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Michael Engelhardt

Publications and source records attributed to Michael Engelhardt.

At least 19 recordsLinked to original sources

Neural Network Representation of Generalized Parton Distributions (NNGPD)

We present a neural-network-based framework for modeling generalized parton distributions, referred to as NNGPD, in which GPDs are represented as flexible functions constrained through physically motivated integral relations. In this approach, experimental and theoretical information is incorporated into the training procedure via loss functions enforcing convolution integrals that define Compton form factors, as well as Mellin moments related to generalized form factors accessible in lattice QCD. This formulation reflects the inverse-problem character of GPD phenomenology without assuming a specific functional ansatz. As a proof of concept, we benchmark the NNGPD framework using a phenomenological spectator-based GPD model, from which synthetic training data for Compton form factors and Mellin moments are generated. The neural network is trained solely on these aggregate observables, and the resulting GPDs are compared directly with the underlying model distributions in a closure-type test. We find that the neural-network representation reproduces the main features of the GPDs over the relevant kinematic domain, despite being constrained only by their integral projections. This study demonstrates the viability of neural-network representations of GPDs constrained by global physical observables and provides a basis for future phenomenological applications combining experimental measurements of deeply virtual Compton scattering, including those anticipated at the Electron Ion Collider, with lattice QCD inputs for Mellin moments and generalized form factors.

hep-ph

Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD

Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments $\left< x^2 \right>$ of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and 2+1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. This is the first direct calculation of these observables performed at the physical pion mass.

hep-lat

Generalized Parton Distributions from Symbolic Regression

AI/ML informed Symbolic Regression is the next stage of scientific modeling. We utilize a highly customizable symbolic regression package ``PySR" to model the $x$ and $t$ dependence of the flavor isovector combination $H_{u-d}(x,t,\xi)$ at $\xi=0$. These PySR models were trained on GPD results provided by both Lattice QCD and phenomenological sources GGL, GK, and VGG. We demonstrate, for the first time, the consistency and systematic convergence of Symbolic Regression by quantifying the disparate models through their Taylor expansion coefficients. In addition to PySR penalizing models with higher complexity and mean-squared error, we implement schemes that test specific physics hypotheses, including force-factorized $x$ and $t$ dependence and Regge behavior in PySR GPDs. We show that PySR can identify factorizing GPD sources based on their response to the Force-Factorized model. Knowing the precise behavior of the GPDs, and their uncertainties in a wide range in $x$ and $t$, crucially impacts our ability to concretely and quantitatively predict hadronic spatial distributions and their derived quantities.

hep-ph

Likelihood and Correlation Analysis of Compton Form Factors for Deeply Virtual Exclusive Scattering on the Nucleon

A likelihood analysis of the observables in deeply virtual exclusive photoproduction off a proton target, $ep \rightarrow e' p' \gamma'$, is presented. Two processes contribute to the reaction: deeply virtual Compton scattering, where the photon is produced at the proton vertex, and the Bether-Heitler process, where the photon is radiated from the electron. We consider the unpolarized process for which the largest amount of data with all the kinematic dependences are available from corresponding datasets with unpolarized beams and unpolarized targets from Jefferson Lab. We provide and use a method which derives a joint likelihood of the Compton form factors, which parametrize the deeply virtual Compton scattering amplitude in QCD, for each observed combination of the kinematic variables defining the reaction. The unpolarized twist-two cross section likelihood fully constrains only three of the Compton form factors (CFFs). The impact of the twist-three corrections to the analysis is also explored. The derived likelihoods are explored using Markov chain Monte Carlo (MCMC) methods. Using our proposed method we derive CFF error bars and covariances. Additionally, we explore methods which may reduce the magnitude of error bars/contours in the future.

hep-ph

Transverse Orbital Angular Momentum in the Proton

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining the decomposition of the proton's quark transverse angular momentum into its spin and orbital components. The new decomposition can be understood as a twist-three relation, with the quark transverse spin described by the parton distribution $g_T$. We find that the orbital component can be expressed in terms of a moment in the quark transverse momentum, $k_T$, of the generalized transverse momentum-dependent distribution $F_{12}$, or alternatively in terms of the twist-three generalized parton distributions $H_{2T}$ and $\widetilde{E}_{2T}$.

hep-ph

Variational autoencoder inverse mapper for extraction of Compton form factors: Benchmarks and conditional learning

Deeply virtual exclusive scattering processes (DVES) serve as precise probes of nucleon quark and gluon distributions in coordinate space. These distributions are derived from generalized parton distributions (GPDs) via Fourier transform relative to proton momentum transfer. QCD factorization theorems enable DVES to be parameterized by Compton form factors (CFFs), which are convolutions of GPDs with perturbatively calculable kernels. Accurate extraction of CFFs from DVCS, benefiting from interference with the Bethe-Heitler (BH) process and a simpler final state structure, is essential for inferring GPDs. This paper focuses on extracting CFFs from DVCS data using a variational autoencoder inverse mapper (VAIM) and its constrained variant (C-VAIM). VAIM is shown to be consistent with Markov Chain Monte Carlo (MCMC) methods in extracting multiple CFF solutions for given kinematics, while C-VAIM effectively captures correlations among CFFs across different kinematic values, providing more constrained solutions. This study represents a crucial first step towards a comprehensive analysis pipeline towards the extraction of GPDs.

hep-ph

AI for Nuclear Physics: the EXCLAIM project

In overview of the recent activity of the newly funded EXCLusives with AI and Machine learning (EXCLAIM) collaboration is presented. The main goal of the collaboration is to develop a framework to implement AI and machine learning techniques in problems emerging from the phenomenology of high energy exclusive scattering processes from nucleons and nuclei, maximizing the information that can be extracted from various sets of experimental data, while implementing theoretical constraints from lattice QCD. A specific perspective embraced by EXCLAIM is to use the methods of theoretical physics to understand the working of ML, beyond its standardized applications to physics analyses which most often rely on industrially provided tools, in an automated way.

hep-ph

Moments of Nucleon Unpolarized, Polarized, and Transversity Parton Distribution Functions from Lattice QCD at the Physical Point

The second Mellin moments $\langle x\rangle$ of the nucleon's unpolarized, polarized, and transversity parton distribution functions (PDFs) are computed. Two lattice QCD ensembles at the physical pion mass are used: these were generated using a tree-level Symanzik-improved gauge action and 2+1 flavour tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. The moments are extracted from forward matrix elements of local leading twist operators. We determine renomalization factors in RI-(S)MOM and match to $\overline{\mathrm{MS}}$ at scale $2\,\mathrm{GeV}$. Our findings show that operators that exhibit vanishing kinematics at zero momentum can have significantly reduced excited-state contamination. The resulting polarized moment is used to quantify the longitudinal contribution to the quark spin-orbit correlation. All our results agree within two sigma with previous lattice results.

hep-lat

Moments of Parton Distributions Functions from Lattice QCD at the Physical Point

We present a Lattice QCD calculation of the second Mellin moments of the nucleon axial, vector and tensor parton distribution functions (PDFs). The calculation is performed at the physical pion mass with two different lattice spacings, and includes both zero and non-zero nucleon momenta. In our preliminary analysis, we identify operators that greatly reduce excited-state contamination.

hep-lat

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance.

hep-ph

TMD Handbook

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

hep-ph

Universality of the Collins-Soper kernel in lattice calculations

The Collins-Soper (CS) kernel is a nonperturbative function that characterizes the rapidity evolution of transverse-momentum-dependent parton distribution functions (TMDPDFs) and wave functions. In this Letter, we calculate the CS kernel for pion and proton targets and for quasi-TMDPDFs of leading and next-to-leading power. The calculations are carried out on the CLS ensemble H101 with dynamical $N_f=2+1$ clover-improved Wilson fermions. Our analyses demonstrate the consistency of different lattice extractions of the CS kernel for mesons and baryons, as well as for twist-two and twist-three operators, even though lattice artifacts could be significant. This consistency corroborates the universality of the lattice-determined CS kernel and suggests that a high-precision determination of it is in reach.

hep-lat

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

hep-lat

Determination of the Collins-Soper Kernel from Lattice QCD

We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin moments of quasi-TMDs evaluated at different nucleon momenta.The analysis is done with dynamical $N_f=2+1$ clover fermions for the CLS ensemble H101 ($a=0.0854\,\mathrm{fm}$, $m_{\pi}=m_K=422\,\mathrm{MeV}$). The computed CS kernel is in good agreement with experimental extractions and previous lattice studies.

hep-lat

Energy of a point-like neutron in an external electromagnetic field

A point-like neutron in an external electromagnetic field experiences a shift in energy that mimicks the effect of an actual structural deformation of an extended neutron, i.e., a proper polarizability. In order to be able to differentiate between the former and the latter, a Foldy-Wouthuysen transformation is constructed which yields the energy shift of a point-like neutron quadratic in the external field in a derivative expansion, generalizing a long-known result for the dipole electric polarizability due to Foldy. The ten leading Foldy contributions to the energy are determined for a zero-momentum neutron. In addition, eliminating the momentum operator in favor of the velocity operator, analogous results are derived for a zero-velocity neutron. In this case, operator ordering ambiguities are encountered that permit only a determination of eight of the ten Foldy terms.

hep-ph

Parton distributions and lattice QCD calculations: toward 3D structure

The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.

hep-ph

Excited-state effects in nucleon structure on the lattice using hybrid interpolators

It would be very useful to find a way of reducing excited-state effects in lattice QCD calculations of nucleon structure that has a low computational cost. We explore the use of hybrid interpolators, which contain a nontrivial gluonic excitation, in a variational basis together with the standard interpolator with tuned smearing width. Using the clover discretization of the field strength tensor, a calculation using a fixed linear combination of standard and hybrid interpolators can be done using the same number of quark propagators as a standard calculation, making this a cost-effective option. We find that such an interpolator, optimized by solving a generalized eigenvalue problem, reduces excited-state contributions in two-point correlators. However, the effect in three-point correlators, which are needed for computing nucleon matrix elements, is mixed: for some matrix elements such as the tensor charge, excited-state effects are suppressed, whereas for others such as the axial charge, they are enhanced. The results illustrate that the variational method is not guaranteed to reduce the net contribution from excited states except in its asymptotic regime, and suggest that it may be important to use a large basis of interpolators capable of isolating all of the relevant low-lying states.

hep-lat

Hadrons and Nuclei

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD calculations related to the structure and spectroscopy of hadrons and nuclei. An overview of recent lattice calculations of the structure of the proton and other hadrons is presented along with prospects for future extensions. Progress and prospects of hadronic spectroscopy and the study of resonances in the light, strange and heavy quark sectors is summarized. Finally, recent advances in the study of light nuclei from lattice QCD are addressed, and the scope of future investigations that are currently envisioned is outlined.

hep-lat