arXiv subjects

Robert G. Edwards

Publications and source records attributed to Robert G. Edwards.

At least 19 recordsLinked to original sources

arXiv2026

First Two-Hadron Form Factor from QCD

We present the first QCD determination of an energy-dependent form factor for a two-hadron scattering state. In particular, we calculate the QCD contribution to the forward electromagnetic $\pi^+\pi^+ + \gamma\to\pi^+\pi^+$ amplitude at $m_\pi\approx 400$~MeV using lattice QCD. Because lattice calculations are performed in a finite Euclidean spacetime, where asymptotic scattering states are absent, this amplitude cannot be accessed directly from correlation functions. Instead, we can constrain this and related amplitudes nonperturbatively using a finite-volume formalism that requires two ingredients: the discrete finite-volume spectrum and finite-volume matrix elements of the electromagnetic current. We calculate three-point correlation functions coupling $\pi^+\pi^+$ finite-volume states and extract the corresponding electromagnetic matrix elements. Combining these results with the previously determined spectrum, we constrain the infinite-volume $\pi^+\pi^+ + \gamma\to\pi^+\pi^+$ amplitude in the forward limit. Using constraints from Lorentz symmetry, unitarity, and analyticity, we describe this amplitude in terms of a single real-valued energy-dependent two-hadron form factor. The resulting amplitude and form factor agree with the Ward-Takahashi identity across all energies and moving frames considered, providing the first QCD validation of this finite-volume approach and a pathway toward first-principles studies of the electromagnetic structure and electroweak responses of resonances and multi-hadron bound states.

hep-lat↗

arXiv2026

Femtoscale imaging of the proton with Ioffe-time distributions

Mapping how strongly interacting constituents are distributed within protons is a key goal of nuclear physics and a major direction of the future Electron Ion Collider program. We propose a novel space-time description of hadron structure in terms of impact-parameter Ioffe-time distributions, relating spatial density in the plane transverse to the proton momentum and the time between the probe's absorption and the product's emission in the longitudinal direction. Using lattice Quantum Chromodynamics, we perform the first calculation of the Ioffe-time-dependent mean squared proton radii and compare our results with estimates in the Goloskokov-Kroll model. We derive a relationship between the experimentally measurable Compton form factor and the generalized Ioffe-time distribution, which allows us to perform the first extraction of the Compton form factor from lattice calculations.

hep-ph↗

arXiv2026

Radiative decays of the $h_c$ meson from lattice QCD

We explore, for the first time in lattice QCD, the radiative decays to $\gamma \eta$ and $\gamma \eta'$ of the $J^{PC}=1^{+-}$ charmonium state, $h_c$. This work expands upon a previous calculation of $J/\psi$ decays to the same final states, incorporating novel technology to access the $h_c$ where it is an excited state and to separate the independent electric dipole and longitudinal form--factors. Results for the radiative decay rates, computed on three-flavor lattices with $m_\pi \sim $ 391 MeV show a suppression relative to experiment that is similar to that observed in the prior calculation of $J/\psi \to \gamma \eta^{(\prime)}$. The timelike $Q^2$ dependence of both form--factors together influence the Dalitz decays, $h_c \to \ell^+ \ell^- \eta^{(\prime)}$, which are as yet unmeasured experimentally.

hep-lat↗

arXiv2026

Reconstructing the full kinematic dependence of GPDs from pseudo-distributions

We propose a reconstruction of the full $(x, ξ, t)$ dependence of unpolarized isovector proton generalized parton distributions (GPDs) $H^{u-d}$ and $E^{u-d}$ from lattice QCD data in the pseudo-distribution formalism. For the first time, we extract double distributions (DDs) directly from lattice data, enforcing therefore an important property of GPDs linked to Lorentz symmetry. We use the flexible framework of multidimensional Gaussian process regression to regularize the inverse problem and present an assessment of the impact of model dependence on the systematic uncertainty. Our lattice ensemble corresponds to a pion mass $m_π= 358$~MeV and a lattice spacing $a = 0.094$~fm. We use larger hadron momenta, up to 2.7~GeV, and kinematic coverage compared to our previous computations and extract additional skewness-dependent moments of the GPD.

hep-lat↗

arXiv2026

$D\bar{D}$ interactions are weak near threshold in QCD

We study near-threshold $D\bar{D}$ scattering in $S$ and $D$-wave to determine whether or not resonances or bound states are present. Working in the approximation where charm-annihilation is forbidden, with two degenerate light-quark flavors and a heavier strange quark, isospin is a good quantum number, and the only other other channel that is kinematically open is $\eta_c\eta$. Using lattice QCD we compute, as a function of varying light-quark mass, the $S$-matrix for coupled-channel $\eta_c\eta - D\bar{D}$ scattering and find only weakly interacting meson pairs. In contrast to several other studies, we find no evidence for any bound-state or resonance singularity in the energy region between the deeply-bound $\chi_{c0}(1P)$ state and the $D_s\bar{D}_s$ threshold.

hep-lat↗

arXiv2025

Isotensor $πππ$ scattering with a $ρ$ resonant subsystem from QCD

This work presents a lattice quantum chromodynamics (QCD) determination of $πππ$ scattering amplitudes for the isospin-2 channel with angular momentum and parity $J^{P} = 1^+$. The calculation is performed using unphysically heavy light-quark masses, corresponding to a pion mass of $m_π \approx 400$~MeV, for which the $ρ$ meson manifests as a narrow resonance. The analysis employs a previously developed formalism that non-perturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for $ππ$ systems with isospins 1 and 2 with new determinations of the isospin-2 three-pion finite-volume spectrum, obtained for three cubic, periodic lattice volumes with box length ranging from $\approx 4/m_π$ to $6/m_π$. These combined data constrain the low-lying partial waves of the infinite-volume three-pion K matrix, from which we solve a set of coupled integral equations to extract the corresponding scattering amplitudes.

hep-lat↗

arXiv2025

Fast Algorithms for Scheduling Many-body Correlation Functions on Accelerators

Computation of correlation functions is a key operation in Lattice quantum chromodynamics (LQCD) simulations to extract nuclear physics observables. These functions involve many binary batch tensor contractions, each tensor possibly occupying hundreds of MBs of memory. Performing these contractions on GPU accelerators poses the challenge of scheduling them as to optimize tensor reuse and reduce data traffic. In this work we propose two fast novel scheduling algorithms that reorder contractions to increase temporal locality via input/intermediate tensor reuse. Our schedulers take advantage of application-specific features, such as contractions being binary and locality within contraction trees, to optimize the objective of minimizing peak memory. We integrate them into the LQCD analysis software suite Redstar and improve time-to-solution. Our schedulers attain upto 2.1x improvement in peak memory, which is reflected by a reduction of upto 4.2x in evictions, upto 1.8x in data traffic, resulting in upto 1.9x faster correlation function computation time.

cs.DC↗

arXiv2025

$η$ and $η'$ meson production in $J/ψ$ radiative decays from lattice QCD

We report on the computation of amplitudes describing the radiative decay processes $J/ψ\to γ\, η$ and $J/ψ\to γ\, η'$ from first principles via lattice QCD. Using lattices with two degenerate flavors of light quark and a heavier strange quark where $m_π\sim 391$ MeV, we compute three-point correlation functions using optimized meson operators with a range of momenta. The use of optimized operators allows access to the $η'$, even though it appears as an excited state, lying above the ground-state $η$ in the isoscalar pseudoscalar channel. Statistically precise signals are obtained in this disconnected process by averaging over large numbers of kinematically equivalent correlators. We determine transition form-factors as a function of photon virtuality across the timelike region, which describe also the 'Dalitz' processes $J/ψ\to e^+ e^- \, η^{(\prime)}$. Significantly lower magnitudes of transition form-factor for both the $η$ and $η'$ are found than those extracted from experimental data, and possible explanations for this observation are presented.

hep-lat↗

arXiv2025

$η$ and $η'$ production in $J/ψ$ radiative decays from quantum chromodynamics

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the $J/ψ$ into the light pseudoscalar mesons $η$ and $η'$. Within a lattice computation we obtain the transition form-factors as a function of photon virtuality from the timelike region, accessible experimentally via the 'Dalitz' decay $J/ψ\to e^+ e^-\, η^{(\prime)} $, through to the real photon point corresponding to $J/ψ\to γ\, η^{(\prime)} $. This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the $η'$ appears as the first-excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators, use of which also improves the purity of the $J/ψ$ and $η$ signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the $η'$ over the $η$ in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.

hep-lat↗

arXiv2024

Optimising stochastic algorithms for hadron correlation function computations in lattice QCD using a localised distillation basis

Distillation is a quark-smearing method for the construction of a broad class of hadron operators useful in lattice QCD computations and defined via a projection operator into a vector space of smooth gauge-covariant fields. A new orthonormal basis for this space is constructed which builds in locality. This basis is useful for the construction of stochastic methods to estimate the correlation functions computed in Monte Carlo calculations relevant for hadronic physics.

hep-lat↗

arXiv2024

Towards Unpolarized GPDs from Pseudo-Distributions

We present an exploration of the unpolarized isovector proton generalized parton distributions (GPDs) $H^{u-d}(x, ξ, t)$ and $E^{u-d}(x, ξ, t)$ in the pseudo-distribution formalism using distillation. Taking advantage of the large kinematic coverage made possible by this approach, we present results on the moments of GPDs up to the order $x^3$ -- including their skewness dependence -- at a pion mass $m_π= 358$ MeV and a lattice spacing $a = 0.094$ fm.

hep-lat↗

arXiv2024

Determination of crossing-symmetric $ππ$ scattering amplitudes and the quark mass evolution of the $σ$ constrained by lattice QCD

Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the $σ$, leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice--determined $ππ$ partial-wave scattering amplitudes with isospin--0,1,2. We will show that only certain combinations of amplitude parameterizations satisfy all constraints, and that when we restrict to these, the $σ$ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained $σ$ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance.

hep-lat↗

arXiv2023

Toward coherent quantum computation of scattering amplitudes with a measurement-based photonic quantum processor

In recent years, applications of quantum simulation have been developed to study properties of strongly interacting theories. This has been driven by two factors: on the one hand, needs from theorists to have access to physical observables that are prohibitively difficult to study using classical computing; on the other hand, quantum hardware becoming increasingly reliable and scalable to larger systems. In this work, we discuss the feasibility of using quantum optical simulation for studying scattering observables that are presently inaccessible via lattice QCD and are at the core of the experimental program at Jefferson Lab, the future Electron-Ion Collider, and other accelerator facilities. We show that recent progress in measurement-based photonic quantum computing can be leveraged to provide deterministic generation of required exotic gates and implementation in a single photonic quantum processor.

quant-ph↗

arXiv2023

Quark mass dependence of $ππ$ scattering in isospin 0, 1, and 2 from lattice QCD

Using lattice QCD we extract $ππ$ scattering amplitudes with isospin--0,1,2 in low partial-waves at two values of the light quark mass corresponding to $m_π\sim 283$ and $330$ MeV. We confirm expectations of weak repulsion in isospin--2, and the presence of a narrow $ρ$ resonance in isospin--1, and study the pion mass dependence of these channels. In isospin--0 we find that the two pion masses considered straddle the point at which the $σ$ transitions from being a stable bound-state to being either a virtual bound-state or a subthreshold resonance. We discuss the ability of lattice calculations like these to precisely determine the $σ$ pole location when it is a resonance, and propose an approach in which the full complement of amplitudes computed in this paper can be used simultaneously to provide more constraint.

hep-lat↗

arXiv2023

Charmonium $χ_{c0}$ and $χ_{c2}$ resonances in coupled-channel scattering from lattice QCD

In order to explore the spectrum of hidden-charm scalar and tensor resonances, we study meson-meson scattering with $J^{PC}=0^{++}, 2^{++}$ in the charmonium energy region using lattice QCD. Employing a light-quark mass corresponding to $m_π\approx 391$ MeV, we determine coupled-channel scattering amplitudes up to around 4100 MeV considering all kinematically relevant channels consisting of a pair of open-charm mesons or a charmonium meson with a light meson. A single isolated scalar resonance near 4000 MeV is found with large couplings to $D\bar{D}$, $D_s \bar{D}_s$ and the kinematically closed $D^* \bar{D}^*$ channel. A single tensor resonance at a similar mass couples strongly to $D\bar{D}$, $D\bar{D}^*$ and $D^* \bar{D}^*$. We compare the extracted resonances to contemporary experimental candidate states, previous lattice results and theoretical modeling. In contrast to several other studies, we do not find any significant feature in the scalar amplitudes between the ground state $χ_{c0}(1P)$ and the resonance found around 4000 MeV.

hep-lat↗

arXiv2023

Scalar and tensor charmonium resonances in coupled-channel scattering from QCD

We determine $J^{PC}=0^{++}$ and $2^{++}$ hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at $m_π\approx 391$ MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single $χ_{c0}$ and a single $χ_{c2}$ resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically-closed $D^* \bar{D}^*$ channels in $S$-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state $χ_{c0}$, no other scalar bound-states or near-$D\bar{D}$ threshold resonances are found, in contrast to several theoretical and experimental studies.

hep-lat↗

arXiv2022

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional $z^2$ contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional $z^2$ contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale $μ^2$. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned $z^2$ contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

hep-lat↗

arXiv2022

Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

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