Related papers: Comparison of numerical solutions for Q^2 evolutio…
In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that the virtual and unresolved-real…
We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning $x$-space which is closed under the considered evolution equation. Using these functions as a basis, the…
A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…
In processes taking place at energies much higher than the weak scale, electroweak corrections can be taken into account by using electroweak evolution equations, that are analogous to the DGLAP equations in QCD. We show that weak isospin…
A complete numerical implementation, in both singlet and non-singlet sectors, of a very elegant method to solve the QCD Evolution equations, due to Furmanski and Petronzio, is presented. The algorithm is directly implemented in x-space by a…
A numerical method to solve linear integro-differential equations is presented. This method has been used to solve the QCD Altarelli-Parisi evolution equations within the H1 Collaboration at DESY-Hamburg. Mathematical aspects and numerical…
Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The…
Parton distribution functions play a pivotal role in hadron collider phenomenology. They are non-perturbative quantities extracted from fits to available data, and their scale dependence is dictated by the DGLAP evolution equations. In this…
We present an analytical method to solve the leading order (LO) Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, which describe how parton distribution functions (PDFs) vary through different energy scales. Our…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
Using a recursive algorithm to solve the renormalization group equations of N=1 QCD (DGLAP), we describe the most general supersymmetric evolution of the parton distributions. The analysis involves the regular DGLAP evolution, a partial…
A matrix-based approach to numerical integration of the DGLAP evolution equations is presented. The method arises naturally on discretisation of the Bjorken x variable, a necessary procedure for numerical integration. Owing to peculiar…
We derive evolution equations for the truncated Mellin moments of the parton distributions. We find that the equations have the same form as those for the partons themselves. The modified splitting function for n-th moment $P'(n,x)$ is…
We present the exact and precise (~0.1%) numerical solution of the QCD evolution equations for the parton distributions in a wide range of $Q$ and $x$ using Monte Carlo (MC) method, which relies on the so-called Markovian algorithm. We…
QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution,…
The standard analytic solution to the DGLAP equation in Mellin space is improved by resumming the large x divergences. Explicit results are given to next-to-leading order and next-to-leading logarithmic accuracy. Numerically, the…
We explain particular, unique, approximate solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations and also solutions of DGLAP evolution equations by using regge behaviour of structure functions and method of…
We start from the two existing QCD evolution equations for structure functions, the BFKL and DGLAP equations, and discuss the theoretical hints for a unifying picture of the evolution in $x$ and $Q^2.$ The main difficulty is due to the…
Aspects of the QCD parton densities are briefly reviewed, drawing some parallels to the density matrix formulation of quantum mechanics, exemplified by Wigner functions. We elaborate on the solution of their evolution equations using…
The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong…