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M. Burkardt

Publications and source records attributed to M. Burkardt.

At least 19 recordsLinked to original sources
arXiv2019

The angular momentum decomposition in the scalar diquark model

One of the challenges of hadronic physics is to fully understand the structure of the proton. In particular, there is nowadays a great interest in the decomposition of its total angular momentum into orbital angular momentum and intrinsic spin, as well as identifying contributions from valence quarks, sea quarks and gluons. The most common decompositions of angular momentum are the Jaffe-Manohar (canonical) and Ji (kinetic) decompositions, which differ in the way contributions are attributed to quarks and gluons. Using perturbation theory, explicit one-loop calculations found that the difference between such decompositions vanishes. We justify within the diquark model in QED that the difference appears at two-loop level, supporting the interpretation of such a difference as originating from the torque exerted by the spectator system on the struck quark.

hep-ph↗
arXiv2016

Two-dimensional light-front $ϕ^4$ theory in a symmetric polynomial basis

We study the lowest-mass eigenstates of $ϕ^4_{1+1}$ theory with both odd and even numbers of constituents. The calculation is carried out as a diagonalization of the light-front Hamiltonian in a Fock-space representation. In each Fock sector a fully symmetric polynomial basis is used to represent the Fock wave function. Convergence is investigated with respect to the number of basis polynomials in each sector and with respect to the number of sectors. The dependence of the spectrum on the coupling strength is used to estimate the critical coupling for the positive-mass-squared case. An apparent discrepancy with equal-time calculations of the critical coupling is resolved by an appropriate mass renormalization.

hep-th↗
arXiv2016

Modelling the nucleon structure

We review the status of our understanding of nucleon structure based on the modelling of different kinds of parton distributions. We use the concept of generalized transverse momentum dependent parton distributions and Wigner distributions, which combine the features of transverse-momentum dependent parton distributions and generalized parton distributions. We revisit various quark models which account for different aspects of these parton distributions. We then identify applications of these distributions to gain a simple interpretation of key properties of the quark and gluon dynamics in the nucleon.

hep-ph↗
arXiv2013

Pion momentum distributions in the nucleon in chiral effective theory

We compute the light-cone momentum distributions of pions in the nucleon in chiral effective theory using both pseudovector and pseudoscalar pion-nucleon couplings. For the pseudovector coupling we identify δ-function contributions associated with end-point singularities arising from the pion-nucleon rainbow diagrams, as well as from pion bubble and tadpole diagrams which are not present in the pseudoscalar model. Gauge invariance is demonstrated, to all orders in the pion mass, with the inclusion of Kroll-Ruderman couplings involving operator insertions at the πNN vertex. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.

hep-ph↗
arXiv2011

Gluons and the quark sea at high energies: distributions, polarization, tomography

This report is based on a ten-week program on "Gluons and the quark sea at high-energies", which took place at the Institute for Nuclear Theory in Seattle in Fall 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. This report is organized around four major themes: i) the spin and flavor structure of the proton, ii) three-dimensional structure of nucleons and nuclei in momentum and configuration space, iii) QCD matter in nuclei, and iv) Electroweak physics and the search for physics beyond the Standard Model. Beginning with an executive summary, the report contains tables of key measurements, chapter overviews for each of the major scientific themes, and detailed individual contributions on various aspects of the scientific opportunities presented by an EIC.

nucl-th↗
arXiv2011

Transverse Momentum Dependent Parton Distribution/Fragmentation Functions at an Electron-Ion Collider

We present a summary of a recent workshop held at Duke University on Partonic Transverse Momentum in Hadrons: Quark Spin-Orbit Correlations and Quark-Gluon Interactions. The transverse momentum dependent parton distribution functions (TMDs), parton-to-hadron fragmentation functions, and multi-parton correlation functions, were discussed extensively at the Duke workshop. In this paper, we summarize first the theoretical issues concerning the study of partonic structure of hadrons at a future electron-ion collider (EIC) with emphasis on the TMDs. We then present simulation results on experimental studies of TMDs through measurements of single spin asymmetries (SSA) from semi-inclusive deep-inelastic scattering (SIDIS) processes with an EIC, and discuss the requirement of the detector for SIDIS measurements. The dynamics of parton correlations in the nucleon is further explored via a study of SSA in D (`D) production at large transverse momenta with the aim of accessing the unexplored tri-gluon correlation functions. The workshop participants identified the SSA measurements in SIDIS as a golden program to study TMDs in both the sea and valence quark regions and to study the role of gluons, with the Sivers asymmetry measurements as examples. Such measurements will lead to major advancement in our understanding of TMDs in the valence quark region, and more importantly also allow for the investigation of TMDs in the sea quark region along with a study of their evolution.

hep-ex↗
arXiv2009

Spin-polarized high-energy scattering of charged leptons on nucleons

The proton is a composite object with spin one-half, understood to contain highly relativistic spin one-half quarks exchanging spin-one gluons, each possibly with significant orbital angular momenta. While their fundamental interactions are well described by Quantum ChromoDynamics (QCD), our standard theory of the strong interaction, nonperturbative calculations of the internal structure of the proton based directly on QCD are beginning to provide reliable results. Most of our present knowledge of the structure of the proton is based on experimental measurements interpreted within the rich framework of QCD. An area presently attracting intense interest, both experimental and theoretical, is the relationship between the spin of the proton and the spins and orbital angular momenta of its constituents. While remarkable progress has been made, especially in the last decade, the discovery and investigation of new concepts have revealed that much more remains to be learned. This progress is reviewed and an outlook for the future is offered.

hep-ph↗
arXiv2002

Violation of Sum Rules for Twist-3 Parton Distributions

Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a $δ$-function at $x=0$. We confirm and clarify this result by constructing $h_L$ and $h_L^3$ (quark-gluon interaction dependent part of $h_L$) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating $h_L(x,Q^2)$ using light-front time-ordered pQCD to ${O}(α_S)$ on a quark target.

hep-ph↗
arXiv2001

B-Mesons on the Transverse Lattice

We present results from a first study of $B$-mesons that is based on a transverse lattice formulation of light-front QCD. The shape of the Isgur-Wise form factor is in very good agreement with experimental data. However, the calculations yield rather large values for $f_B$ and $\barΛ$ compared to contemporary calculations based on other techniques.

hep-ph↗
arXiv2001

Violation of Sum Rules for Twist-3 Parton Distributions in QCD

Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a $δ$-function at $x=0$. We confirm and clarify this result by constructing $h_L$ and $h_L^3$ (quark-gluon interaction dependent part of $h_L$) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating $h_L(x,Q^2)$ using light-front time-ordered pQCD to ${\cal O}(α_S)$ on a quark target. A $δ(x)$ term is also found in $e(x,Q^2)$, but not in $g_T(x,Q^2)$, to this order in ${\cal O}(α_S)$.

hep-ph↗
arXiv2001

A Study of Light Mesons on the Transverse Lattice

We present results from a study of light meson spectra and structure obtained within the framework of light-front QCD formulated on a transverse lattice. We discuss how imposing Lorentz covariance conditions on meson dispersion relations allows determination of parameters in the transverse lattice Hamiltonian. The pion distribution amplitude obtained in this framework is rather close to its asymptotic shape.

hep-ph↗
arXiv2001

QCD on a transverse lattice

We present results from a transverse lattice study of low lying mesons. Special emphasis is put on the issue of Lorentz invariant energy-momentum dispersion relations for these mesons. The light-cone wave function for the $π$ obtained in this framework is very close to its asymptotic shape.

hep-ph↗
arXiv2000

Off-forward parton distributions and impact parameter dependent parton structure

The connection between parton distributions as a function of the impact parameter and off-forward parton distributions is discussed in the limit of vanishing skewedness parameter $ξ$, i.e. when the off-forwardness is purely transverse. It is also illustrated how to relate $ξ\neq 0$ data to $ξ=0$ data, which is important for experimental measurements of these observables.

hep-ph↗
arXiv2000

Fermions on the Light-Front

Issues that are specific for formulating fermions in light-cone quantization are discussed. Special emphasis is put on the use of parity invariance in the non-perturbative renormalization of light-cone Hamiltonians.

hep-th↗
arXiv1999

Light Front Nuclear Physics: Toy Models, Static Sources and Tilted Light Front Coordinates

The principles behind the detailed results of a light-front mean field theory of finite nuclei are elucidated by deriving the nucleon mode equation using a simple general argument, based on the idea that a static source in equal time coordinates corresponds to a moving source in light front coordinates. This idea also allows us to solve several simple toy model examples: scalar field in a box, 1+1 dimensional bag model, three-dimensional harmonic oscillator and the Hulthén potential. The latter provide simplified versions of momentum distributions and form factors of relevance to experiments. In particular, the relativistic correction to the mean square radius of a nucleus is shown to be very small. Solving these simple examples suggests another more general approach-- the use of tilted light front coordinates. The simple examples are made even simpler.

nucl-th↗
arXiv1999

Sum rules for higher-twist parton distributions

In deep-inelastic scattering experiments, there is a general connection between subtractions in dispersion relations, violations of sum-rules and $δ$-functions in parton distribution functions. It is explained why one might expect a small violation in sum rules for the twist-3 distribution functions $g_T(x)$ and $h_L(x)$ when the sum-rules are applied to $x\neq 0$ data only. The non-perturbative predictions are studied in the context of a one-loop model.

hep-ph↗
arXiv1999

Light-Front Nuclear Physics: Mean Field Theory for Finite Nuclei

A light-front treatment for finite nuclei is developed from a relativistic effective Lagrangian (QHD1) involving nucleons, scalar mesons and vector mesons. We show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator $P^+$ to be the same as that for $P^-$. This is the same as minimizing the sum of the total momentum operators: $P^-+P^+$. We obtain a new light-front version of the equation that defines the single nucleon modes. The solutions of this equation are approximately a non-trivial phase factor times certain solutions of the usual equal-time Dirac equation. The ground state wave function is treated as a meson-nucleon Fock state, and the meson fields are treated as expectation values of field operators in that ground state. The resulting equations for these expectation values are shown to be closely related to the usual meson field equations. A new numerical technique to solve the self-consistent field equations is introduced and applied to $^{16}$O and $^{40}$Ca. The computed binding energies are essentially the same as for the usual equal-time theory. The nucleon plus momentum distribution (probability for a nucleon to have a given value of $p^+$) is obtained, and peaks for values of $p^+$ about seventy percent of the nucleon mass. The mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions, with a result that the vector mesons carry about thirty percent of the nuclear plus-momentum. The vector meson momentum distribution becomes more concentrated at $p^+=0$ as $A$ increases.

nucl-th↗
arXiv1999

Rotational Invariance In Nuclear Light-Front Mean Field Theory

A light-front treatment for spherical nuclei is developed from a relativistic effective Lagrangian and employing the mean field approximation. Minimizing the nuclear minus momentum subject to the constraint that, in the rest frame, the expectation values of the plus- and minus-momenta are the same leads to a formalism in which rotational invariance is recovered.

nucl-th↗