In this work, we investigate the time-like pion form factor from lattice QCD in the isosymmetric limit, a quantity that plays an important role in understanding hadron physics with substantial phenomenological applications. This observable can be calculated in the elastic region using the finite-volume approach, up to the first (four-particle) open channel. With the goal of accessing the exclusive two-pion form factor in the inelastic region, starting from a three-point correlator involving the vector current and two (temporally-displaced) pion interpolating operators, we examine the associated underlying spectral density and calculate the form factor using a formalism based on the LSZ reduction. A preliminary analysis on one ensemble generated by the RBC/UKQCD collaboration using domain-wall fermions is presented.

The knowledge of isospin-breaking effects in hadronic τ decays is required for a high-precision determination of the Hadronic-Vacuum-Polarization contribution to (g-2)_μ from experimental τ data. In this work we present a strategy for their calculation in a fully inclusive setup from first-principles Lattice QCD+QED simulations. We separate radiative corrections in three infrared safe classes, which we study individually. We provide analytic expressions for their effects in the initial state and propose a strategy for final-state corrections directly in Euclidean space. We also examine the non-factorizable contributions and highlight the challenges associated with their analytic continuation from Euclidean to Minkowski space. By studying short-distance corrections in the context of momentum schemes, we provide a prescription for the renormalization of the individual terms at first order in the ispospin-breaking parameters.

We present a study using the distillation method to analyze the spectra of nucleon, nucleon-pion, and nucleon-pion-pion states in the positive-parity sector, as well as nucleon and nucleon-pion states in the negative-parity sector. The study uses seven domain-wall fermion ensembles with varying pion masses (mor = 139-279 MeV), lattice spacings (a-1 = 1.730 GeV and a-1 = 2.359 GeV) and volumes (morL = 3.8-7.5). To address the large number of contractions in this project, we implemented an algorithm to automate the contraction of nucleon-pion correlation functions that contain an arbitrary number of pions. In the positive-parity sector, we extrapolate the nucleon mass to the physical point. This study demonstrates the effectiveness of the distillation method for baryonic quantities with a focus on multihadronic states and establishes a foundation for future work.

Lattice QCD simulations are computationally expensive, with the solution of the Dirac equation being the major computational bottleneck of many calculations. We introduce a novel gauge-equivariant neural-network architecture for preconditioning the Dirac equation in the regime where critical slowing down occurs. We study the behavior of this preconditioner as a function of topological charge and lattice volume and show that it mitigates critical slowing down. We also show that this preconditioner transfers to unseen gauge configurations without any retraining, therefore enabling applications not possible with competing methods.

The long-distance contribution of QED corrections to the hadronic vacuum polarization is particularly challenging to compute in lattice QCD + QED. Currently, it is one of the limiting factors toward matching the precision of the recent result by the Fermilab E989 experiment for the muon g - 2. In this work, we present a method for obtaining high-precision results for this contribution by reconstructing exclusive finite-volume state contributions. We find relations between the pion-photon contributions of individual diagrams and demonstrate the reconstruction method with lattice QCD + QED data at a single lattice spacing of a-1 1.73 GeV and m pi 275 MeV.

In the recent Muon g-2 Theory Initiative white paper update, the hadronic vacuum polarization (HVP) contribution -- which dominates the theoretical uncertainty -- is evaluated as an average of different lattice QCD calculations. Since lattice simulations are mostly carried out in isospin symmetric QCD, corrections due to the mass difference of the up and down quarks and the coupling to photons have to be accounted for. These isospin breaking effects are of order 1\% and can be treated as corrections to the result for the HVP contribution in isospin symmetric QCD. In the current estimate of the HVP contribution, these effects are a large source of uncertainty due to the extensive computational cost to compute all occurring Wick contractions and degrading signal-to-noise behaviour especially for quark disconnected diagrams. We present the current status of the calculation of isospin breaking corrections in the HVP contribution for the RBC/UKQCD collaborations. We use a dataset of propagators computed using stochastic coordinate sampling (SCS) to construct all necessary Wick contractions for the electromagnetic and strong isospin breaking effects. We employ different versions of QED on the lattice, such as QED$_L$, QED$_r$ and QED$_\infty$ to improve our estimate of finite-volume uncertainties.

The separation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment into Euclidean windows allows for a tailored approach to address the different dominant challenges at short, intermediate, and long distances. We present a novel approach to compute the short-distance window without the need for using perturbative QCD. We combine a quenched continuum extrapolation using 18 lattice spacings (1.6 GeV a-1 6.1 GeV) with a separate continuum extrapolation of the sea quark effects. This method allows for the computationally expensive sea quark effects to be estimated using only a smaller number of ensembles at coarser lattice spacings, while largely confining the logarithmic dependency of the continuum extrapolation to the quenched component.

The Field-Transformation Hybrid Monte-Carlo (FTHMC) algorithm potentially mitigates the issue of critical slowing down by combining the HMC with a field transformation, originally proposed by Lüscher and motivated as trivializing the theory. For the transformation, we use a single invertible discrete smearing step inspired by the Wilson flow but which resembles a Jacobian-computable generalisation of the stout smearing step. This is applied to a system with Iwasaki gauge fields and 2+1 Domain-Wall fermions. We have studied the effect of different smearing parameter values on autocorrelation times of Wilson-flowed energies with different flow time. We have found a reduction of exponential autocorrelation times for infra-red observables such as Wilson flowed energy densities and topological charge densities when a larger value of the smearing parameter is used. The autocorrelation times of local observables are computed using an approach akin to the master-field technique, allowing us to estimate the effect of the field transformation with different parameters based on a small number of configurations.

In previous work [D. Giusti, et al., Methods for high-precision determinations of radiative-leptonic decay form factors using lattice QCD, Phys. Rev. D 107, 074507 (2023)], we showed that form factors for radiative leptonic decays of pseudoscalar mesons can be determined efficiently and with high precision from lattice QCD using the "three-dimensional (3D) method," in which three-point functions are computed for all values of the current insertion time and the time integral is performed at the data-analysis stage. Here, we demonstrate another benefit of the 3D method: the form factors can be extracted for any number of nonzero photon virtualities from the same three-point functions at no extra cost. We present results for the Ds -* l nu gamma* vector form factor as a function of photon energy and photon virtuality, for both positive and negative virtuality, for a single ensemble with 340 MeV pion mass and 0.11 fm lattice spacing. In our analysis, we separately consider the two different time orderings and the different quark flavors in the electromagnetic current. We discuss in detail the behavior of the unwanted exponentials contributing to the three-point functions, as well as the choice of fit models and fit ranges used to remove them for various values of the virtuality. While positive photon virtuality is relevant for decays to multiple charged leptons, negative photon virtuality suppresses soft contributions and is of interest in QCD-factorization studies of the form factors.

We develop a method to compute the pion transition form factor directly at arbitrary space-like photon momenta and use it to determine theπ0-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon. The calculation is performed using eight gauge ensembles generated with 2+1 flavor domain wall fermions, incorporating multiple pion masses, lattice spacings, and volumes. By introducing a pion structure function and performing a Gegenbauer expansion, we demonstrate that about 98% of theπ0-pole contribution can be extracted in a model-independent manner, thereby ensuring that systematic effects are well controlled. After applying finite-volume corrections, as well as performing chiral and continuum extrapolations, we obtain the final result for theπ0-pole contribution to the hadronic light-by-light scattering in the muon's anomalous magnetic moment,aμπ0-pole=61.2(1.7)×10-11, and theπ0decay width,Γπ0→γγ=7.60(27)eV.

We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the SU(N) group into the space of general complex matrices, MN(C). Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of W E MN(C) as the dynamical variables without group theoretic constraints. The framework enables us to introduce nonseparable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC.

The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, (g−2)/2, is computed in the infinite volume QED framework with lattice QCD. We report aμHLbL=12.47(1.15)(0.95)×10−10 where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor Möbius domain wall fermion ensemble with inverse lattice spacing a−1=1.73 GeV, lattice size L=5.5 fm, and mπ=139 MeV, generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations. Published by the American Physical Society 2025

The Riemannian Manifold HMC (RMHMC) is designed to tackle critical slowing down by utilizing a rational function of the SU(3) gauge covariant laplace operator in place of the canonical mass term in the HMC algorithm. The RMHMC has been demonstrated to be effective at increasing the rate of change of long-distance modes. We present the results of the recent studies done to tune the algorithm and improve its efficiency.

In previous work Phys. Rev. D 107, 074507 (2023), we showed that form factors for radiative leptonic decays of pseudoscalar mesons can be determined efficiently and with high precision from lattice QCD using the “3d method,” in which three-point functions are computed for all values of the current-insertion time and the time integral is performed at the data-analysis stage. Here, we demonstrate another benefit of the 3d method: the form factors can be extracted for any number of nonzero photon virtualites from the same three-point functions at no extra cost. We present results for the D_s→^* vector form factor as a function of photon energy and photon virtuality, for both positive and negative virtuality. In our analysis, we separately consider the two different time orderings and the different quark flavors in the electromagnetic current. We discuss in detail the behavior of the unwanted exponentials contributing to the three-point functions, as well as the choice of fit models and fit ranges used to remove them for various values of the virtuality. While positive photon virtuality is relevant for decays to multiple charged leptons, negative photon virtuality suppresses soft contributions and is of interest in QCD-factorization studies of the form factors.

We demonstrate that gauge-equivariant pooling and unpooling layers can perform as well as traditional restriction and prolongation layers in multigrid preconditioner models for lattice QCD. These layers introduce a gauge degree of freedom on the coarse grid, allowing for the use of explicitly gauge-equivariant layers on the coarse grid. We investigate the construction of coarse-grid gauge fields and study their efficiency in the preconditioner model. We show that a combined multigrid neural network using a Galerkin construction for the coarse-grid gauge field eliminates critical slowing down.

We compute the standard Euclidean window of the hadronic vacuum polarization using multiple independent blinded analyses. We improve the continuum and infinite-volume extrapolations of the dominant quark-connected light-quark isospin-symmetric contribution and address additional sub-leading systematic effects from sea-charm quarks and residual chiral-symmetry breaking from first principles. We find $a_\mu^{\rm W} = 235.56(65)(50) \times 10^{-10}$, which is in $3.8\sigma$ tension with the recently published dispersive result of Colangelo et al., $a_\mu^{\rm W} = 229.4(1.4) \times 10^{-10}$, and in agreement with other recent lattice determinations. We also provide a result for the standard short-distance window. The results reported here are unchanged compared to our presentation at the Edinburgh workshop of the g-2 Theory Initiative in 2022.

We present a study of lattice-QCD methods to determine the relevant hadronic form factors for radiative leptonic decays of pseudoscalar mesons. We provide numerical results for $D_s^+ \to \ell^+ \nu \gamma$. Our calculation is performed using a domain-wall action for all quark flavors and on a single RBC/UKQCD lattice gauge-field ensemble. The first part of the study is how to best control two sources of systematic error inherent in the calculation, specifically the unwanted excited states created by the meson interpolating field, and unwanted exponentials in the sum over intermediate states. Using a 3d sequential propagator allows for better control over unwanted exponentials from intermediate states, while using a 4d sequential propagator allows for better control over excited states. We perform individual analyses of the 3d and 4d methods as well as a combined analysis using both methods, and find that the 3d sequential propagator offers good control over both sources of systematic uncertainties for the smallest number of propagator solves. From there, we further improve the use of a 3d sequential propagator by employing an infinite-volume approximation method, which allows us to calculate the relevant form factors over the entire allowed range of photon energies. We then study improvements gained by performing the calculation using a different three-point function, using ratios of three-point functions, averaging over positive and negative photon momentum, and using an improved method for extracting the structure-dependent part of the axial form factor. The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration.

We demonstrate that a state-of-the-art multigrid preconditioner can be learned efficiently by gaugeequivariant neural networks. We show that the models require minimal retraining on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as communication avoidance are straightforward to implement in this framework.

The two pion channel in Lattice QCD has long been a primary testing ground for studying multiparticle scattering in finite volume QCD. With the development of sophisticated techniques such as distillation, it is possible to carefully study two-pion scattering in order to constrain associated low-energy constants. In this work, correlation functions with multiparticle interpolating operators are constructed to compute pion scattering phase shifts and scattering lengths in the isospin 0 and 2 channels with both sea and valence quarks at physical mass. Contamination from vacuum and thermal contributions are explicitly quantified with dedicated calculations and the results obtained after subtracting these nuisance terms are compared with the traditional correlator time series subtraction method. Two physical point ensembles with different lattice actions are used, and our finest ensemble gives results for scattering lengths and phase shifts consistent with phenomenology to within the reported statistical uncertainty.