Searcharxiv⌕ Search

arXiv subjects

William Detmold

Publications and source records attributed to William Detmold.

At least 19 recordsLinked to original sources
arXiv2026

Parton physics from a heavy-quark operator product expansion: Dynamical lattice QCD calculation of moments of the pion and kaon light-cone distribution amplitudes

The light-cone distribution amplitude (LCDA) is a fundamental non-perturbative quantity for understanding hadron structure and exclusive scattering processes. We report on our calculation of the pion and kaon LCDAs using the heavy-quark operator product expansion (HOPE) framework. This method employs an OPE analysis of hadronic amplitudes through the inclusion of a fictitious valence heavy quark. In these proceedings, we report progress on the determination of the first three nontrivial Mellin moments of the kaon LCDAs from dynamical lattice QCD calculations, and we summarize the recently published continuum-limit result for the pion fourth Mellin moment obtained in the quenched approximation, thereby demonstrating the feasibility of the HOPE method for accessing higher moments.

hep-lat↗
arXiv2026

Excited-state uncertainties in lattice-QCD calculations of multi-hadron systems

Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not require assumptions beyond Hermiticity, but often give very conservative systematic uncertainty estimates. Here, a more-constraining set of gap bounds is introduced for hadron spectroscopy. These bounds provide tighter constraints whose validity requires an explicit assumption about an energy gap. Exactly solvable lattice field theory correlators are used to test the utility of residual and gap bounds at finite and infinite statistics. Two-sided bounds and other analysis methods are then applied to a high-statistics LQCD calculation of nucleon-nucleon scattering at $m_\pi \sim 800$ MeV. Generalized eigenvalue problem (GEVP) and Lanczos energy estimators are compatible when applied to the same correlator data, but analyses including different interpolating operators show statistically significant inconsistencies. However, two-sided bounds from all operators are consistent. Under the assumption that the number of energy levels below $N\Delta$ and $\Delta\Delta$ thresholds is the same as for non-interacting nucleons, gap bounds are sufficient to constrain nucleon-nucleon scattering amplitudes at phenomenologically relevant precision. Lanczos methods further reveal that energy-eigenstate estimates from previously studied asymmetric correlators have not converged over accessible imaginary times. Nevertheless, data-driven examples demonstrate why assumptions are required to draw conclusions about the natures of two-nucleon ground states at these masses.

hep-lat↗
arXiv2026

Excited-state uncertainties in lattice-QCD calculations of hadron masses and scattering phase shifts

Lattice QCD has historically produced energy results interpretable as either estimates relying on implicit assumptions about asymptotic behavior or one-sided upper bounds. New Lanczos methods providing two-sided bounds with less-restrictive assumptions are introduced and quantified in a high-statistics calculation with unphysical quark masses. Two-sided bounds without spectral assumptions provide sub-percent constraints on the nucleon mass. Other bounds, which assume all states in a given energy window are resolved, provide meaningful two-sided constraints on nucleon-nucleon scattering phase shifts.

hep-lat↗
arXiv2025

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory

Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such as Conjugate Gradient (CG), which are time-consuming and computationally expensive. Preconditioners can effectively accelerate this process, with the state-of-the-art being multigrid preconditioners. However, constructing useful preconditioners can be challenging, adding additional computational overhead, especially in large linear systems. We propose a framework, leveraging operator learning techniques, to construct linear maps as effective preconditioners. The method in this work does \emph{not} rely on explicit matrices from either the original linear systems or the produced preconditioners, allowing efficient model training and application in the CG solver. In the context of the Schwinger model U(1) gauge theory in 1+1 spacetime dimensions with two degenerate-mass fermions), this preconditioning scheme effectively decreases the condition number of the linear systems and approximately halves the number of iterations required for convergence in relevant parameter ranges. We further demonstrate the framework learns a general mapping dependent on the lattice structure which leads to zero-shot learning ability for the Dirac operators constructed from gauge field configurations of different sizes.

hep-lat↗
arXiv2025

Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the fourth moment of the pion distribution amplitude

The pion light-cone distribution amplitude (LCDA) is an essential non-perturbative input for a range of high-energy exclusive processes in quantum chromodynamics. Building on our previous work, the continuum limit of the fourth Mellin moment of the pion LCDA is determined in quenched QCD using quark masses which correspond to a pion mass of $m_\pi = 550$ MeV. This calculation finds $\langle\xi^2\rangle = 0.202(8)(9)$ and $\langle \xi^4 \rangle = 0.039(28)(11)$ where the first error indicates the combined statistical and systematic uncertainty from the analysis and the second indicates the uncertainty from working with Wilson coefficients computed to next-to-leading order. These results are presented in the $\overline{\text{MS}}$ scheme at a renormalization scale of $\mu = 2$ GeV.

hep-lat↗
arXiv2025

Empirical investigation of nuclear correlation function distributions in lattice QCD

Two-point correlation functions of systems with baryon number $B \in \{1,2,3,4\}$ are investigated using lattice Quantum Chromodynamics (QCD). In particular, the empirical distributions of importance-sampling Monte-Carlo samples of these correlation functions are examined as a function of the spacetime separation between the two points and the baryon number. While the exact forms of these distributions are not known for QCD, recent work has determined asymptotic expressions for analogous correlation function distributions in simpler theories such as scalar field theory and the disordered phase of the $O(N)$ model. The theoretical O(N) model distributions are found to provide an accurate description of the empirical QCD distributions at zero momentum over a wide range of temporal separations for each baryon number when assessed with a range of different statistical tests. In particular, the behaviour of the baryon number $B$ QCD correlation function at large temporal separation is well-reproduced by the $O(N \sim 2/B)$ model distribution.

hep-lat↗
arXiv2025

Aspects of Propagator Sparsening in Lattice QCD

In lattice field theory, field sparsening aims to replace quantum fields, or objects constructed from them, with approximations that preserve the appropriate symmetries and maintain many aspects of the physics that the fields determine. For example, an effective sparsening of a quark propagator provides an efficient map from a quark propagator on a fine lattice geometry to a quark propagator defined on a coarser geometry in order to reduce storage and computational costs of subsequent calculational stages while maintaining long-distance correlations and corresponding low-energy physical information. Previous studies have focused on decimating lattice sites or randomly sampling lattice sites to reduce the size of the propagator and subsequent costs of Wick contractions. Here, we extend the study of sparsening to incorporate covariant averaging of spatial sites and examine the effects on two-point and three-point correlation functions involving various hadrons. We find that sparsening is most effective in reproducing the unsparsened versions of these correlation functions when weighted covariant-averaging is sequentially applied many times.

hep-lat↗
arXiv2024

Exploring gauge-fixing conditions with gradient-based optimization

Lattice gauge fixing is required to compute gauge-variant quantities, for example those used in RI-MOM renormalization schemes or as objects of comparison for model calculations. Recently, gauge-variant quantities have also been found to be more amenable to signal-to-noise optimization using contour deformations. These applications motivate systematic parameterization and exploration of gauge-fixing schemes. This work introduces a differentiable parameterization of gauge fixing which is broad enough to cover Landau gauge, Coulomb gauge, and maximal tree gauges. The adjoint state method allows gradient-based optimization to select gauge-fixing schemes that minimize an arbitrary target loss function.

hep-lat↗
arXiv2024

QCD constraints on isospin-dense matter and the nuclear equation of state

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the non-perturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential, $\mu_I$, bounds the partition function for a baryon chemical potential $\mu_B=3\mu_I/2$, these calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time.

hep-lat↗
arXiv2024

Position-space renormalization schemes for four-quark operators in HQET

X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and MSbar in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to MSbar-renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O($\alpha_S$) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B-Bbar mixing.

hep-lat↗
arXiv2024

Constraints on the finite volume two-nucleon spectrum at $m_\pi \approx 806$ MeV

The low-energy finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of $m_\pi \approx 806$ MeV is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Phys.Rev.D 107 (2023) 9, 094508] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated.

hep-lat↗
arXiv2024

Multi-particle interpolating operators in quantum field theories with cubic symmetry

Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct multi-particle interpolating operators for quantum field theories with cubic symmetry. The algorithm automates the block diagonalization required to combine multiple operators of definite linear momentum into irreducible representations of the appropriate little group. Examples are given for distinguishable and indistinguishable particles including cases with both zero and non-zero spin. An implementation of the algorithm is publicly available at https://github.com/latticeqcdtools/mhi.

hep-lat↗
arXiv2024

Long-Distance Nuclear Matrix Elements for Neutrinoless Double-Beta Decay from Lattice QCD

Neutrinoless double-beta ($0\nu\beta\beta$) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on $0\nu\beta\beta$-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum-chromodynamics (LQCD) calculation of the matrix element for $0\nu\beta\beta$ decay in a multi-nucleon system, specifically the $nn \rightarrow pp ee$ transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of $m_\pi = 806$ MeV at a single lattice spacing and volume. The statistically cleaner $\Sigma^- \rightarrow \Sigma^+ ee$ transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for $0\nu\beta\beta$ decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of $0\nu\beta\beta$ decay.

hep-lat↗
arXiv2023

Lattice QCD Constraints on the Fourth Mellin Moment of the Pion Light Cone Distribution Amplitude using the HOPE method

The light-cone distribution amplitude (LCDA) of the pion contains information about the parton momentum carried by the quarks and is an important theoretical input for various predictions of exclusive processes at high energy, including the pion electromagnetic form factor. Progress towards constraining the fourth Mellin moment of the LCDA using the heavy-quark operator product expansion (HOPE) method is presented.

hep-lat↗
arXiv2023

Signal-to-noise improvement through neural network contour deformations for 3D $SU(2)$ lattice gauge theory

Complex contour deformations of the path integral have been demonstrated to significantly improve the signal-to-noise ratio of observables in previous studies of two-dimensional gauge theories with open boundary conditions. In this work, new developments based on gauge fixing and a neural network definition of the deformation are introduced, which enable an effective application to theories in higher dimensions and with generic boundary conditions. Improvements of the signal-to-noise ratio by up to three orders of magnitude for Wilson loop measurements are shown in $SU(2)$ lattice gauge theory in three spacetime dimensions.

hep-lat↗
arXiv2023

Lattice quantum chromodynamics at large isospin density: 6144 pions in a box

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of $n$-pion correlation functions for $n \in \{ 1, \dots, N\}$ using a single $N \times N$ matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 $π^+$s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass $m_π= 170$ MeV and spacetime volumes of $(4.4^3\times 8.8)\ {\rm fm}^4$ and $(5.8^3\times 11.6)\ {\rm fm}^4$. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential $μ_I\sim 1.5 m_π$, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit ($c_s^2\leq 1/3$) over a wide range of chemical potential before falling towards the asymptotic expectation at $μ_I\sim 15 m_π$. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

hep-lat↗
arXiv2023

Large-time correlation functions in bosonic lattice field theories

Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, however little is known about the statistical properties of these quantities. In this work, the asymptotic form of the distributions of the correlation functions at vanishing momentum is determined for bosonic interacting lattice field theories with a unique gapped vacuum. It is demonstrated that the deviations from the asymptotic form at large Euclidean times can be utilized to determine the spectrum of the theory.

hep-lat↗