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We have computed the complete next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of unpolarized parton densities in perturbative QCD. Our results agree with all partial results available in…

High Energy Physics - Phenomenology · Physics 2009-11-10 S. Moch , J. A. M. Vermaseren , A. Vogt

We extend our previous derivation of an exact expression for the leading-order (LO) gluon distribution function $G(x,Q^2)=xg(x,Q^2)$ from the DGLAP evolution equation for the proton structure function $F_2^{\gamma p}(x,Q^2)$ for deep…

High Energy Physics - Phenomenology · Physics 2009-02-13 Martin M. Block , Loyal Durand

We present a next-to-next-to-leading order (NNLO) global QCD analysis of the proton's helicity parton distribution functions (PDFs), the first of its kind. To obtain the distributions, we use data for longitudinal spin asymmetries in…

High Energy Physics - Phenomenology · Physics 2025-03-31 Ignacio Borsa , Daniel de Florian , Rodolfo Sassot , Marco Stratmann , Werner Vogelsang

We present particular and unique solutions of singlet and non-singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) and gluon, sea and valence quark…

High Energy Physics - Phenomenology · Physics 2007-05-23 R Rajkhowa , J K Sarma

In this paper, we discuss the algorithms used in the LO evolution program for nondiagonal parton distributions in the DGLAP region and discuss the stability of the code. Furthermore, we demonstrate that we can reproduce the case of the LO…

High Energy Physics - Phenomenology · Physics 2007-05-23 Andreas Freund , Vadim Guzey

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…

High Energy Physics - Phenomenology · Physics 2010-05-07 R. Rajkhowa

The next-to-leading order (NLO) evolution of the parton distribution functions (PDFs) in QCD is a common tool in the lepton-hadron and hadron-hadron collider data analysis. The standard NLO DGLAP evolution is formulated for inclusive…

High Energy Physics - Phenomenology · Physics 2010-02-02 S. Jadach , M. Skrzypek , A. Kusina , M. Slawinska

In this paper we make predictions for nondiagonal parton distributions in a proton in the LLA. We calculate the DGLAP-type evolution kernels in the LLA, solve the nondiagonal GLAP evolution equations with a modified version of the…

High Energy Physics - Phenomenology · Physics 2014-11-17 L. L. Frankfurt , A. Freund , V. Guzey , M. Strikman

We briefly discuss recent results on the evolution of unpolarized parton densities and structure functions in massless perturbative QCD. Present partial results on the next-to-next-to-leading order (NNLO) evolution kernels prove sufficient…

High Energy Physics - Phenomenology · Physics 2009-10-31 W. L. van Neerven , A. Vogt

Numerical solution of DGLAP $Q^2$ evolution equations is studied for polarized parton distributions by using a ``brute-force" method. NLO contributions to splitting functions are recently calculated,and they are included in our analysis.…

High Energy Physics - Phenomenology · Physics 2007-05-23 M. Hirai , S. Kumano , M. Miyama

Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark-hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in…

High Energy Physics - Phenomenology · Physics 2015-05-28 M. Hirai , S. Kumano

We present recent progress towards a global determination of parton distribution functions (PDFs) at approximate N$^3$LO (aN$^3$LO) accuracy within the NNPDF framework. We construct a parametrisation of the $\mathcal{O}(\alpha_s^4)$ QCD…

High Energy Physics - Phenomenology · Physics 2023-06-28 Felix Hekhorn , Giacomo Magni

We develop the analysis of diphoton exclusive photoproduction in the kinematics where a collinear QCD factorization framework applies, namely nearly forward large invariant mass diphoton production. We work at the leading twist level and at…

High Energy Physics - Phenomenology · Physics 2022-06-01 Oskar Grocholski , Bernard Pire , Paweł Sznajder , Lech Szymanowski , Jakub Wagner

In this paper, we derive two second- order of differential equation for the gluon and singlet distribution functions by using the Laplace transform method. We decoupled the solutions of the singlet and gluon distributions into the initial…

High Energy Physics - Phenomenology · Physics 2015-10-23 G. R. Boroun , S. Zarrin , F. Teimoury

In this work, we investigate the constituent parton distribution functions (PDFs) of the kaon and heavy pseudoscalar mesons within the light-cone quark model. Starting from the initial scale quark and antiquark PDFs, obtained by evaluating…

High Energy Physics - Phenomenology · Physics 2026-05-19 Satyajit Puhan

The dynamics of high partonic density QCD is presented considering, in the double logarithm approximation, the parton recombination mechanism built in the AGL formalism, developed including unitarity corrections for the nucleon as well for…

High Energy Physics - Phenomenology · Physics 2014-11-17 M. B. Gay Ducati

We summarize recent results on the evolution of unpolarized parton densities and deep-inelastic structure functions in massless perturbative QCD. Due to last year's extension of the integer-moment calculations of the three-loop splitting…

High Energy Physics - Phenomenology · Physics 2008-11-26 W. L. van Neerven , A. Vogt

Study of parton distribution function (PDF) is a topic of significant interest in QCD. To overcome the shortcomings of conventional PDFs, several alternative methods have been suggested in recent years. The present work reports the x…

High Energy Physics - Phenomenology · Physics 2009-10-14 D. K. Choudhury , Pijush Kanti Dhar

We recall our recent description of quark parton densities of the proton at $Q^2=4 GeV^2$ in terms of Fermi-Dirac distributions parametrized with very few free parameters. We have also proposed some simple assumptions to relate unpolarized…

High Energy Physics - Phenomenology · Physics 2016-09-01 Claude Bourrely , Jacques Soffer

We provide code to solve the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the nucleon transversity parton distribution functions (PDFs), which encode nucleon transverse spin structure. Though codes are widely…

High Energy Physics - Phenomenology · Physics 2025-12-18 Congzhou M Sha , Bailing Ma