Transverse-Momentum Dependent Parton Densities: Definition, Renormalization, Evolution and All That

Igor O. Cherednikov
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia

Recent results of our study of the transverse-momentum dependent parton densities ("TMDs"), which 
are important ingredients of the description of semi-inclusive hadronic processes, are presented. 
Special attention is payed to renormalization and gauge invariance properties of TMDs. As an 
illustration, their leading-order anomalous dimensions are calculated in the light-cone gauge with 
different additional gauge-fixing conditions. It is shown that the RG properties are helpful to 
reveal, in an economic way, the general structure of the gauge links entering the operator 
definition of TMDs. The evolution equations for TMDs, as well as the status of factorization in 
semi-inclusive hadronic processes, are considered. The current open problems of the TMD-approach 
are discussed.