NNLL Transverse Momentum Dependent evolution in the Parton Branching method

In the preparation period for precision measurements in the newly planned collider experiments, the understanding of the 3D structure of hadron is becoming increasingly urgent. This triggers the activities to include elements of Transverse Momentum Dependent (TMD) factorization physics in Monte Carlo (MC) event generators. The method designed especially to address this need is the TMD Parton Branching (PB) method. The equivalence of the PB Sudakov form factor, both perturbative and non-perturbative, to the one of Collins-Soper-Sterman (CSS) is demonstrated and the recent development to increase the low-qt resummation precision of the PB Sudakov up to next-to-next-to-leading logarithmic order by using effective soft-gluon coupling is discussed. The Collins-Soper (CS) kernel is extracted from PB Drell-Yan (DY) predictions obtained with different modelling of radiation.