Papers

We investigate excited-state effects in nucleon sigma-terms in lattice QCD using twisted-mass clover-improved fermion ensembles. We study correlation functions with nucleon and multihadron nucleon-$\sigma$-meson interpolating operators. The analysis is performed using three gauge ensembles, including one ensemble simulated with two degenerate light, a strange, and a charm quark with quark masses tuned to approximately their physical value. We solve the generalized eigenvalue problem that arises from the matrix of correlators and show that the three-point function for the light sigma-term obtained using the optimal linear combination of interpolating operators has substantially reduced time dependence without loss of statistical precision. We apply Laplace filtering and investigate residual excited-state contributions in the extraction of $\sigma_{\pi N}$. Using the same optimal linear combination of correlators as for $\sigma_{\pi N}$ for the strange sigma-term we also observe suppressed excited state contributions over an extended range of source–sink time separations. For the charm sigma-term, we observe negligible time dependence within the large statistical uncertainties, and these improvements show no significant effect.

We study short-range three-nucleon forces (3NFs) in nuclear lattice effective field theory with a chiral two-nucleon interaction at N${}^3$LO. The one-pion-exchange ($c_D$) and contact ($c_E$) terms of the leading 3NF are decomposed into locally and non-locally smeared components and supplemented by partial-wave-resolved pair contacts coupled to the density of a third nucleon. We determine their coefficients from nuclear binding energies for nuclei in the mass range from $A=3$ to $A=40$ and neutron–alpha finite-volume energies. This allows to work out the minimal three-nucleon force that can be used for future precision studies in NLEFT.

The gradient flow exact renormalization group (GFERG) is a formulation of the exact renormalization group for gauge theories that provides a renormalization group flow preserving the gauge Ward–Takahashi identity exactly. In this paper, we nonperturbatively solve the GFERG flow equation for the simplest nontrivial gauge-invariant Wilson action, introduced in a previous paper, for $D$-dimensional quantum electrodynamics with~$N_f$ flavors (for all~$D$, flavors are counted in units of four-component spinors). For $D=3$ and~$D=2$, a nontrivial infrared fixed point exists even for~$N_f=1$, and the structure of the critical exponents at the fixed point is qualitatively the same as that in the large-$N_f$ limit. We also obtain the gauge-field propagator in the continuum limit; for~$D=2$, it reproduces the dynamical mass of the Schwinger model within a few percent. To the best of our knowledge, apart from the large-$N_f$ approximation, this is the first example in which the Wilson renormalization group in a gauge theory is solved nonperturbatively while manifestly preserving gauge symmetry.

We introduce a new Euclidean quantum model with zero-spin scaled scalar fields on a spacetime hypercubic lattice, which we refer to as the hybrid model. The model coupling parameters are the hopping parameter $\kappa^2>0$ and the field interaction coupling $\alpha>0$. Using the technique of lattice scaled fields, with a noncanonical scaling that corresponds to a partial renormalization (wave function renormalization), we show that the partition function of this model satisfies both thermodynamic and ultraviolet stability bounds, with constants which are uniform in the lattice volume $\Lambda_s$ and the lattice spacing $a\in(0,1]$. As a consequence, the model has a finite free energy per degree of freedom in the thermodynamic limit $\Lambda_s\nearrow\infty$, at least in the subsequential sense. Subsequently, we can also take the ultraviolet or continuum limit $a\searrow 0$. Besides the finiteness property of the free energy, for sufficiently small values of the model coupling parameters $\kappa^2$ and $\alpha$, we show the model satisfies Osterwalder-Schrader positivity and construct the underlying physical quantum mechanical Hilbert space, and, using a polymer expansion, we show correlations also remain bounded in the thermodynamic limit. Finally, we perturbatively compute an infinite volume truncated four-point correlation showing it is nonzero. Noting that, for fixed $a$, perturbation series in $\kappa^2$ and $\alpha$ converges, these results are sufficient to show that our hybrid model makes sense as a lattice quantum field theory in spacetime dimension $d=3,4$, with possible extensions to other higher values of $d$.

Following the discovery of the exotic state $X(3872)$ in the charmonium spectrum, the possible existence of an analogous state, $X_b$, in the bottomonium sector has attracted considerable attention of the hadronic physics community. In this work, we lay the ground for the development of Born-Oppenheimer chiral effective field theory (BO$\chi$EFT), that allows us to include both quark and hadron degrees of freedom as well as the full complexity of the meson-exchange potential in a systematic way. For illustration, the formalism to leading order (LO) is applied to the system of $\chi_{b1}$ states and in particular the $X_b$. The two parameters that are present at this order are constrained using experimental information on the bottomonium spectrum together with lattice input on static quark-antiquark potentials, including string breaking effects. The framework identifies the observed $1^{++}$ state at 10.513 GeV with a predominantly molecular $X_b$, the bottom counterpart of the $X(3872)$, and predicts an additional predominantly compact bottomonium state at 10.544 GeV, about 60 MeV below the $B\bar{B}^*$ threshold.

Sampling equilibrium field configurations remains a major computational bottleneck in lattice field theory, motivating the development of generative samplers that can produce independent configurations. Diffusion models are promising for this purpose, but their standard denoising score matching objective requires samples from the target distribution, seemingly reintroducing the original sampling problem. Here, we show that diffusion models can instead be trained from their own generated samples using the target score identity, provided access to the unnormalized probability density. Importance-weighted formulations of this identity yield a consistent target throughout training, while unweighted variants define a self-consistent fixed-point training scheme. We benchmark the different approaches in two-dimensional \(\phi^4\) theory and identify effective choices that enable efficient training and sampling across the symmetric, critical, and broken phases. Ultimately, our data-free training approach achieves comparable performance to training on HMC reference data.

Gauge-equivariant graph neural networks generate ordered products of gauge links through local message passing, but the geometry of these internal structures is not captured by the receptive field alone. We investigate the statistical ensemble of closed lattice walks generated by recursive node- and edge-feature operations, independently of network training. Analytical and numerical results reveal a separation between rapid growth of contour length and much slower spatial expansion: deeper compositions generate increasingly long paths through repeated traversal of relatively compact regions. Loop expansions of fermionic observables provide a physical interpretation of this hierarchy, showing how spatial locality remains compatible with high-order dependence on nearby gauge fields. These findings identify complementary roles of network depth in extending spatial reach and enriching the representations constructed within that reach, providing a geometrical perspective on learning lattice gauge observables.

Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure $SU(3)$ lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model $\texttt{H2-2}$, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires $\sim 25n$ entangling gates for $n$ Trotter steps.

Using continuum Schwinger function methods, we deliver parameter-free pointwise predictions for the complete set of twelve Standard Model (SM) $\bar B_{(s)} \to D_{(s)}^{(\ast)}$, i.e., $b\to c$, semileptonic transition form factors on the entire kinematically accessible domain. Therewith, we calculate SM theory values for the decay-rate ratios of $\tau$ and $\mu$ final states: $\{ R(D) \, , \, R(D)^\ast \} = \{ 0.290(11) \, , \, 0.267(5) \}$, $\{ R(D_{s}) \, , \, R(D_{s}^{\ast}) \} = \{ 0.283(11) \, , \, 0.251(5) \}$. The former is consistent with an existing average of SM estimates, but disagrees with the experimental average by $2.8\sigma$. Comparing transitions with light quark and strange quark spectators, we find a $2.3\sigma$ signal for violation of SU$(3)$ flavour symmetry, expressed at the 5% level in $D_{(s)}^\ast$ final states. It is induced by Higgs boson couplings into the strong interaction and modulated by phenomena deriving from emergent features of the strong interaction.

We study the potential impact of lattice QCD window observables on nucleon isovector quark transversity parton distribution functions (PDFs) using the ePump Hessian-updating framework. Window observables, recently proposed in arXiv:2505.22795 as benchmark quantities enabling direct quantitative comparison between lattice QCD and phenomenological PDF extractions, are weighted integrals of PDFs over a range of Bjorken-$x$ for which both approaches are reliable. Experimental determinations of transversity PDFs carry uncertainties of 50–100%, while current lattice calculations have achieved comparable or better precision, creating an opportunity for lattice inputs to significantly constrain a global analysis. We evaluate the constraining power of existing lattice QCD computations of transversity window moments and Gaussian windows against current phenomenological PDF. We additionally examine prospective tensor charges in the transversity channel and estimate the PDF uncertainty reduction achievable at current and near-future lattice precision. Our results provide quantitative guidance on which window observables will most constrain global PDF analyses.

Quantum computation offers a promising alternative to classical Monte Carlo methods by naturally avoiding sign problems through unitary evolution. A common misconception follows from this: because quantum simulation sidesteps the sign problem, it is often assumed to be an essentially perfect substitute for classical sampling. This is false—quantum measurements are intrinsically stochastic, and estimating observables often requires a number of samples that grows exponentially with system size, time separation, or inverse temperature, exactly as in the classical signal-to-noise problem. In this work, we analyze the origin and structure of signal-to-noise problems in quantum computation, drawing parallels with classical Monte Carlo, and demonstrate that such noise persists even in sign-problem-free regimes. We discuss strategies to mitigate it, in particular a quantum generalization of Stein control variates construction, in which unbiased estimators are built from operator commutators $[X,A]$ and their discrete diagonal counterparts, and validate the approach with exactly solvable numerical examples that quantify the achievable variance reduction. Our results underscore that variance reduction, not merely sign-problem avoidance, is required to make quantum algorithms practically viable for many-body physics.

We investigate the perturbative renormalization of Noether currents associated with chiral symmetry and supersymmetry transformations in $\mathcal{N}=1$ supersymmetric Yang-Mills theory, regularized on the lattice using improved discretizations. In particular, we study the chiral current and the supercurrent operator for a broad class of lattice actions: Wilson fermions with one-step stout-smeared links and a clover term, together with a family of Symanzik-improved gluon actions. Since the supercurrent mixes with both gauge-invariant and gauge-noninvariant operators, we compute the corresponding renormalization factors and mixing coefficients at one-loop order. We analyze the impact of improved gluon and gluino actions on this mixing pattern and investigate whether suitable choices of lattice parameters, such as the clover and stout coefficients, can reduce unwanted lattice artifacts at one loop. Our results provide perturbative input for the implementation of Ward identities and for matching lattice observables to their continuum counterparts, while also offering guidance for simulations aimed at restoring supersymmetry in the continuum limit.

The Roy equations for the $S$ and $P$ waves are solved for pion masses below the physical value in the region between threshold and $s_A=0.84\GeV^2$. The analysis is based on the assumption that the phenomenological input above $s_A$ can be used essentially unchanged. Moreover, for $M_\pi \le M_{\pi,\mathrm{phys}}$, the chiral perturbation theory predictions for the two $S$-wave scattering lengths provide a very reliable additional input to the Roy equations. The outcome is an accurate description of the $S$ and $P$ partial waves as the light-quark masses decrease towards the chiral limit. As a test of the approach, we evaluate the first few threshold parameters of the $S$, $P$, and $D$ waves via Wanders' sum rules and find excellent agreement with chiral perturbation theory across the entire range $0 \le M_\pi \le M_{\pi,\mathrm{phys}}$. We further solve the Roy equations for pion masses above the physical value (up to $240\MeV$) and show that the resulting solutions agree well with existing lattice data at $M_\pi=239\MeV$. The present work paves the way for analyses of lattice data that fully incorporate the constraints of analyticity, unitarity, and crossing symmetry, and provides the basis for an accurate study of the dependence of the $\sigma$ and $\rho$ resonances on the light-quark masses, both of which will be addressed in future work.

We study the spectrum of two-particle bound states of Kähler-Dirac fermions coupled via gravity in Euclidean Dynamical Triangulations (EDT). We work in the quenched approximation, where the geometry is allowed to fluctuate, but there is no back-reaction from the matter on the geometry. The Kähler-Dirac action respects an exact $U(1)$ symmetry that is related to continuum chiral symmetry, and this $U(1)$ symmetry ensures that some of the bound-state masses vanish in the chiral limit of vanishing fermion bare mass. The bound-state masses that are not protected by the $U(1)$ symmetry do not vanish in the chiral limit, but the scale associated with the symmetry breaking does not appear to be a physical scale like the Planck mass or the curvature scale of the emergent de Sitter background. Rather, the mass scale associated with this non-degeneracy appears to be a positive power of the lattice spacing, decreasing as the continuum limit is approached. This suggests that Kähler-Dirac fermions in EDT can be interpreted as the gravity analog of staggered fermions in flat-space lattice field theories, with similar behavior.

We report the first Monte Carlo simulation of quantum field theory on Euclidean de Sitter space, $S^4$. Rather than discretizing space, we use a spectral lattice based on spherical harmonics, keeping all symmetries exact at finite cutoff. For a massless $\lambda\phi^4$ theory, the zero-mode distribution reproduces the Starobinsky-Yokoyama equilibrium at weak coupling, and deviations closely follow the one-loop renormalization of $\lambda$. At strong bare coupling, the renormalized quartic coupling saturates near the ceiling of the one-loop renormalization-group flow. This saturation is the de Sitter counterpart of the triviality mechanism that bounds the Higgs mass in flat space. Our results confirm nonperturbatively that the infrared divergences of light scalars in de Sitter are correctly resummed by the stochastic formalism. More broadly, this work opens up de Sitter space to lattice Monte Carlo methods.

Machine learning (ML) in high-energy nuclear physics (HENP) is entering a new stage in which physical knowledge is incorporated more directly into data analysis, simulation, and physics inference. This mini-review focuses on developments that have matured in the past several years. Whereas earlier applications emphasized event classification, pattern recognition, and surrogate models for selected observables, recent work has moved toward physics-integrated workflows: calibrated Bayesian extraction of QCD matter properties, dense-matter equation-of-state inference from heavy-ion and neutron-star data, generative event modeling, neural unfolding of weak physical signals, differentiable inverse solvers, gauge-equivariant and diffusion-based lattice-field samplers, and neural reconstruction of model functions in holographic QCD. We survey recent applications of ML in heavy-ion collisions, neutron-star physics, lattice QFT, and holographic or continuum QCD. The emphasis is not on ML architectures alone, but on how they enter concrete physics workflows, how physical constraints such as symmetries, conservation laws, causality, thermodynamic stability, and topology are imposed, and how uncertainty quantification and validation determine whether an AI-assisted result can support a reliable physics conclusion.

Non-Abelian gauge theories above four dimensions may admit an interacting ultraviolet fixed point through the competition between canonical scaling and gauge-field antiscreening. Using the four-loop $\overline{\mathrm{MS}}$ beta function continued to $D=4+2\epsilon$, we determine the largest dimension $D_{\mathrm{pt}}=4+2\epsilon_{\mathrm{pt}}$ below which successive loop corrections to the fixed point remain hierarchically ordered under a specified ratio criterion, and map $D_{\mathrm{pt}}$ over color and flavor numbers for fermions in the fundamental representation of $SU(N)$. At $D=5$, we construct rational anomalous dimensions with a fixed, pole-regularized denominator inspired by the functional renormalization group (fRG). Matching to the $\overline{\mathrm{MS}}$ series through one, two, and three loops produces progressively smaller shifts in the critical flavor number and coupling at the ultraviolet–infrared merger (the point where the infrared and ultraviolet fixed points coincide), yielding $N_f^{\mathrm{cr}}\simeq 2.09 \, N$ at large $N$ in the three-loop construction. This low-order stabilization, together with qualitative evidence from fRG flows including higher gauge operators, suggests a potential merger scenario that bounds the candidate asymptotically safe region in flavor number. The resulting color–flavor map provides guidance for five-dimensional model building by displaying both the baseline perturbative-control boundary and the candidate three-loop merger boundary. Four-loop matching, however, retains an interacting ultraviolet fixed point beyond the three-loop merger boundary, with no merger found for integer $2\le N\le15$ and $0\le N_f/N\le11/2$. The sensitivity of the fixed-point structure to higher-order terms leaves both scenarios open, highlighting fixed-point annihilation as a potential constraint on five-dimensional asymptotic safety.

The BESIII Collaboration recently extracted the properties of the $X(2370)$ from a fit to the one-dimensional $K_S^0K_S^0\pi^0$ invariant-mass spectrum in $J/\psi\to\gamma K_S^0K_S^0\pi^0$. The intermediate two-body structures visible in the mass correlations, including the $K_0^*(1430)$ bands, require a coherent treatment of cross-channel interference when interpreting the enhancement near 2.3 GeV. We reassess the need for an additional $X(2370)$ contribution by fitting the published data using an effective coupled-channel framework. The three-body parent amplitude is parameterized by a $K$-matrix as the scattering among several quasi-two-body channels. The seven- and eight-bare-state models give similar mass distributions. Adding the eighth bare state lowers the Poisson deviance by 1.26% and produces an additional pole at $E=(2424-i\,149)$ MeV, substantially broader than the $X(2370)$ mass-width reference. This pole is model-dependent, and its identification with the $X(2370)$ is not clear. The present analysis does not establish the need for an additional $X(2370)$ contribution in $J/\psi\to\gamma K_S^0K_S^0\pi^0$, thereby weakening the flavor-singlet argument based on the suppression of $K^*\bar K$ relative to the total $K\bar K\pi$ contribution. A more comprehensive experimental amplitude analysis, incorporating coherent interference, mass and angular correlations, and detector effects across related decay channels, is needed to establish the role and decay properties of the $X(2370)$.

One of the challenging components of modern lattice-QCD computations of the leading hadronic vacuum polarization contribution to the muon $(g-2)_\mu$ is the isospin-breaking correction due to electromagnetism. Dominated by long distances, this correction suffers from severe signal-to-noise issues and finite-volume effects. To provide infinite-volume benchmarks for various quark-level Wick contractions, we estimate their sizes phenomenologically at the physical point, using a previously developed vector-meson-dominance model. The pion contributions in this model sum to around $-7.1\times 10^{-10}$, dominated by the electromagnetic pion mass shift. The ultraviolet-finite (2+2)a ("dumbbell") contraction accounts for approximately two thirds of this model sum; for both, about 30% comes from Euclidean times beyond 2.8 fm.

We compute the chiral-odd form factors $H_T$, $E_T$ and $\hT$ of the nucleon in light-cone QCD sum rules, separately for the $u$ and $d$ quarks, and organise them into the tensor monopole, dipole and quadrupole moments $g_T$, $\kappa_T$ and $Q_T$. The quadrupole moment, with no chiral-even counterpart at leading twist, and the isoscalar channel, whose sum rules were derived but never evaluated, are new in this framework. The form factors are read from a Lorentz basis independent only after canonical ordering of the Dirac strings; three of the eight surviving structures give the three form factors separately, and the one usually used for the tensor charge is not among the eight. Two exact results follow analytically. The $d$-quark contributions to $E_T$ and $\hT$ are equal and opposite in the chiral limit, broken in proportion to the quark mass and the twist-six amplitude $\mathcal{V}_6$, so the $d$-quark sector carries a single independent function; and the isoscalar tensor charge receives no leading-twist contribution, its twist-three terms cancelling between the flavours. Neither is visible without resolving the flavours. At $\mu^2=1$~GeV$^2$ the two distribution-amplitude sets give $g_T^{u-d}=1.27(7)$, $1.08(6)$, $\kappa_T^{u-d}=1.35(62)$, $1.58(59)$, $Q_T^{u-d}=-4.40(83)$, $-4.20(73)$ and $g_T^{u+d}=0.39(7)$, $0.38(6)$, $\kappa_T^{u+d}=4.47(62)$, $4.32(59)$, $Q_T^{u+d}=2.41(53)$, $1.56(30)$. The mean-field relation $2\hT^{u-d}=-E_T^{u-d}$, tested without any large-$N_c$ assumption, holds in sign and order of magnitude, with ratio $0.64(16)$ and $0.67(15)$ against the predicted unity. In the impact-parameter plane the moments displace the two flavour distributions in opposite transverse directions by nearly equal amounts, $\langle b_y\rangle=0.37$ and $-0.37$~fm, and elongate both across the polarisation axis, the $d$ quark some five to six times more strongly

Understanding the dynamics of interacting quantum fields remains a fundamental challenge. We propose a superconducting transmission line for analog quantum simulation of $(1+1)$-dimensional $\phi^4$ field theory. The transmission line comprises fluxonium-like circuit elements whose continuous and unbounded phase variables encode a scalar field without Hilbert-space truncation. Their anharmonic potentials provide strong interactions. Tuning the circuit parameters provides access to two distinct regimes. In the first, the transmission line emulates $\phi^4$ field theory with a single-well potential. We confirm this correspondence through lattice Monte Carlo calculations of the low-energy spectra of both the circuit and lattice $\phi^4$ theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates $\phi^4$ theory in the symmetry-broken phase and hosts degenerate vacua. Interfaces between the two vacua form topological kinks, and the transmission line can simulate kink-antikink collisions. We present state preparation and measurement protocols for both collision experiments, enabling spatially resolved, real-time studies of particle and soliton scattering in an interacting quantum field theory.

I propose a Hamiltonian framework for chiral gauge theories (CGT) based on a Euclidean formulation which uses 2n dimensional chiral fermions on the boundary of a 2n+1 dimensional disk. In the original Euclidean formulation, boundary gauge fields were extended into the bulk using $2n + 1$ dimensional gauge field equations of motion (EOM) which creates a bottleneck for constructing a Hamiltonian. I present an alternate proposal for extending the gauge fields into the bulk that is compatible with both a Hamiltonian framework and a Euclidean path integral. Applying this to Abelian gauge fields produces exact expressions of interior fields as a functional of the boundary fields, which can be directly used in a Hamiltonian formulation. Euclidean analysis of the new gauge field extension shows that it can preserve the non-perturbative content of the original construction, including the behavior of topological charge, associated chiral fermion zero modes and an absence of the strong CP problem when applied to the Standard Model. This construction opens up a route to a Hamiltonian treatment and future quantum simulation of CGTs on a disk boundary.

Estimating the symbolic or analytical form of probability density functions (PDFs) from observed samples is a fundamental challenge in statistical and computational modelling. This process is critical for deriving interpretable and generalizable relationships characterizing the underlying phenomenon. Traditionally, this estimation depends strongly on domain expertise and prior field-specific knowledge, with experts selecting appropriate functional forms or parametric families based on empirical evidence and theoretical understanding. The coefficients of these forms are then typically determined through parameter estimation. In this paper, we develop a framework for estimating symbolic expressions of unnormalized distributions from observed samples using domain-specific prior knowledge, such as the range of interactions and a predefined set of primitive functions. We integrate deep generative models with symbolic regression (SR), incorporating inductive biases, such as factorizing large distributions, to keep the problem tractable. The deep generative models we examine include likelihood-based models, viz., flow models, and score-based models. Experiments show the effectiveness of the proposed framework for estimating density functions for multivariate toy distributions as well as lattices from computational physics, namely, XY model and $\phi^4$ theory. When applied to the renormalization problem in $\phi^4$ theory, the proposed framework estimates compact symbolic approximations of the hamiltonian function at different scales directly from samples, yielding expressions that may be challenging to derive using traditional perturbative or analytic approaches in nonperturbative settings.

We present results from a detailed finite-size scaling analysis of the $3$-$d$, $Z(2)$ and $O(2)$ spin models in an external field $H$. Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to $\widetilde{z}_L^2=1/(H L^{3/(1+1/\delta))})^{2}$. This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing $H$. In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3$-$d$, $O(2)$ and $Z(2)$ universality classes.

Motivated by the recent HAL QCD lattice results on the $D$ - $D^*$ potential at nearly physical point $m_\pi=146.4$ MeV, we theoretically examine effects from the two-pion exchange in (semi-)long-range parts of the $DD^*$ system. We employ the framework of heavy-meson chiral perturbation theory with heavy-quark spin symmetry. The pion exchanges up to next-to-next-to-leading order (N$^2$LO) are taken into account. In order to separate the (semi-)long-range contributions, we apply the dispersion-relation method to one-loop diagrams. As a result, we find that the lattice data on the $D$ - $D^*$ potential in the regime of $0.5\, {\rm fm} \lesssim r$ is reproduced by adjusting the unknown $O(p^2)$ couplings. In particular, it turns out that contributions from isospin-independent N$^2$LO triangle diagrams play a central role in reproducing the lattice data of the form $V^{DD^*}\sim \left({\rm e}^{-m_\pi r}/r\right)^2$ in $1.0\, {\rm fm} \lesssim r\lesssim 2.0\, {\rm fm}$. We also present predictions of other $D^{(*)}$ - $D^{(*)}$ potentials, where the similar two-pion exchange tail is predicted. Our findings provide useful information on the (semi-)long-range regime of the $D$ - $D^*$ potential focusing on two-pion exchanges.

We present a lattice determination of the Bjorken sum rule via a Feynman-Hellmann calculation of the polarised forward Compton amplitude. We evaluate the lowest moment of the nucleon's polarised structure function, $g_1$, which we calculate over the range $0.5\lesssim Q^2 \lesssim 8$ GeV$^2$, covering both non-perturbative and perturbative regions. We compare our calculated moments with the Bjorken sum rule, and discuss implications for the calculation of higher-twist effects, as well as evaluations of $\alpha_s(Q^2)$ from hadronic quantities to complement phenomenological and other lattice methods.

The increasing diversity of high performance computing systems makes separate, architecture specific implementations of lattice gauge theory algorithms costly to maintain. We present kwqft, a performance portable Kokkos implementation of Wilson pure gauge Monte Carlo simulation for $\mathrm{SU}(N)$ Yang-Mills theory in an arbitrary number of space-time dimensions. The gauge group order $N$ and the dimension $D$ are compile time parameters. A single source targets the Serial, OpenMP, CUDA, HIP, and SYCL execution spaces, with MPI halo exchange overlapped with interior updates. The implementation reproduces the exact two-dimensional plaquette and published three and four dimensional values for gauge groups up to $\mathrm{SU}(17)$. On an NVIDIA A100 the Kokkos CUDA backend is competitive with a native CUDA code, SIMD acceleration improves the OpenMP path on Armv9 processors, and a large scale speedup is demonstrated for an $\mathrm{SU}(4)$ lattice on the LineShine supercomputer, currently ranked first on the TOP500 list.

In the Wilson formulation of lattice gauge theory, the fundamental degrees of freedom are group-valued link variables, while the action is a sum over the trace of the plaquettes, the smallest Wilson loops. For generative sampling methods such as normalizing flows, this poses a challenge: the distribution of an individual plaquette is easy to model, but mapping sampled plaquettes to the links is the obstruction. We explore a statistical way around this in two dimensions for the $\mathrm{SU}(N)$ gauge theory with the Wilson plaquette action. The action can be written in terms of holonomy variables, which determine the links once a consistency condition at the four corners of an extended lattice is satisfied. Using a boundary condition that only affects the holonomies, we trade this consistency condition for a conditional sampling problem, which reduces to sampling $X,Y\in\mathrm{SU}(N)$ given the group commutator $Z=XYX^\dagger Y^\dagger$, where $Z\in\mathrm{SU}(N)$ depends on the four corners. Plaquettes are sampled independently, and the resulting configurations carry weights due to the additional conditional sampling. We obtain the density of $Z$, which determines these weights, in closed form for $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$. A normalizing flow models the single-plaquette distribution for $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$; for the group-commutator problem we use a closed-form sampler for $\mathrm{SU}(2)$ and a trained normalizing flow for $\mathrm{SU}(3)$. In our tests on $2\times2$ and $32\times32$ lattices at two couplings each, per-plaquette acceptance rates exceed $99\%$ and the effective sample size of the final weights is moderate, typically above one half.

We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.

We present the first holographic study of gravitational form factors (GFFs) of scalar, pseudoscalar and canonical-spin-averaged tensor glueball targets. These observables test gravitational cubic couplings whose physical validity is not established by spectra and static-force calibration. We construct a dynamical Einstein–scalar–axion representation inspired by the Babington–Crooks–Evans adjoint-mass deformation of $\mathcal N=4$ super-Yang–Mills theory and its Type-IIB supergravity dual. Leading ultraviolet source data are retained, while a soft-wall-like infrared reconstruction incorporates asymptotically linear radial mass-squared trajectories. Spectra and Wilson observables fix the parameters at a common Sommer scale without GFF input. The full constrained cubic vertices fail to describe 27 correlated scalar lattice observations, giving $\chi^2/\mathrm{dof}=73.60/27=2.73$. We propose normalized heavy-target (HT) effective cubic couplings for pure-glue matching. HT adopts leading radial shapes suggested by infinitely heavy targets at fixed probe dynamics and normalizes their overlap weights on the physical ground states. With the background, modes and propagators unchanged, HT gives $\chi^2/\mathrm{dof}=16.98/27=0.63$, without numerical adjustment to GFF data. Tensor and scalar source overlaps determine $A$ and the physical normalized trace; the exact finite-mass energy–momentum-tensor relation determines $D$. We predict the pseudoscalar and tensor form factors and three-target Breit pressure and shear profiles. On the reference infrared-decaying axion branch, the HT Breit mass radii are $0.276$, $0.300$ and $0.311\,\mathrm{fm}$, respectively. The results identify gravitational cubic matching as a distinct step beyond background calibration and provide a prescription for further lattice tests.