We have a solid understanding that quarks and gluons serve as the fundamental constituents of hadrons. However, we continually strive for more detailed information regarding their momentum and position distributions.
The most accessible information is catched in Drell-Yan and semi-inclusive deep inelastic scattering, where a virtual photon probes the quark momentum distributions in 1D (getting PDF and fragmentation functions) and 3D (getting TMD, that is, transverse momentum dependent distributions). These fundamental distributions are theoretically obtained through a power expansion of the cross sections.
I will review how the factorization can be achieved with the background field method, the importance of the Collins-Soper kernel (a QCD vacuum distribution) and present the most recent extraction of TMD at N4LL from Drell-Yan experiments (including latest results from LHC).
Andrea Pelloni, Tanjona Rabemananjara, Tommaso Giani