Collinear and TMD quark and gluon densities from parton branching solution of QCD evolution equations

Abstract

We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1% over a range of five orders of magnitude both in evolution scale and in longitudinal momentum fraction. We make predictions for the evolution of transverse momentum distributions. We perform fits to the high-precision deep inelastic scattering (DIS) structure function measurements, and we present a set of NLO TMD distributions based on the parton branching approach.

TMD densities from the Parton branching method

“…In [1,2] we demonstrated that at LO and NLO these PDFs from Parton branching method are within 1% identical with the semi-analytical solution of the DGLAP evolution as implemented in QCDNUM [6]. Such precision was achieved with z m = 1 − 10 −3 and higher z m gives even better agreement.…”

“…Motivated by easy implementation and extensibility and good control over the uncertainties we decided for Monte Carlo technique which employs Markov chain of the branching to solve equation (2.1). Within this method the ∆ a (µ 2 2 )/∆ a (µ 2 1 ) is employed as a non-branching probability between two consequent scales µ 2 1 and µ 2 2 and the splitting function integrated over z < z m represents the branching probability. The method is described in more detail in [2].…”

“…Within this method the ∆ a (µ 2 2 )/∆ a (µ 2 1 ) is employed as a non-branching probability between two consequent scales µ 2 1 and µ 2 2 and the splitting function integrated over z < z m represents the branching probability. The method is described in more detail in [2].…”

“…It is nicely visible that for z m = 1 − 10 −6 there are more soft emissions with z → 1 (vertical lines) than for z m = 1 − 10 −2 . On the other hand, we tested that the obtained PDFs for these two cases are nearly identical [2].…”

“…We discus some aspects of the Parton branching evolution method recently developed in [1,2]. This formalism can be compared with existing evolution equations working in the special part of the phase space: CSS at low transverse momentum [3] and/or CCFM at high energy and low-x region [4].…”