arXiv subjects
Publications and source records attributed to Matthias Burkardt.
We calculate the orbital angular momentum of the `quark' in the scalar diquark model as well as that of the electron in QED (to order $α$). We compare the orbital angular momentum obtained from the Jaffe-Manohar decomposition to that obtained from the Ji relation and estimate the importance of the vector potential in the definition of orbital angular momentum.
The sign of the Boer-Mulders function $h_1^\perp$ is related to the sign of the GPD $\bar{E}_T$ through the mechanism of chromodynamic lensing. Model calculations of the sign of $\bar{E}_T$ indicate that the sign of $h_1^\perp$ may be the same in all ground state hadrons.
Several examples for the role of orbital angular momentum and spin-orbit correlations in hadron structure are discussed.
We summarize the intuitive connection between deformations of parton distributions in impact parameter space and single-spin asymmetries. Lattice results for the $x^2$-moment of the twist-3 polarized parton distribution $g_2(x)$ are used to estimate the average transverse force acting on the active quark in SIDIS in the instant after being struck by the virtual photon.
We revisit the light-cone wave function representation for generalized parton distributions with $ζ\neq 0$. After translating the $t$-slope into a $Δ_\perp^2$-slope, the two-dimensional Fourier transform of GPDs is interpreted as the transition matrix element as a function of the separation between the active quark and the center of momentum of the spectators. In the limit $x\to ζ$ it is discussed how this information can be used to learn about the dependence of the mean separation between the active quark and the spectators on the momentum fraction carried by the active quark.
Chirally odd generalized parton distributions (GPDs) and the Boer-Mulders function provide valuable information about spin-orbit correlations for quarks in nucleons and other hadrons. We compare results for the relevant GPD $\bar{E}^q_T$ from a variety of phenomenological models as well as recent lattice results. We find that $\bar{E}^q_T>0$ for nucleons as well as the pion and for both $u$ and $d$ quark. As a result, the corresponding Boer Mulders functions are all expected to be negative. The sign of $\bar{E}^q_T$ arises from the relative sign between the upper and lower Dirac components for the quark wave functions.
Generalized parton distributions describe the distribution of partons in the transverse plane. For transversely polarized quarks and/or nucleons, these impact parameter dependent parton distributions are not axially symmetric. These transverse distortions can be related to spin-orbit correlations as well as to (intuitively) to transverse single-spin asymmetries, allowing novel insights into quark orbital angular momentum from measurements of the Sivers and Boer-Mulders functions.
We derive an inequality for the distribution of quarks with non-zero orbital angular momentum, and thus demonstrate, in a model-independent way, that a non-vanishing anomalous magnetic moment requires both a non-zero size of the target as well as the presence of wave function components with quark orbital angular momentum L_z>0.
Generalized parton distributions involving transverse polarization are transversely deformed. The deformation of chirally odd GPDs is related to a transversity decomposition of the quark angular momentum. Potential consequences for T-odd single-spin asymmetries (Sivers and Boer-Mulders effects) are discussed.
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.
Generalized parton distributions can be used to obtain information about the dependence of parton distributions on the impact parameter. Potential consequences for T-odd single-spin asymmetries are discussed.
We illustrate, in a semi-classical picture, how the Wilson line phase factor in gauge invariantly defined unintegrated parton density can lead to a nonzero single-spin asymmetry (Sivers effect).
We study T-odd gauge invariantly defined T-odd unintegrated gluon densities in QCD. The average $\perp$ momentum of the gluons in a $\perp$ polarized nucleon can be nonzero due to the Sivers mechanism. However, we find that the sum of the transverse momenta due to the Sivers mechanism from gluons and all quark flavors combined vanishes, i.e. $<{\bf k_{\perp,g}}> + \sum_q < {\bf k_{\perp,q}}> =0$.
The $t$-dependence of generalized parton distrbutions for $x\to 1$ is discussed. We argue that constituent quark models, where the $t$-dependence for $x\to 1$ is through the product $(1-x)t$, are inconsistent. Instead we suggest a leading dependence in terms of $(1-x)^n t$, where $n\geq 2$, for $x\to 1$.
The relation between GPD's and color transparency is explored. The discovery of color transparency in pionic diffractive dissociation reactions allows us to make specific predictions for the behavior of the pion generalized parton distribution, and provide a further test of any model of the pion form factor.
We analyze the Sivers asymmetry in light-cone gauge. The average transverse momentum of the quark distribution is related to the correlation between the quark distribution and the transverse component of the gauge field at $x^-\pm \infty$. We then use finiteness conditions for the light-cone Hamiltonian to relate the transverse gauge field at $x^-=\pm \infty$ to the color density integrated over $x^-$. This result allows us to relate the average transverse momentum of the active quark to color charge correlations in the transverse plane.
Recently, it has been pointed out that there exists a connection between the generalized parton distribution $E(x,0,t)$ and the Sivers asymmetry. For transversely polarized nucleon targets, generalized parton distributions are asymmetric in impact parameter space. This impact parameter space asymmetry, together with the final state interaction of the active quark, gives rise to the Sivers asymmetry in momentum space. We demonstrate this phenomenon explicitly in the scalar diquark model. This result also illustrates the physics that underlies the correlation between the anomalous magnetic moment and the Sivers asymmetry for a given quark flavor.
The physical interpretation of generalized parton distributions (in the limit $ξ=0$) as Fourier transforms of impact parameter dependent parton distributions is discussed. Particular emphasis is put on the role of the target polarization. For transversely polarized targets we expect a significant deviation from axial symmetry for the distribution in the transverse plane. We conjecture that this transverse distortion, in combination with the final state provides a natural explanation for the sign of the Sivers contribution to semi-inclusive single-spin asymmetries.