Pressure Distribution and Shear Forces inside the Proton

The distributions of pressure and shear forces inside the proton are investigated using lattice quantum chromodynamics (LQCD) calculations of the energy momentum tensor, allowing the first model-independent determination of these fundamental aspects of proton structure. This is achieved by combining recent LQCD results for the gluon contributions to the energy momentum tensor with earlier calculations of the quark contributions. The utility of LQCD calculations in exploring, and supplementing, the assumptions in a recent extraction of the pressure distribution in the proton from deeply virtual Compton scattering is also discussed. Based on this study, the target kinematics for experiments aiming to determine the pressure and shear distributions with greater precision at Thomas Jefferson National Accelerator Facility and a future electron ion collider are investigated.National Science Foundation (U.S.) (Grant CAREER-1841699)United States. Department of Energy (Award DE-SC0010495)United States. Department of Energy (Grant DE-SC0011090)United States. Department of Energy (Award DE-SC0018121

Gluonic transversity from lattice QCD

We present an exploratory study of the gluonic structure of the ϕ meson using lattice QCD (LQCD). This includes the first investigation of gluonic transversity via the leading moment of the twist-2 double-helicity-flip gluonic structure function Δ(χ,Q²). This structure function only exists for targets of spin J ≥ 1 and does not mix with quark distributions at leading twist, thereby providing a particularly clean probe of gluonic degrees of freedom. We also explore the gluonic analogue of the Soffer bound which relates the helicity flip and nonflip gluonic distributions, finding it to be saturated at the level of 80%. This work sets the stage for more complex LQCD studies of gluonic structure in the nucleon and in light nuclei where Δ(χ,Q²) is an “exotic glue” observable probing gluons in a nucleus not associated with individual nucleons.United States. Department of Energy (DE- SC0010495)United States. Department of Energy (DE-SC0011090

Machine learning action parameters in lattice quantum chromodynamics

Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that arc currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. The high information content and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development

Gravitational form factors of the proton from lattice QCD

The gravitational form factors (GFFs) of a hadron encode fundamental aspects of its structure, including its shape and size as defined from e.g., its energy density. This work presents a determination of the flavor decomposition of the GFFs of the proton from lattice QCD, in the kinematic region $0\leq -t\leq 2~\text{GeV}^2$. The decomposition into up-, down-, strange-quark, and gluon contributions provides first-principles constraints on the role of each constituent in generating key proton structure observables, such as its mechanical radius, mass radius, and $D$-term.Comment: Additional comparisons added to Figures 2 and 4. 8 pages, 4 figures, 1 table in the main text plus 11 pages, 8 figures, 2 tables in the supplementary materia

Signal-to-noise improvement through neural network contour deformations for 3D SU(2)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.Comment: 9 pages, 3 figures. Proceedings for the 40th Lattice conference at Fermilab from July 31 to August 4, 202

The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for Lattice Quantum Chromodynamics (LQCD) in the research frontier in fundamental symmetries and signals for new physics. LQCD, in synergy with effective field theories and nuclear many-body studies, provides theoretical support to ongoing and planned experimental programs in searches for electric dipole moments of the nucleon, nuclei and atoms, decay of the proton, $n$-$\overline{n}$ oscillations, neutrinoless double-$\beta$ decay of a nucleus, conversion of muon to electron, precision measurements of weak decays of the nucleon and of nuclei, precision isotope-shift spectroscopy, as well as direct dark matter detection experiments using nuclear targets. This whitepaper details the objectives of the LQCD program in the area of Fundamental Symmetries within the USQCD collaboration, identifies priorities that can be addressed within the next five years, and elaborates on the areas that will likely demand a high degree of innovation in both numerical and analytical frontiers of the LQCD research.Comment: A whitepaper by the USQCD Collaboration, 30 pages, 9 figure

Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics

Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising tool in this space, building on the success of this approach in applications such as image, text, and audio generation. Often, however, generative tasks in scientific domains have unique structures and features -- such as complex symmetries and the requirement of exactness guarantees -- that present both challenges and opportunities for ML. This Perspective outlines the advances in ML-based sampling motivated by lattice quantum field theory, in particular for the theory of quantum chromodynamics. Enabling calculations of the structure and interactions of matter from our most fundamental understanding of particle physics, lattice quantum chromodynamics is one of the main consumers of open-science supercomputing worldwide. The design of ML algorithms for this application faces profound challenges, including the necessity of scaling custom ML architectures to the largest supercomputers, but also promises immense benefits, and is spurring a wave of development in ML-based sampling more broadly. In lattice field theory, if this approach can realize its early promise it will be a transformative step towards first-principles physics calculations in particle, nuclear and condensed matter physics that are intractable with traditional approaches.Comment: 11 pages, 5 figure

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.Comment: 27 pages. An implementation of the algorithm is publicly available at https://github.com/latticeqcdtools/mh

Gravitational form factors of the pion from lattice QCD

The two gravitational form factors of the pion, $A^{\pi}(t)$ and $D^{\pi}(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\leq -t< 2~\text{GeV}^2$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass $m_{\pi}\approx 170~\text{MeV}$ and $N_f=2+1$ quark flavors. The flavor decomposition of these form factors into gluon, up/down light-quark, and strange quark contributions is presented in the $\overline{\text{MS}}$ scheme at energy scale $\mu=2~\text{GeV}$, with renormalization factors computed non-perturbatively via the RI-MOM scheme. Using monopole and (modified) $z$-expansion fits to the gravitational form factors, we obtain estimates for the pion momentum fraction and $D$-term that are consistent with the momentum fraction sum rule and the next-to-leading order chiral perturbation theory prediction for $D^{\pi}(0)$.Comment: 28 pages, 17 figures, 7 table