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