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Many lattice QCD simulations now have many lattice spacings available, and it is of interest to investigate how they scale. In this talk we first derive renormalisation group equations appropriate for 2+1 clover fermions. This is then used together with pion mass and gradient flow results at five lattice spacings to study scaling., Comment: Contribution to the Proceedings of the 41st International Symposium on Lattice Field Theory, 28 July - 3 August 2024, University of Liverpool, UK

We present first-order nonconforming Crouzeix-Raviart discretizations for the nonlinear generalized Stokes equations with $(r,\epsilon)$-structure. Thereby the velocity-errors are independent of the pressure-error; i.e., the method is pressure robust. This improves suboptimal rates previously experienced for non pressure robust methods.

The Compton amplitude subtraction function is an essential component in work concerning both the proton radius puzzle and the proton-neutron mass difference. However, owing to the difficulty in determining the subtraction function, it remains a key source of uncertainty in these two contexts. Here, we use the Feynman-Hellmann method to determine this subtraction function directly from lattice QCD. Furthermore, we demonstrate how to control dominant discretisation artefacts for this calculation, eliminating a major source of systematic error. This calculation is performed for a range of hard momentum scales, and three different sets of gauge configurations for pion masses about 400 MeV. Our results show good agreement with continuum OPE expectations. As such, this work paves the way for model-independent and precise determinations of the subtraction function over a wide range of kinematics., Comment: 15 pages, 8 figures

We present a novel variational derivation of the Maxwell-GLM system, which augments the original vacuum Maxwell equations via a generalized Lagrangian multiplier approach (GLM) by adding two supplementary acoustic subsystems and which was originally introduced by Munz et al. for purely numerical purposes in order to treat the divergence constraints of the magnetic and the electric field in the vacuum Maxwell equations within general-purpose and non-structure-preserving numerical schemes for hyperbolic PDE. Among the many mathematically interesting features of the model are: i) its symmetric hyperbolicity, ii) the extra conservation law for the total energy density and, most importantly, iii) the very peculiar combination of the basic differential operators, since both, curl-curl and div-grad combinations are mixed within this kind of system. A similar mixture of Maxwell-type and acoustic-type subsystems has recently been also forwarded by Buchman et al. in the context of a reformulation of the Einstein field equations of general relativity in terms of tetrads. This motivates our interest in this class of PDE, since the system is by itself very interesting from a mathematical point of view and can therefore serve as useful prototype system for the development of new structure-preserving numerical methods. Up to now, to the best of our knowledge, there exists neither a rigorous variational derivation of this class of hyperbolic PDE systems, nor do exactly energy-conserving and asymptotic-preserving schemes exist for them. The objectives of this paper are to derive the Maxwell-GLM system from an underlying variational principle, show its consistency with Hamiltonian mechanics and special relativity, extend it to the general nonlinear case and to develop new exactly energy-conserving and asymptotic-preserving finite volume schemes for its discretization.

Single-spin asymmetries observed in polarised deep-inelastic scattering are important probes of hadron structure. The Sivers asymmetry has been the focus of much attention in QCD phenomenology and is yet to be understood at the quark level. In this Letter, we present a lattice QCD calculation of the spatial distribution of a colour-Lorentz force acting on the struck quark in a proton. We determine a spin-independent confining force, as well as spin-dependent force distributions with local forces on the order of 3 GeV/fm. These distributions offer a complementary picture of the Sivers asymmetry in transversely polarised deep-inelastic scattering., Comment: 16 pages, 16 figures

We propose a new full discretization of the Biot's equations in poroelasticity. The construction is driven by the inf-sup theory, which we recently developed. It builds upon the four-field formulation of the equations obtained by introducing the total pressure and the total fluid content. We discretize in space with Lagrange finite elements and in time with backward Euler. We establish inf-sup stability and quasi-optimality of the proposed discretization, with robust constants with respect to all material parameters. We further construct an interpolant showing how the error decays for smooth solutions.

We analyze the two-field formulation of the quasi-static Biot's equations by means of the inf-sup theory. For this purpose, we exploit an equivalent four-field formulation of the equations, introducing the so-called total pressure and total fluid content as independent variables. We establish existence, uniqueness and stability of the solution. Our stability estimate is two-sided and robust, meaning that the regularity established for the solution matches the regularity requirements for the data and the involved constants are independent of all material parameters. We prove also that additional regularity in space of the data implies, in some cases, corresponding additional regularity in space of the solution. These results are instrumental to the design and the analysis of discretizations enjoying accurate stability and error estimates.

We propose a high order discontinuous Galerkin (DG) scheme with subcell finite volume (FV) limiter to solve a monolithic first--order hyperbolic BSSNOK formulation of the coupled Einstein--Euler equations. The numerical scheme runs with adaptive mesh refinement (AMR) in three space dimensions, is endowed with time-accurate local time stepping (LTS) and is able to deal with both conservative and non-conservative hyperbolic systems. The system of governing partial differential equations was shown to be strongly hyperbolic and is solved in a monolithic fashion with one numerical framework that can be simultaneously applied to both the conservative matter subsystem as well as the non-conservative subsystem for the spacetime. Since high order unlimited DG schemes are well-known to produce spurious oscillations in the presence of discontinuities and singularities, our subcell finite volume limiter is crucial for the robust discretization of shock waves arising in the matter as well as for the stable treatment of puncture black holes. We test the new method on a set of classical test problems of numerical general relativity, showing good agreement with available exact or numerical reference solutions. In particular, we perform the first long term evolution of the inspiralling merger of two puncture black holes with a high order ADER-DG scheme., Comment: 27 pages, 16 figures. Matches version published on Physical Review D

We present a new, monolithic first--order (both in time and space) BSSNOK formulation of the coupled Einstein--Euler equations. The entire system of hyperbolic PDEs is solved in a completely unified manner via one single numerical scheme applied to both the conservative sector of the matter part and to the first--order strictly non--conservative sector of the spacetime evolution. The coupling between matter and space-time is achieved via algebraic source terms. The numerical scheme used for the solution of the new monolithic first order formulation is a path-conservative central WENO (CWENO) finite difference scheme, with suitable insertions to account for the presence of the non--conservative terms. By solving several crucial tests of numerical general relativity, including a stable neutron star, Riemann problems in relativistic matter with shock waves and the stable long-time evolution of single and binary puncture black holes up and beyond the binary merger, we show that our new CWENO scheme, introduced two decades ago for the compressible Euler equations of gas dynamics, can be successfully applied also to numerical general relativity, solving all equations at the same time with one single numerical method. In the future the new monolithic approach proposed in this paper may become an attractive alternative to traditional methods that couple central finite difference schemes with Kreiss-Oliger dissipation for the space-time part with totally different TVD schemes for the matter evolution and which are currently the state of the art in the field., Comment: 26 pages, 14 figures

In this work we aim at developing a new class of high order accurate well-balanced finite difference (FD) Weighted Essentially Non-Oscillatory (WENO) methods for numerical general relativity, which can be applied to any first-order reduction of the Einstein field equations, even if non-conservative terms are present. We choose the first-order non-conservative Z4 formulation of the Einstein equations, which has a built-in cleaning procedure that accounts for the Einstein constraints and that has already shown its ability in keeping stationary solutions stable over long timescales. Upon the introduction of auxiliary variables, the vacuum Einstein equations in first order form constitute a ..., Comment: Accepted in APJS (The Astrophysical Journal Supplement Series)

Exciton-polaritons, hybrid light-matter elementary excitations arising from the strong coupling regime between excitons in semiconductors and photons in photonic nanostructures, offer a fruitful playground to explore the physics of quantum fluids of light as well as to develop all-optical devices. However, achieving room temperature propagation of polaritons with a large excitonic fraction, which would be crucial, e.g., for nonlinear light transport in prospective devices, remains a significant challenge. } Here we report on experimental studies of exciton-polariton propagation at room temperature in resonant metasurfaces made from a sub-wavelength lattice of perovskite pillars. Thanks to the large Rabi splitting, an order of magnitude larger than the optical phonon energy, the lower polariton band is completely decoupled from the phonon bath of perovskite crystals. The long lifetime of these cooled polaritons, in combination with the high group velocity achieved through the metasurface design, enables long-range propagation regardless of the polariton excitonic fraction. Remarkably, we observed propagation distances exceeding hundreds of micrometers at room temperature, even when the polaritons possess a very high excitonic component, approximately {80}$\%$. Furthermore, the design of the metasurface introduces an original mechanism for directing uni-directional propagation through polarization control. This discovery of a ballistic propagation mode, leveraging high-speed cooled polaritons, heralds a promising avenue for the development of advanced polaritonic devices.

Gamma Ray Bursts (GRBs) bridge relativistic astrophysics and multi-messenger astronomy. Space-based gamma/X-ray wide field detectors have proven essential to detect and localize the highly variable GRB prompt emission, which is also a counterpart of gravitational wave events. We study the capabilities to detect long and short GRBs by the High Energy Rapid Modular Ensemble of Satellites (HERMES) Pathfinder (HP) and SpIRIT, namely a swarm of six 3U CubeSats to be launched in early 2025, and a 6U CubeSat launched on December 1st 2023. We also study the capabilities of two advanced configurations of swarms of >8 satellites with improved detector performances (HERMES Constellations). The HERMES detectors, sensitive down to ~2-3 keV, will be able to detect faint/soft GRBs which comprise X-ray flashes and high redshift bursts. By combining state-of-the-art long and short GRB population models with a description of the single module performance, we estimate that HP will detect ~195^{+22}_{-21} long GRBs (3.4^{+0.3}_{-0.8} at redshift z>6) and ~19^{+5}_{-3} short GRBs per year. The larger HERMES Constellations under study can detect between ~1300 and ~3000 long GRBs per year and between ~160 and ~400 short GRBs per year, depending on the chosen configuration, with a rate of long GRBs above z>6 between 30 and 75 per year. Finally, we explore the capabilities of HERMES to detect short GRBs as electromagnetic counterparts of binary neutron star (BNS) mergers detected as gravitational signals by current and future ground-based interferometers. Under the assumption that the GRB jets are structured, we estimate that HP can provide up to 1 (14) yr^{-1} joint detections during the fifth LIGO-Virgo-KAGRA observing run (Einstein Telescope single triangle 10 km arm configuration). These numbers become 4 (100) yr^{-1}, respectively, for the HERMES Constellation configuration., Comment: 13 pages, 6 figures, 4 tabels. Accepted for publication by Astronomy & Astrophysics

We present a determination of the structure functions of the off-forward Compton amplitude $\mathcal{H}_1$ and $\mathcal{E}_1$ from the Feynman-Hellmann method in lattice QCD. At leading twist, these structure functions give access to the generalised parton distributions (GPDs) $H$ and $E$, respectively. This calculation is performed for an unphysical pion mass of $m_{\pi}=412\;\text{MeV}$ and four values of the soft momentum transfer, $t\approx 0, -0.3, -0.6, -1.1\;\text{GeV}^2$, all at a hard momentum scale of $\bar{Q}^2\approx 5\;\text{GeV}^2$. Using these results, we test various methods to determine properties of the real-time scattering amplitudes and GPDs: (1) we fit their Mellin moments, and (2) we use a simple GPD ansatz to reconstruct the entire distribution. Our final results show promising agreement with phenomenology and other lattice results, and highlight specific systematics in need of control., Comment: 20 pages, 14 figures. Minor updates to text. Version to appear in Phys. Rev. D

In this paper, we propose a novel conceptual framework to detect outliers using optimal transport with a concave cost function. Conventional outlier detection approaches typically use a two-stage procedure: first, outliers are detected and removed, and then estimation is performed on the cleaned data. However, this approach does not inform outlier removal with the estimation task, leaving room for improvement. To address this limitation, we propose an automatic outlier rectification mechanism that integrates rectification and estimation within a joint optimization framework. We take the first step to utilize the optimal transport distance with a concave cost function to construct a rectification set in the space of probability distributions. Then, we select the best distribution within the rectification set to perform the estimation task. Notably, the concave cost function we introduced in this paper is the key to making our estimator effectively identify the outlier during the optimization process. We demonstrate the effectiveness of our approach over conventional approaches in simulations and empirical analyses for mean estimation, least absolute regression, and the fitting of option implied volatility surfaces.

In 2022 the DART mission spacecraft impacted the asteroid Dimorphos, the secondary body of the binary Didymos system, ejecting a large number of dust particles, rocks and boulders. The ESA Hera mission will reach the system in 2026 for post--impact studies and possible detection of orbiting fragments. We investigate the long term dynamics of the large boulders ejected by DART to test if any of these objects survive in orbit until the arrival of the Hera mission. To model the dynamics of the boulders we use a numerical model which includes the gravity of non-spherical Didymos and Dimorphos, the solar gravity and the radiation pressure. The SPICE kernels are used to define the correct reference frame for the integration. The dynamics of the boulders is highly chaotic and 1% of the initial boulders survive at least for 4 years on quasi--stable orbits. These orbits are characterised by wide oscillations in eccentricity in antiphase with those in inclination (including spin flips), a mechanism similar to the Kozai one. This behaviour may protect these bodies from close encounters with both asteroids. We also compute the distribution on the surfaces of the asteroids of sesquinary impacts which may influence the dust emission, after the initial DART impact, and the surface composition of the asteroids. The probability of observing boulders by the mission Hera is small but not negligible and an almost constant flux of escaping boulders is expected in the coming years since their lifetime after the DART impact covers a large time interval. Most of re--impacts on Dimorphos occur in the hemisphere opposite to the impact site, preferentially close to the equatorial plane., Comment: Accepted in A&A

The dominant contribution to the theoretical uncertainty in the extracted weak parameters of the Standard Model comes from the hadronic uncertainties in the electroweak boxes, i.e. $\gamma-W^\pm/Z$ exchange diagrams. A dispersive analysis relates the box diagrams to the parity-odd structure function, $F_3$, for which the experimental data either do not exist or belong to a separate isospin channel. Therefore a first-principles calculation of $F_3$ is highly desirable. In this contribution, we report on the QCDSF/UKQCD Collaboration's progress in calculating the moments of the $F_3^{\gamma Z}$ structure function from the forward Compton amplitude at the SU(3) symmetric point., Comment: 9 pages, 3 figures. Contribution to the 40th International Symposium on Lattice Field Theory (Lattice 2023) July 31st - August 4th, 2023, Fermi National Accelerator Laboratory, Batavia IL, USA

We study the stability of the antiferromagnetic all-in--all-out state observed in dipolar-octupolar pyrochlores that have neodymium as the magnetic species. Different types of disorder are considered, either affecting the immediate environment of the Nd$^{3+}$ ion, or substituting it with a non-magnetic ion. Starting from the well studied Nd$_2$Zr$_2$O$_7$ compound, Ti substitution on the Zr site and dilution on the Nd magnetic site with La substitution are investigated. The recently discovered entropy stabilized compound NdMox, which exhibits a high degree of disorder on the non magnetic site is also studied. Using a range of experimental techniques, especially very low-temperature magnetization and neutron scattering, we show that the all-in--all-out state is very robust and withstands substitutional disorder up to large rates. From these measurements, we estimate the Hamiltonian parameters and discuss their evolution in the framework of the phase diagram of dipolar-octupolar pyrochlore magnets., Comment: 19 pages, 20 figures (main text: 12 pages, 13 figures)

The structure of hadrons relevant for deep-inelastic scattering are completely characterised by the Compton amplitude. A direct calculation of the Compton amplitude in a lattice QCD setup provides a way to accessing the structure functions, circumventing the operator mixing and renormalisation issues of the standard operator product expansion approach. In this contribution, we focus on the QCDSF/UKQCD Collaboration's advances in calculating the forward Compton amplitude via an implementation of the second-order Feynman-Hellmann theorem. We highlight our progress in investigating the moments of nucleon structure functions., Comment: Presented at DIS2023: XXX International Workshop on Deep-Inelastic Scattering and Related Subjects, Michigan State University, USA, 27-31 March 2023. arXiv admin note: substantial text overlap with arXiv:2212.09197, arXiv:2110.01310

In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein--Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Z4 system, which is composed of 59 equations, is analyzed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete version of the equilibrium solution from the discretized time-dependent PDE system. Special care has also been taken in the design of the numerical viscosity so that the well-balancing property is achieved. As for the treatment of low density matter, e.g. when simulating massive compact objects like neutron stars surrounded by vacuum, we have introduced a new filter in the conversion from the conserved to the primitive variables, preventing superluminal velocities when the density drops below a certain threshold, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows. Thanks to these improvements, all standard tests of numerical relativity are successfully reproduced, reaching three achievements: (i) we are able to obtain stable long term simulations of stationary black holes, including Kerr black holes with extreme spin, which after an initial perturbation return perfectly back to the equilibrium solution up to machine precision; (ii) a (standard) TOV star under perturbation is evolved in pure vacuum ($\rho$=$p$=0) up to t=1000 with no need to introduce any artificial atmosphere around the star; and, (iii) we solve the head on collision of two punctures black holes, that was previously considered un--tractable within the Z4 formalism., Comment: This manuscript matches the version accepted by Journal of Computational Physics

The Feynman--Hellmann approach to computing matrix elements in lattice QCD by first adding a perturbing operator to the action is described using the transition matrix and the Dyson expansion formalism. This perturbs the energies in the two-point baryon correlation function, from which the matrix element can be obtained. In particular at leading order in the perturbation we need to diagonalise a matrix of near-degenerate energies. While the method is general for all hadrons, we apply it here to a study of a Sigma to Nucleon baryon transition vector matrix element., Comment: 50 pages. Minor typos fixed. Published version

With increasing requirements for greater precision, it becomes essential to describe the effects of isospin breaking induced by both quark masses and electro-magnetic effects. In this work we perform a lattice analysis of the weak decay constants of the neutral pseudoscalar mesons including such isospin breaking effects, with particular consideration being given to the state mixing of the $\pi^0$, $\eta$ and $\eta^\prime$. We also detail extensions to the non-perturbative RI$^\prime$-MOM renormalization scheme for application to non-degenerate flavour-neutral operators which are permitted to mix, and present initial results. Using flavour-breaking expansions in terms of quark masses and charges we determine the leptonic decay constants for the $\pi^0$ and $\eta$ mesons, demonstrating in principle how precision determinations of all neutral pseudoscalar decay constants could be reached in lattice QCD with QED and strong isospin-breaking accounted for., Comment: 10 pages, 5 figures, analysis of charged mesons has been removed

At the TeV scale, low-energy precision observations of neutron characteristics provide unique probes of novel physics. Precision studies of neutron decay observables are susceptible to beyond the Standard Model (BSM) tensor and scalar interactions, while the neutron electric dipole moment, $d_n$, also has high sensitivity to new BSM CP-violating interactions. To fully utilise the potential of future experimental neutron physics programs, matrix elements of appropriate low-energy effective operators within neutron states must be precisely calculated. We present results from the QCDSF/UKQCD/CSSM collaboration for the isovector charges $g_T,~g_A$ and $g_S$ of the nucleon, $\Sigma$ and $\Xi$ baryons using lattice QCD methods and the Feynman-Hellmann theorem. We use a flavour symmetry breaking method to systematically approach the physical quark mass using ensembles that span five lattice spacings and multiple volumes. We extend this existing flavour breaking expansion to also account for lattice spacing and finite volume effects in order to quantify all systematic uncertainties. Our final estimates of the nucleon isovector charges are $g_T~=~1.010(21)_{\text{stat}}(12)_{\text{sys}},~g_A=1.253(63)_{\text{stat}}(41)_{\text{sys}}$ and $g_S~=~1.08(21)_{\text{stat}}(03)_{\text{sys}}$ renormalised, where appropriate, at $\mu=2~\text{GeV}$ in the $\overline{\text{MS}}$ scheme., Comment: 19 pages, 11 figures, 10 tables

Geometrical frustration, as in pyrochlore lattices made of corner-sharing tetrahedra, precludes the onset of conventional magnetic ordering, enabling the stabilization of fluctuating spin states at low temperature. Disorder is a subtle ingredient that can modify the nature of these exotic non-ordered phases. Here, we study the interplay between disorder and magnetic frustration in the new pyrochlore Tb$_{2}$ScNbO$_{7}$ where the non magnetic site presents a charge disorder Nb$^{5+}$/Sc$^{3+}$. Its quantification with sophisticated diffraction techniques (electrons, X-rays, neutrons) allows us to estimate the distribution of the splitting of the magnetic Tb$^{3+}$ non-Kramers ground state doublets and to compare it with excitations measured in inelastic neutron scattering. Combining macroscopic and neutron scattering measurements, we show that a clear spin glass transition at 1 K stems out while retaining strong spin liquid correlations. Our results suggest that Tb$_{2}$ScNbO$_{7}$ stabilizes one of the novel disorder induced quantum spin liquid or topological glassy phases recently proposed theoretically., Comment: Main text: 9 pages, 5 figures ; Supplemental Material: 6 pages, 7 figures

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on September 26, 2022 as a planetary defense test. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defense, intended to validate kinetic impact as a means of asteroid deflection. Here we report the first determination of the momentum transferred to an asteroid by kinetic impact. Based on the change in the binary orbit period, we find an instantaneous reduction in Dimorphos's along-track orbital velocity component of 2.70 +/- 0.10 mm/s, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact. For a Dimorphos bulk density range of 1,500 to 3,300 kg/m$^3$, we find that the expected value of the momentum enhancement factor, $\beta$, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg/m$^3$, $\beta$= 3.61 +0.19/-0.25 (1 $\sigma$). These $\beta$ values indicate that significantly more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos., Comment: accepted by Nature

The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator and the other from the operator to the hadron sink. Here we consider an alternative formalism, based on the Dyson expansion leading to the Feynman-Hellmann theorem, which only requires the computation of two-point correlation functions. Both the cases of degenerate energy levels and quasi-degenerate energy levels which correspond to diagonal and transition matrix elements respectively can be considered in this formalism. As an example numerical results for the Sigma to Nucleon vector transition matrix element are presented., Comment: Proceedings of the 39th International Symposium on Lattice Field Theory, 8-13 August 2022, Bonn, Germany