The well established theory of strong interactions (Quantum Chromodynamics) has yielded a huge amount of understanding how the nucleon and other hadrons are built from quarks and gluons, the fundamental degrees of freedom in QCD.
To investigate hadron structure we study deep inelastic scattering processes, where individual quarks and gluons are resolved.
The parton densities extracted from such processes encode the distribution of longitudinal momentum carried by quarks, antiquarks and gluons within a fast moving hadron. They have provided much to shape our physical picture of hadron structure.
However, key pieces of information are not included in these quantities. For example how partons are distributed in the plane transverse to the direction in which the hadron is moving, or how important their orbital angular momentum is in making up the total spin of a nucleon.
The transverse momentum and impact parameter distributions are encoded in Generalized Transverse Momentum Dependent Distributions (GTMDs). Certain semi-inclusive or exclusive scattering processes may provide insight through the related transverse momentum dependent distribution (TMDs) or generalized parton distributions (GPDs).
We plan to obtain ab-initio information about these simpler quantities through our lattice simulations which are now feasible due to the existence of pre-exascale computers.