Collinear and Transverse Momentum Dependent parton densities obtained with a Parton Branching Method

We present a solution of the DGLAP evolution equations, written in terms of Sudakov form factors to describe the branching and no-branching probabilities, using a parton branching Monte Carlo method. We demonstrate numerically that this method reproduces the semi-analytical solutions. We show how this method can be used to determine Transverse Momentum Dependent (TMD) parton distribution functions, in addition to the usual integrated parton distributions functions. We discuss numerical effects of the boundary of soft gluon resolution scale parameter on the resulting parton distribution functions. We show that a very good fit of the integrated TMDs to high precision HERA data can be obtained over a large range in x and Q$^2$