Three-dimensional imaging of the nucleon and semi-inclusive high-energy reactions

Abstract

We present a short overview of studies of the transverse-momentum-dependent parton distribution functions of the nucleon. The aim of such studies is to provide three-dimensional imaging of the nucleon and a comprehensive description of semi-inclusive high-energy reactions. By summarizing what we have done in constructing the theoretical framework for inclusive deep inelastic lepton-nucleon scattering and one-dimensional imaging of the nucleon, we try to sketch out an outline of what we need to do to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three-dimensional gauge-invariant parton distributions. Next, we present an overview of what we have already achieved, with an emphasis on the theoretical framework for semi-inclusive reactions in leading-order perturbative quantum chromodynamics but with leading and higher twist contributions. We summarize in particular the results for the differential cross section and azimuthal spin asymmetries in terms of the gauge-invariant transverse-momentum-dependent parton distribution functions. We also briefly summarize the available experimental results on semi-inclusive reactions and the parameterizations of transverse-momentum-dependent parton distributions extracted from them and present an outlook for future studies.

Tensor polarization dependent fragmentation functions ande+e−→VπXat high energies

“…Systematic derivations have been given for such processes (for a recent short summary see e.g. [20]). However, for processes with no less than two hadrons are involved, systematic derivation for collinear expansion is still lacking.…”

“…If we consider e + e − → γ * → VπX, i.e. annihilate via electromagnetic interaction only, we have, 20) while the parity violating components,…”

Azimuthal and spin asymmetries in $e^+e^-\to V πX$ at high energies and 3D fragmentation functions

“…the lepton-hadron plane. It is also interesting to see that these transverse components also exist in the inclusive process e + e − → Z 0 → V X, we have (1) in T q 2 (y)D LT , S y LT (1) in = F (1) in T q 3 (y)G LT , (4.41)…”

Spin alignment of vector mesons in high energy pp collisions

“…Recently, progresses in the theoretical study have been achieved in particular in the formal QCD description of the spin dependence of FFs [57][58][59][60][61][62][63][64][65][66][67]. In the QCD field theory, FFs are defined via Lorentz decompositions of the quark-quark correlator.…”