Spin densities in the transverse plane and generalized transversity distributions

Abstract

We show how generalized quark distributions in the nucleon describe the density of polarized quarks in the impact parameter plane, both for longitudinal and transverse polarization of the quark and the nucleon. This density representation entails positivity bounds including chiral-odd distributions, which tighten the known bounds in the chiral-even sector. Using the quark equations of motion, we derive relations between the moments of chiral-odd generalized parton distributions of twist two and twist three. We exhibit the analogy between polarized quark distributions in impact parameter space and transverse momentum dependent distribution functions.

Nucleon structure from generalized parton distributions in lattice QCD

“…More details of the p-pole parametrization and some numerical results for the parameters can be found in [16][17][18]. Let us note that the values for the power p we are using for the different GFFs lead to a regular behavior of the quark densities in the limit b ⊥ → 0, as discussed in [19]. In order to check our dipole ansatz, we invert Eq.…”

“…It turns out that these correlations in the transverse plane are governed by quark helicity flip (or tensor) GPDs. The lowest moment of the quark transverse spin density reads [19] …”

“…We plan to extend the analysis of moments of generalized parton distributions, including a study of the lowest two moments of transverse spin densities for up-and down-quarks, and to investigate improved positivity bounds for GPDs which have been obtained in [19].…”

Status of DVMP, DVCS and GPDs

“…This profile function is a simplified version of a more complicated one that has been proposed in [17,18] …”

“…In this kinematical situation the contributions from the GPD E to the cross section can be ignored. The valence-quark GPDs H at zero skewness are investigated in great detail in an analysis of the nucleon form factors [17] using the ansatz (4) with the profile function (8) and relying on the CTEQ6M(NLO) PDFs [28]. The resulting valence-quark GPDs in the small −t approximation …”