arXiv subjects

Matthias Burkardt

Publications and source records attributed to Matthias Burkardt.

At least 19 recordsLinked to original sources

arXiv2023

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↗

arXiv2020

Deep Learning Analysis of Deeply Virtual Exclusive Photoproduction

We present a Machine Learning based approach to the cross section and asymmetries for deeply virtual Compton scattering from an unpolarized proton target using both an unpolarized and polarized electron beam. Machine learning methods are needed to study and eventually interpret the outcome of deeply virtual exclusive experiments since these reactions are characterized by a complex final state with a larger number of kinematic variables and observables, exponentially increasing the difficulty of quantitative analyses. Our deep neural network (FemtoNet) uncovers emergent features in the data and learns an accurate approximation of the cross section that outperforms standard baselines. FemtoNet reveals that the predictions in the unpolarized case systematically show a smaller relative median error than the polarized that can be ascribed to the presence of the Bethe Heitler process. It also suggests that the $t$ dependence can be more easily extrapolated than for the other variables, namely the skewness, $ξ$ and four-momentum transfer, $Q^2$. Our approach is fully scalable and will be capable of handling larger data sets as they are released from future experiments.

hep-ph↗

arXiv2020

Potential linear and angular momentum in the scalar diquark model

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

hep-ph↗

arXiv2020

Study of the potential transverse momentum and potential angular momentum within the scalar diquark model

We make use of a simple scalar diquark model to study the potential transverse momentum and potential angular momentum, defined as the difference between the Jaffe-Manohar and Ji notions of transverse momentum and orbital angular momentum, respectively. A non-vanishing potential angular momentum has been previously found in lattice calculations and is believed to appear due to the effects of initial/final state interactions between the spectator system and the struck quark in high energy scattering processes. Such re-scattering phenomena are similar in nature to those who are responsible for generating the Sivers shift. This motivates us to search for an estimate of the potential angular momentum in terms of the expectation value of the transverse momentum of the struck quark.

hep-ph↗

arXiv2020

Probing Nucleons and Nuclei in High Energy Collisions

This volume is a collection of contributions for the 7-week program "Probing Nucleons and Nuclei in High Energy Collisions" that was held at the Institute for Nuclear Theory in Seattle, WA, USA, from October 1 until November 16, 2018. The program was dedicated to the physics of the Electron Ion Collider (EIC), the world's first polarized electron-nucleon (ep) and electron-nucleus (eA) collider to be constructed in the USA. These proceedings are organized by chapters, corresponding to the weeks of the program: Week I, Generalized parton distributions; Week II, Transverse spin and TMDs; Week III, Longitudinal spin; Week IV, Symposium week; Weeks V & VI, eA collisions; Week VII, pA and AA collisions. We hope these proceedings will be useful to readers as a compilation of EIC-related science at the end of the second decade of the XXI century.

hep-ph↗

arXiv2020

Transverse Force Imaging

While twist-2 GPDs allow for a determination of the distribution of partons on the transverse plane, twist-3 GPDs contain quark-gluon correlations that provide information about the average transverse color Lorentz force acting on quarks. As an example, we use the nonforward generalization of $g_T(x)$, to illustrate how twist-3 GPDs can provide transverse position information about that force.

hep-ph↗

arXiv2020

Aspects of Quark Orbital Angular Momentum

The difference between the quark orbital angular momentum (OAM) defined in light-cone gauge (Jaffe-Manohar) compared to defined using a local manifestly gauge invariant operator (Ji) is interpreted in terms of the change in quark OAM as the quark leaves the target in a DIS experiment.

hep-ph↗

arXiv2020

Lorentz invariance relations for twist-3 quark distributions

We calculate twist-3 parton ditribution functions (PDFs) using cut and uncut diagrams. Uncut diagrams lead to a Dirac delta function term. No such term appears when cut diagrams are used. We show that a $δ(x)$ is necessary to satisfy the Lorentz invariance relations of twist-3 PDFs, except for the Burkhardt-Cottingham sum rule in QCD.

hep-ph↗

arXiv2019

Transverse Force Tomography

While twist-2 GPDs allow for a determination of the distribution of partons on the transverse plane, twist-3 GPDs contain quark-gluon correlations that provide information about the average transverse color Lorentz force acting on quarks. We demonstrate how twist-3 GPDs can be used to provide transverse position information about that force.

hep-ph↗

arXiv2018

Singularities in Twist-3 Quark Distributions

We find in one-loop calculations and spectator models that twist-3 GPDs exhibit discontinuities. In the forward limit these discontinuities grow into Dirac delta functions which are essential to satisfy the sum rules involving twist-3 PDFs. We calculate twist-3 quasi-PDFs as a function of longitudinal momentum and identify the Dirac delta function terms with momentum components in the nucleon state that do not scale as the nucleon is boosted to the infinite momentum frame.

nucl-th↗

arXiv2018

Neutron magnetic polarisability with Landau mode operators

The application of a uniform background magnetic field makes standard quark operators utilising gauge-covariant Gaussian smearing inefficient at isolating the ground state nucleon at nontrivial field strengths. In the absence of QCD interactions, Landau modes govern the quark energy levels. There is evidence that residual Landau mode effects remain when the strong interaction is turned on. Here we introduce novel quark operators constructed from the two-dimensional $U(1)$ Laplacian eigenmodes that describe the Landau levels of a charged particle on a periodic finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Using asymmetric source and sink operators, we are able to encapsulate the predominant effects of both the QCD and QED interactions in the interpolating fields for the neutron. The neutron magnetic polarizability is calculated using these techniques on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. In conjunction with a chiral effective-field theory analysis, we obtain a neutron magnetic polarizability of $β^n = 2.05(25)(19) \times 10^{-4}$ fm$^3$, where the numbers in parentheses describe statistical and systematic uncertainties.

hep-lat↗

arXiv2018

Twist-3 GPDs in Deeply-Virtual Compton Scattering

The sub-leading power of the scattering amplitude for deeply-virtual Compton scattering (DVCS) off the nucleon contains leading-twist and twist-3 generalized parton distributions (GPDs). We point out that in DVCS, at twist-3 accuracy, one cannot address any individual twist-3 GPD. This complication appears on top of the deconvolution issues familiar from the twist-2 DVCS amplitude. Accessible are exclusively linear combinations involving both vector and axial-vector twist-3 GPDs. This implies, in particular, that the (kinetic) orbital angular momentum of quarks can hardly be constrained by twist-3 DVCS observables. Moreover, using the quark-target model, we find that twist-3 GPDs can be discontinuous. The discontinuities however cancel in the DVCS amplitude, which further supports the hypothesis of factorization at twist-3 accuracy.

hep-ph↗

arXiv2017

Background field Landau mode operators for the nucleon

The introduction of a uniform background magnetic field breaks three-dimensional spatial symmetry for a charged particle and introduces Landau mode effects. Standard quark operators are inefficient at isolating the nucleon correlation function at nontrivial field strengths. We introduce novel quark operators constructed from the two-dimensional Laplacian eigenmodes that describe a charged particle on a finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Preliminary results are obtained for the neutron and proton magnetic polarisabilities using these methods.

hep-lat↗

arXiv2017

Nucleon Magnetic Properties from Lattice QCD with the Background Field Method

The magnetic moment and magnetic polarisability of the neutron and proton are investigated using the uniform background-field method and lattice QCD. The results are calculated using 32^3 x 64 dynamical QCD lattices provided by the PACS-CS collaboration through the ILDG. Methods of isolating the energy of the hadrons accounting for Landau level energies are explored. Effective energy shifts are formed from combinations of correlation functions and their efficiency in isolating the magnetic moment and polarisability terms is determined.

hep-lat↗

arXiv2017

Angular Momentum Distribution in the Transverse Plane

Several possibilities to relate the $t$-dependence of Generalized Parton Distributions (GPDs) to the distribution of angular momentum in the transverse plane are discussed. Using a simple spectator model we demonstrate that non of them correctly describes the orbital angular momentum distribution that for a longitudinally polarized nucleon obtained directly from light-front wavefunctions.

hep-ph↗

arXiv2016

Quark-Photon-Quark Correlation and Transverse Target Single Spin Asymmetry in Inclusive DIS

We calculate the q q correlation function associated to transverse target lepton-nucleon inclusive deep-inelastic scattering by direct evaluation of the corresponding matrix element. We use the electromagnetic impact parameter potential for a transversely polarized nucleon to define the q q correlation function for each avor in terms of the field components of that avor. The results are compared with the two existing models for the q q correlator. Using the calculated q q correlation function, we estimated the transverse target SSA in IDIS process.

hep-ph↗

arXiv2016

Transverse Force on Transversely Polarized Quarks in Longitudinally Polarized Nucleons

We study the semi-classical interpretation of the $x^3$ and $x^4$ moments of twist-3 parton distribution functions (PDFs). While no semi-classical interpretation for the higher moments of $g_T(x)$ and $e(x)$ was find, the $x^3$ moment of the chirally odd spin-dependent twist-3 PDF $h_L^3(x)$ can be related to the longitudinal gradient of the transverse force on transversely polarized quarks in longitudinally polarized nucleons in a DIS experiment. We discuss how this result relates to the torque acting on a quark in the same experiment. This has further implications for comparisons between tha Jaffe-Manohar and the Ji decompositions of the nucleon spin.

hep-ph↗

arXiv2016

Transverse Target Single Spin Asymmetry in Elastic e-{\p} Scattering

Using the Coulomb Eikonal Phase associated with a transversely polarized nucleon, we calculate the azimuthal single spin asymmetry of unpolarized electrons elastically scattered from a transversely polarized nucleon target. The azimuthal asymmetry in this case is attributed to the fact that in a transversely polarized nucleon, the transverse charge density is no longer axially symmetric and is distorted due to the transverse spin of the nucleon. This asymmetry in the nucleon charge density causes a left-right asymmetry in the azimuthal distribution of the scattered electrons. In our approach, we utilize the relativistic Eikonal approximation to calculate the one and two photon exchange amplitudes from which a non zero azimuthal asymmetry appears due to the interference between the two amplitudes.

hep-ph↗