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DOE OSTI2025

Efficient lattice QCD computation of radiative-leptonic-decay form factors at multiple positive and negative photon virtualities

In previous work [D. Giusti, 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 $D_s → ℓνγ*$ 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

$Ξ$ 𝑐 → $Ξ$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of $Ξ^0_𝑐$ decay rates

We present a lattice quantum chromodynamics (QCD) determination of the vector and axial-vector form factors that describe the charm-baryon semileptonic decays Ξ 𝑐 → Ξ⁢ℓ + ⁢𝜈 ℓ . The calculation uses a domain-wall action for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles of gauge-field configurations generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. We present Standard Model predictions for the decay rates and branching fractions of Ξ$^0_𝑐$ → Ξ$^−_𝑐$⁢ℓ + ⁢𝜈 ℓ and Ξ$^+_𝑐$ → Ξ$^0_𝑐$⁢ℓ + ⁢𝜈 ℓ for ℓ =𝑒, 𝜇. In particular, we obtain Γ⁡(Ξ$^0_𝑐$ → Ξ − ⁢𝑒 + ⁢𝜈 𝑒 )/|𝑉 𝑐⁢𝑠 | 2 = 0.2515⁢(73) ps −1 and ℬ⁡(Ξ$^0_𝑐$ → Ξ − ⁢𝑒 +⁢ 𝜈 𝑒 ) = 3.58⁢(12)%. These values are higher than those predicted by a previous lattice calculation and substantially higher than the experimentally measured values, but consistent with expectations from approximate 𝑆⁢𝑈⁡(3) flavor symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

$Ξ$ 𝑏 → $Ξ$ form factors from lattice QCD and standard-model predictions for $Ξ$ 𝑏 → $Ξ$⁢𝜇 + ⁢𝜇 − and $Ξ$ 𝑏 → $Ξ$⁢𝛾 decays

We present the first lattice QCD determination of the $Ξ$ 𝑏 → $Ξ$ vector, axial-vector, and tensor form factors, which are relevant for the theory of rare decays including $Ξ$ 𝑏 → $Ξ$⁢ℓ + ⁢ℓ − and $Ξ$ 𝑏 → $Ξ$⁢𝛾. The calculation is performed with 2+1 flavors of domain-wall fermions at three different lattice spacings and pion masses in the range from approximately 430 to 230 MeV. The bottom quark is implemented using an anisotropic clover action. Three-point functions with a wide range of source-sink separations and model averaging are used to extract the ground-state contributions. We fit the dependence of the form factors on the momentum transfer, the pion mass, and the lattice spacing using modified 𝑧 expansions that account for subthreshold branch cuts, and apply dispersive bounds and asymptotic behavior constraints to achieve controlled uncertainties in the full semileptonic kinematic region. Using our form factor results, we present standard model predictions for the $Ξ$$^{−}_{𝑏}$ → $Ξ$ − ⁢𝛾 and $Ξ$$^{−}_{𝑏}$ → $Ξ$ − ⁢𝜇 + ⁢𝜇 − branching fractions and two angular observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Binding energy of the 𝑇 𝑏⁢𝑏 tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions

We present a new determination of the $b\bar{b}$𝑢⁢𝑑 (𝐽 𝑃 = 1 + , 𝐼 = 0) tetraquark binding energy using lattice quantum chromodynamics (QCD) with domain-wall light quarks and a nonperturbatively tuned three-parameter anisotropic-clover “relativistic” action for the 𝑏 quarks. We also perform a direct comparison with a reanalysis of data generated in prior work using a lattice-nonrelativistic QCD (NRQCD) action for the 𝑏 quarks and otherwise identical parameters. Using the new data with relativistic 𝑏 quarks from seven different ensembles with multiple lattice spacings and pion masses, we perform combined chiral and continuum extrapolations and obtain (𝑚 𝑇 𝑏⁢𝑏 −𝑚 𝐵 −𝑚 𝐵* ) RHQ =(−76 ±23) MeV. For the NRQCD data from five ensembles, we perform chiral-only extrapolations and obtain (𝑚 𝑇 𝑏⁢𝑏 −𝑚 𝐵 −𝑚 𝐵* ) NRQCD = (−74 ±17 ±10) MeV. The lower magnitude of the results obtained here, compared to the original analysis in [Phys. Rev. D 100, 014503 (2019)], is due to the use of the symmetric parts of the correlation matrices with local four-quark operators only.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Programmable exploration of magnetic states in Lieb-kagome interpolated lattices

We investigate a hybrid modeling framework in which a quantum annealer is used to simulate magnetic interactions in molecular qubit lattices inspired by experimentally realizable systems. Using phthalocyanine assemblies as a structurally constrained prototype, we model a continuous deformation from a Lieb to a kagome lattice, revealing frustration-driven disorder and magnetic field-induced reordering in the spin structure. Here, the goal is to show how a quantum annealer can operate as a physically instantiated, programmable platform to emulate experimentally relevant lattice deformations and produce observables in a manner analogous to an experimental measurement, enabling the characterization of magnetic arrangements beyond the reach of current molecular architectures. This surrogate modeling approach offers a pathway to explore and iteratively design tunable magnetic states in synthetic materials. The synthetic design, structural characterization, and quantum simulation framework established here defines a modular and scalable paradigm for probing the limits of engineered matter across chemistry, condensed matter, and quantum information science.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2022

Cold-atom quantum simulator for string and hadron dynamics in non-Abelian lattice gauge theory

We propose an analog quantum simulator for simulating real-time dynamics of (1+1)-dimensional non-Abelian gauge theory well within the existing capacity of ultracold-atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a one-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on the loop string hadron formalism of SU(2) lattice gauge theory, this simulation technique is completely SU(2) invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is scalable and particularly effective in simulating the theory in the weak-coupling regime, and also a bulk limit of the theory in the strong-coupling regime up to certain approximations. This paper also presents a numerical benchmark comparison of the exact spectrum and real-time dynamics of lattice gauge theory to that of the atomic Hamiltonian with an experimentally realizable range of parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Nearly optimal state preparation for quantum simulations of lattice gauge theories

Here, we present several improvements to the recently developed ground-state preparation algorithm based on the quantum eigenvalue transformation for unitary matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in (2+1) dimensions, as well as propose an alternative application of QETU, a highly efficient preparation of Gaussian distributions. The QETU technique was originally proposed as an algorithm for nearly optimal ground-state preparation and ground-state energy estimation on early fault-tolerant devices. It uses the time-evolution input model, which can potentially overcome the large overall prefactor in the asymptotic gate cost arising in similar algorithms based on the Hamiltonian input model. We present modifications to the original QETU algorithm that significantly reduce the cost for the cases of both exact and Trotterized implementation of the time evolution circuit. We use QETU to prepare the ground state of a U(1) lattice gauge theory in two spatial dimensions, explore the dependence of computational resources on the desired precision and system parameters, and discuss the applicability of our results to general lattice gauge theories. We also demonstrate how the QETU technique can be utilized for preparing Gaussian distributions and wave packets in a way which outperforms existing algorithms for as little as n q ≳ 2–5 qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Spin excitations in the kagome-lattice metallic antiferromagnet Fe 0.89 Co 0.11 Sn

Kagome-lattice materials have attracted tremendous interest due to the broad prospect for seeking superconductivity, quantum spin liquid states, and topological electronic structures. Among them, the transition-metal kagome lattices are high-profile objects for the combination of topological properties, rich magnetism, and multiple-orbital physics. Here we report an inelastic neutron scattering study on the spin dynamics of a kagome-lattice antiferromagnetic metal Fe 0.89 Co 0.11 Sn. Although the magnetic excitations can be observed up to ~250 meV, well-defined spin waves are only identified below ~90 meV and can be modeled using Heisenberg exchange with ferromagnetic in-plane nearest-neighbor coupling J 1 , in-plane next-nearest-neighbor coupling J 2 , and antiferromagnetic (AFM) interlayer coupling J c under linear spin-wave theory. Above ~90 meV, the spin waves enter the itinerant Stoner continuum and become highly damped particle-hole excitations. At the K point of the Brillouin zone, we reveal a possible band crossing of the spin wave, which indicates a potential Dirac magnon. Finally, our results uncover the evolution of the spin excitations from the planar AFM state to the axial AFM state in Fe 0.89 Co 0.11 Sn, solve the magnetic Hamiltonian for both states, and confirm the significant influence of the itinerant magnetism on the spin excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Crystal field splittings and magnetic ground state of the square-lattice antiferromagnets YbBi 2 ⁢ClO 4 and YbBi 2 ⁢IO 4 with J eff = $\frac{1}{2}$

Here, we report on the crystal field level splitting and magnetic ground state of the J eff = $\frac{1}{2}$ square lattice antiferromagnets YbBi 2 ⁢ClO 4 and YbBi 2 ⁢IO 4 using powder inelastic neutron scattering (INS) and neutron diffraction measurements. Both compounds exhibit a well-isolated Γ 7 doublet ground state under a tetragonal crystal field environment, confirming a robust J eff = $\frac{1}{2}$ picture with slight XY-type anisotropic character in the g-tensor. Notably, the ground state wave functions closely resemble the Γ 7 doublet expected in the perfect cubic limit, consistent with the nearly cubic ligand configuration of eight O 2- ions surrounding Yb 3+ . Below T N = 0.21 K, YbBi 2 ⁢IO 4 exhibits a stripe long-range magnetic order characterized by an ordering wave vector q m = (1/2, 0, 0) or its symmetry-equivalent (0, 1/2, 0), with magnetic moments aligned along q m . The ordered moment is approximately 79% of the classical prediction, significantly larger than expected from the isotropic J 1 -J 2 model, suggesting the possible involvement of exchange anisotropy in explaining this observation. We show that symmetry-allowed XXZ and bond-dependent anisotropic exchange terms in a square lattice can play a critical role in stabilizing the stripe order and suppressing the moment reduction as observed. These findings establish YbBi 2 ⁢ClO 4 and YbBi 2 ⁢IO 4 as unique platforms for exploring rich J eff = $\frac{1}{2}$ magnetism from two less investigated perspectives: (i) on a square lattice and (ii) within a (nearly) cubic ligand environment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Lattice model of heavy-light three-body system

We present a study of a $1+1$ dimensional heavy-light three-body system in finite volume. The heavy-light system is simulated by a coupled-channel $\phi^4$ type lattice model, and both ground state and excited states of multiparticle energy spectra are measured on various lattices. The lattice simulation data analysis is performed based on variational approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Geometric quantum information structure in quantum fields and their lattice simulation

An upper limit to distillable entanglement between two disconnected regions of massless noninteracting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. Here, we highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

A study of two-pion scattering for the isospin channels, 𝐼 = 0 and 𝐼 = 2, using lattice QCD is presented. Möbius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of 𝐿 = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states—two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the 𝐼 = 0 and 𝐼 = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for 𝐼 = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying 𝐾 → 𝜋⁢𝜋 decay, on physical-mass ensembles using the GEVP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Light-quark connected intermediate-window contributions to the muon 𝑔 − 2 hadronic vacuum polarization from lattice QCD

We present a lattice-QCD calculation of the light-quark connected contribution to window observables associated with the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a^{HVP,LO}_μ$. We employ the MILC Collaboration’s isospin-symmetric QCD gauge-field ensembles, which contain four flavors of dynamical highly improved staggered quarks with four lattice spacings between $a ≈ 0.06-0.15$ fm and close-to-physical quark masses. We consider several effective-field-theory-based schemes for finite volume and other lattice corrections and combine the results via Bayesian model averaging to obtain robust estimates of the associated systematic uncertainties. After unblinding, our final results for the intermediate and "W2" windows are $a^{U,W}_μ$(conn) = 206.6(1.0) x 10 -10 and $a^{U,W2}_μ$ (conn) = 100.7(3.2) x 10 -10 , respectively

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Counting linearly polarized gluons with lattice QCD

We outline an approach to calculate the transverse-momentum-dependent distribution of linearly polarized gluons inside an unpolarized hadron on the lattice with the help of large momentum effective theory. To achieve this purpose, we propose calculating a Euclidean version of the degree of polarization for a fast-moving hadron on the lattice, which is ultraviolet finite, and no soft function subtraction is needed. It indicates a practical way to explore the distribution of the linearly polarized gluons in a proton and the linearly polarized gluon effects in hadron collisions on the lattice.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Eigenstate thermalization in ( 2 + 1 )-dimensional SU(2) lattice gauge theory

We present preliminary numerical evidence for the hypothesis that the Hamiltonian SU(2) gauge theory discretized on a lattice obeys the eigenstate thermalization hypothesis (ETH). To do so we study three approximations: (a) a linear plaquette chain in a reduced Hilbert space limiting the electric field basis to j = 0 , 1 2 , (b) a two-dimensional honeycomb lattice with periodic or closed boundary condition and the same Hilbert space constraint, and (c) a chain of only three plaquettes but such a sufficiently large electric field Hilbert space ( j ≤ 7 2 ) that convergence of all energy eigenvalues in the analyzed energy window is observed. While an unconstrained Hilbert space is required to reach the continuum limit of SU(2) gauge theory, numerical resource constraints do not permit us to realize this requirement for all values of the coupling constant and large lattices. In each of the three studied cases we check first for random matrix theory (RMT) behavior in the eigenenergy spectrum and then analyze the diagonal as well as the off-diagonal matrix elements between energy eigenstates for a few operators. Within current uncertainties all results for (a), (b) and (c) agree with ETH predictions. Furthermore, we find the off-diagonal matrix elements of the electric energy operator exhibit RMT behavior in frequency windows that are small enough in (b) and (c). To unambiguously establish ETH behavior and determine for which class of operators it applies, an extension of our investigations is necessary. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Operator product expansion for radial lattice quantization of 3D ϕ 4 theory

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3D Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the quantum finite elements method to implement radially quantized critical ϕ 4 theory on simplicial lattices approaching R × S 2 . Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions Δ ε and Δ T as well as ratios of the operator product expansion coefficients f σ σ ε and f σ σ T of the first spin-0 and spin-2 primary operators ε and T of the 3D Ising CFT. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Control variates for lattice field theory

In most lattice field theories, correlators are plagued by a signal-to-noise problem of exponential difficulty in the time separation. We propose a method for improving the signal-to-noise ratio, in which control variates are systematically constructed from lattice Schwinger-Dyson relations. The method is demonstrated on various two-dimensional lattices in scalar field theory, and a strategy for scaling to larger systems is explored. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Nucleon tomography and total angular momentum of valence quarks from synergy between lattice QCD and elastic scattering data

We present an exploratory work on integrating lattice-QCD results with experimental data for elastic scattering. Within the framework of generalized parton distributions, this approach allows for the extraction of detailed information about nucleon tomography and the total angular momentum carried by valence quarks. To accomplish this reliably, we introduce a new quantity, the “double ratio,” which significantly reduces the systematic uncertainties inherent in lattice QCD computations. Moreover, we introduce a “shadow” term in the extraction procedure, which is sensitive only to lattice-QCD results. This term allows us to investigate the model dependence of the extraction, providing a more flexible description of the nucleon that goes beyond the previously considered bell-shaped distribution.

Lattice QCD↗