edge sensors (TES) can reach eV-scale baseline resolution, but the single-channel dc-SQUID readout conventionally used in rare-event searches, with one amplifier chain and several wires per detector, limits practical arrays to a few tens of channels. We propose to apply microwave SQUID multiplexing ($μ$MUX), developed for fast X-ray and neutrino-mass microcalorimeters, to massive BGO (Bi$_4$Ge$_3$O$_{12}$) calorimeters operated at $\simeq 20$~mK; sapphire and TeO$_2$ absorbers are covered by the same framework. Using the established thermal and noise model for massive TES calorimeters, we derive a noise model for the multiplexed readout, including the HEMT, two-level-system and SQUID contributions, and its scaling with the multiplexing factor $N_{\rm mux}$. Since the slow thermal signals require only about a kHz of sampling per channel, the limiting requirement is not bandwidth but an input-coil sensitivity of $( 0.1$ to $1)\,μ$A$/Φ_0$, a factor of $10$ to $30$ beyond current $μ$MUX devices, matched to the detector current noise of ($9$ to $10$)~pA$/\sqrt{\rm Hz}$, which is independent of the absorber mass. With a total flux noise of $\simeq$$1.2\,μΦ_0/\sqrt{\rm Hz}$, the readout degrades the baseline resolution by less than $2\%$ up to $N_{\rm mux}=1000$, negligible compared with the TES-limited resolution. These results are implemented in a single-tower design: 52 BGO crystals of 100~g each and one HEMT amplifier. The tower is the unit of a multi-tower array of several kilograms aimed at CE$ν$NS and dark matter searches.

The multimessenger observation of the binary neutron star merger event GW170817, associated with its electromagnetic counterparts GRB170817A and AT2017gfo, marked a milestone in astrophysics, yet its unified physical explanation remains elusive. We conduct an end-to-end simulation based on a first-principles general-relativistic magnetohydrodynamics neutrino-radiation transfer merger simulation, followed by nucleosynthesis calculations and photon radiative transfer to generate kilonova light curves. We show that the large-scale dynamo simultaneously produces a relativistic jet with an isotropic-equivalent luminosity of $\sim 10^{51}~{\rm erg~s^{-1}}$ and $\approx 0.08M_\odot$ of neutron-rich ejecta, reproducing the GRB170817A afterglow and the AT2017gfo kilonova light curves. Our results establish a unified first-principles framework for interpreting binary neutron star mergers across gravitational wave, gamma-ray burst, and kilonova observations.

Optical photon simulation is among the most computationally demanding tasks in complex and large detector geometries. In the Deep Underground Neutrino Experiment (DUNE), the scale of the far-detector modules makes photon-by-photon transport with \texttt{GEANT4} prohibitively expensive on CPUs. We present the first implementation and performance evaluation of GPU-accelerated optical photon simulation at the 10~kt scale, based on \texttt{Opticks} and applied to the DUNE far-detector horizontal-drift (FD-HD) geometry. On the full FD-HD geometry, \texttt{Opticks} propagates the same photons as \texttt{GEANT4} with a speedup of $313 \pm 3$ over single-threaded and $83 \pm 1$ over four-thread \texttt{GEANT4}, and is validated against the reference \texttt{GEANT4} simulation across all metrics considered. We further integrate \texttt{Opticks} into the \texttt{LArSoft}-based DUNE software stack. Photons simulated on the GPU with \texttt{GEANT4}-equivalent physics retain full Monte Carlo fidelity at a computational cost that makes high-statistics optical studies and the generation of labeled datasets for machine learning feasible at the kiloton scale.

Gamma-ray bursts (GRBs) have long been considered candidate sources of ultrahigh-energy cosmic rays (UHECRs) due to their large energy release and relativistic outflows. The detection of multi-TeV $γ$-rays from GRB~221009A and its rarity have renewed interest in this connection and motivate considering an additional narrow-jet long GRB population in the local Universe. We investigate whether such a local narrow-jet population can contribute to the observed diffuse UHECR energy spectrum. We also examine the associated cosmogenic neutrino and cascade $γ$-ray emissions to assess the multimessenger viability of this scenario. We fit the observed UHECR spectrum and mass composition data using three source-evolution models: a uniform comoving source emissivity, a standard-jet GRB population tracing the star formation rate (SFR), and a standard + narrow-jet GRB population tracing SFR. We propagate a mixed-composition UHECR injection and calculate the cosmogenic neutrino and cascade $γ$-ray fluxes. The standard + narrow jet model fits the observed UHECR spectrum and composition, with the highest-energy flux dominated by the narrow-jet population confined to $z\le z_{\max,*}\simeq0.36$. This low-redshift dominance lowers the cosmogenic neutrino flux compared to the standard-jet GRB population. For the narrow-jet GRB population, the fit implies a baryon loading factor $ξ_{\rm CR}^{\rm nj}\simeq10$. Such a locally enhanced long-GRB population can therefore explain the highest-energy UHECR flux without violating current multimessenger constraints. Future UHE searches can further probe this scenario through the associated cosmogenic fluxes.