More Like this

1. The Eisenstein ideal at prime-square level has constant rank

   https://doi.org/10.1073/pnas.2500729122  

   Lang, Jaclyn; Wake, Preston (July 2025, Proceedings of the National Academy of Sciences)

   LetNandpbe prime numbers with $p\ge 5$such that $p\mid \mid (N+1)$. In a previous paper, we showed that there is a cuspformfof weight 2 and level ${\mathrm{\Gamma }}_0\left(N^2\right)$whoseℓ-th Fourier coefficient is congruent to $\ell +1$modulo a prime abovepfor all primesℓ. In this paper, we prove that this formfis unique up to Galois conjugacy, and the extension of ${\mathbb{Z}}_p$generated by the coefficients offis exactly ${\mathbb{Z}}_p[{\zeta }_p+{\zeta }_p^{-1}]$. We also prove similar results when a higher power ofpdivides $N+1$. 

   more » « less
2. Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

   https://doi.org/10.1088/1361-6382/ae2bd6  

   Tiki, Victoria; Pham, Kiet; Huerta, E A (December 2025, Classical and Quantum Gravity)

   Abstract Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from theNRHybSur3dq8surrogate, which provides spherical-harmonic modes up to $\ell \text{⩽}4$(excluding (4, 0) and $(4,\pm 1)$, and including (5, 5)) for mass ratios $q\text{⩽}8$, dimensionless spin components $s_{1,2}^z\in [-0.8,0.8]$, and inclination angles $\theta \in [0,\pi ]$. Waveforms are supplied on the interval $t\in [-5000\mathrm{M},-100\mathrm{M})$and the model autoregressively generates the plus and cross polarizations $(h_{+},h_{\times })$on $t\in [-100\mathrm{M},130\mathrm{M}]$. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required $\sim 15$ h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of $\mathrm{840,000}$samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth. The model generalises reasonably well to out-of-distribution NR simulations from the SXS catalogue: across 521 NR waveforms with mass ratios up toq = 15 and spin magnitudes $|s|\text{⩽}0.998$, we obtain a median overlap of 0.969, rising to 0.998 for face-on/off orientations. Within the surrogate’s training domain, the transformer provides accurate, millisecond-scale sequence completion of BBH waveforms, including higher-order modes, from early inspiral to ringdown. The NR tests indicate promising performance on higher-fidelity, out-of-distribution data, particularly for detector-favourable orientations. 

   more » « less
3. Measurement of the dynamic charge susceptibility near the charge density wave transition in ErTe ₃

   https://doi.org/10.1073/pnas.2424430122  

   Chaudhuri, Dipanjan; Jiang, Qianni; Guo, Xuefei; Chen, Jin; Kengle, Caitlin S; Hoveyda-Marashi, Farzaneh; Bernal-Choban, Camille; de_Vries, Niels; Chiang, Tai-Chang; Fradkin, Eduardo; et al (June 2025, Proceedings of the National Academy of Sciences)

   A charge density wave (CDW) is a phase of matter characterized by a periodic modulation of valence electron density coupled with lattice distortion. Its formation is closely tied to the dynamical charge susceptibility, $\chi (q,\omega )$, which reflects the collective electron dynamics of the material. Despite decades of study, $\chi (q,\omega )$near a CDW transition has never been measured at nonzero momentum, $q$, with meV energy resolution. Here, we investigate the canonical CDW transition in ErTe ${}_3$using momentum-resolved electron energy loss spectroscopy, a technique uniquely sensitive to valence band charge excitations. Unlike phonons, which soften via the Kohn anomaly, we find the electronic excitations exhibit purely relaxational dynamics well described by a diffusive model, with the diffusivity peaking just below the critical temperature, $T_{C1}$. Additionally, we report for the first time a divergence in the real part of $\chi (q,\omega )$in the static limit ( $\omega \to 0$), a long-predicted hallmark of CDWs. Unexpectedly, this divergence occurs as $T\to 0$, with only a weak thermodynamic signature at $T=T_{C1}$. Our study necessitates a reexamination of the traditional description of CDW formation in quantum materials. 

   more » « less
4. HSTPROMO Internal Proper-motion Kinematics of Dwarf Spheroidal Galaxies. I. Velocity Anisotropy and Dark Matter Cusp Slope of Draco

   https://doi.org/10.3847/1538-4357/ad571c  

   Vitral, Eduardo; van_der_Marel, Roeland P; Sohn, Sangmo Tony; Libralato, Mattia; del_Pino, Andrés; Watkins, Laura L; Bellini, Andrea; Walker, Matthew G; Besla, Gurtina; Pawlowski, Marcel S; et al (July 2024, The Astrophysical Journal)

   Abstract We analyze four epochs of Hubble Space Telescope imaging over 18 yr for the Draco dwarf spheroidal galaxy. We measure precise proper motions for hundreds of stars and combine these with existing line-of-sight (LOS) velocities. This provides the first radially resolved 3D velocity dispersion profiles for any dwarf galaxy. These constrain the intrinsic velocity anisotropy and resolve the mass–anisotropy degeneracy. We solve the Jeans equations in oblate axisymmetric geometry to infer the mass profile. We find the velocity dispersion to be radially anisotropic along the symmetry axis and tangentially anisotropic in the equatorial plane, with a globally averaged value $\overline{{\beta }_{\mathrm{B}}}=-{0.20}_{-0.53}^{+0.28}$, (where 1 – ${\beta }_{\mathrm{B}}\equiv 〈v_{\tan }^2〉/〈v_{\mathrm{rad}}^2〉$in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, Γ_dark, is $-{0.83}_{-0.37}^{+0.32}$, consistent with the inner cusp predicted in ΛCDM cosmology. As expected given Draco’s low mass and ancient star formation history, it does not appear to have been dissolved by baryonic processes. We rule out cores larger than 487, 717, and 942 pc at 1σ, 2σ, and 3σconfidence, respectively, thus imposing important constraints on the self-interacting DM cross section. Spherical models yield biased estimates for both the velocity anisotropy and the inferred slope. The circular velocity at our outermost data point (900 pc) is ${24.19}_{-2.97}^{+6.31}\mathrm{km}{\mathrm{s}}^{-1}$. We infer a dynamical distance of ${75.37}_{-4.00}^{+4.73}$kpc and show that Draco has a modest LOS rotation, with $\left(v/\sigma \right)=0.22\pm 0.09$. Our results provide a new stringent test of the so-called “cusp–core” problem that can be readily extended to other dwarfs. 

   more » « less
5. Observation of $\text{γ}\text{γ}\to \text{τ}\text{τ}$ in proton–proton collisions and limits on the anomalous electromagnetic moments of the τ lepton

   https://doi.org/10.1088/1361-6633/ad6fcb  

   CMS_Collaboration, The (September 2024, Reports on Progress in Physics)

   Abstract The production of a pair of τ leptons via photon–photon fusion, $\text{γ}\text{γ}\to \text{τ}\text{τ}$, is observed for the first time in proton–proton collisions, with a significance of 5.3 standard deviations. This observation is based on a data set recorded with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb⁻¹. Events with a pair of τ leptons produced via photon–photon fusion are selected by requiring them to be back-to-back in the azimuthal direction and to have a minimum number of charged hadrons associated with their production vertex. The τ leptons are reconstructed in their leptonic and hadronic decay modes. The measured fiducial cross section of $\text{γ}\text{γ}\to \text{τ}\text{τ}$is ${\sigma }_{\text{obs}}^{\text{fid}}={12.4}_{-3.1}^{+3.8}\text{fb}$. Constraints are set on the contributions to the anomalous magnetic moment ( $a_{\text{τ}}$) and electric dipole moments ( $d_{\text{τ}}$) of the τ lepton originating from potential effects of new physics on the $\text{γ}\text{τ}\text{τ}$vertex: $a_{\text{τ}}={0.0009}_{-0.0031}^{+0.0032}$and $|d_{\text{τ}}|<2.9\times {10}^{-17}e\text{cm}$(95% confidence level), consistent with the standard model. 

   more » « less