Towards precise collider predictions: the Parton Branching method

The collinear factorization theorem, combined with finite-order calculations in perturbative QCD, provides a powerful framework to obtain predictions for many collider observables. However, for observables which involve multiple energy scales, transverse degrees of freedom cannot be neglected, and finite-order perturbative calculations have to be combined with resummed calculations to all orders in the QCD running coupling in order to obtain reliable theoretical predictions, capable of describing experimental measurements. This is traditionally done either by analytic resummation methods or by parton shower (PS) Monte Carlo (MC) methods. In this talk we present the Parton Branching (PB) MC method to obtain QCD collider predictions based on Transverse Momentum Dependent (TMD) factorization. The PB provides evolution equations for TMD Parton Distribution Functions (PDFs) which, upon fitting TMD PDFs to experimental data, can be used in TMD MC event generators. We present the basic concepts of the method and illustrate its applications to collider measurements focusing on Drell-Yan (DY) lepton-pair production in different kinematic ranges, from fixed-target to LHC energies. We discuss the latest developments of the method concentrating especially on the matching of next-to-leading-order (NLO) TMD evolution with MC-at-NLO calculations of NLO matrix elements.