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The $x$-dependence of the symmetries of (1+1)-dimensional scalar translationally invariant evolution equations is described. The sufficient condition of (quasi)polynomiality in time $t$ of the symmetries of evolution equations with constant…

Analysis of PDEs · Mathematics 2007-05-23 Artur Sergyeyev

Semi-Inclusive Deep-Inelastic Scattering provides unique access to the three-dimensional momentum and spin structure of the proton, enabling precise studies of parton dynamics and hadronization in QCD. We present a transverse-momentum…

High Energy Physics - Phenomenology · Physics 2026-02-09 Jun Gao , Hai Tao Li , Hua Xing Zhu , Yu Jiao Zhu

Its cornerstone were studies of hadron production in deep inelastic scattering (DIS), which can be interpreted in the transverse-momentum-dependent (TMD) factorisation framework, allowing to access the distributions of polarisation and…

High Energy Physics - Experiment · Physics 2026-05-13 Jan Matousek

I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. I summarize basic results while attempting to trace their development over that…

High Energy Physics - Phenomenology · Physics 2016-07-20 Ted C. Rogers

The Parton Branching (PB) approach describes the evolution of transverse momentum dependent (TMD) parton densities. We propose to extend the PB method by including TMD splitting functions, instead of the DGLAP splitting functions which…

High Energy Physics - Phenomenology · Physics 2022-03-29 Lissa Keersmaekers

We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the…

High Energy Physics - Phenomenology · Physics 2009-11-11 P. Rembiesa , A. M. Stasto

I show that the forms of the Collins-Soper-Sterman and renormalization-group equations for the evolution of transverse-momentum-dependent (TMD) parton densities in QCD follow from the structure of TMD factorization. A derivation does not…

High Energy Physics - Phenomenology · Physics 2019-11-28 John Collins

I present a highly efficient method for evolving parton distributions in perturbative QCD. The method allows evolving the parton distribution functions according to any of the commonly-used truncations of the evolution equations (which…

High Energy Physics - Phenomenology · Physics 2014-11-17 David A. Kosower

The Fortran package QCD-PEGASUS is presented. This program provides fast, flexible and accurate solutions of the evolution equations for unpolarized and polarized parton distributions of hadrons in perturbative QCD. The evolution is…

High Energy Physics - Phenomenology · Physics 2014-11-17 A. Vogt

I present some results about transverse momentum dependent distribution and fragmentation functions. Firstly I illustrate a simple model, with predictive power about the energy behavior, for T-odd, chiral odd functions. Moreover I propose a…

High Energy Physics - Phenomenology · Physics 2008-11-26 E. Di Salvo

This talk reports on recent work where we studied the connection between the description of semi-inclusive DIS at high transverse momentum (based on collinear factorization) and low transverse momentum (based on…

High Energy Physics - Phenomenology · Physics 2008-09-04 Alessandro Bacchetta , Daniel Boer , Markus Diehl , Piet J. Mulders

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,…

High Energy Physics - Phenomenology · Physics 2017-08-23 F. Hautmann , H. Jung , A. Lelek , V. Radescu , R. Zlebcik

The typical transverse momentum of a quark in the proton is a basic property of any QCD based model of nucleon structure. However, calculations in phenomenological models typically give rather small values of transverse momenta, which are…

High Energy Physics - Phenomenology · Physics 2022-02-01 A. I. Signal , F. G. Cao

We describe a QCD based model which incorporates the main properties of the inclusive particle distributions expected for diffractive processes, including the diffractive dissociation at high energies. We study, in turn, the total cross…

High Energy Physics - Phenomenology · Physics 2021-03-17 V. A. Khoze , A. D. Martin , M. G. Ryskin

Based on a recent work on the quantum chromodynamic (QCD) factorization for semi-inclusive deep-inelastic scattering (DIS), we present a set of factorization formulas for the spin-dependent DIS and Drell-Yan cross sections at low transverse…

High Energy Physics - Phenomenology · Physics 2009-11-10 Xiangdong Ji , Jian-Ping Ma , Feng Yuan

The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated…

High Energy Physics - Phenomenology · Physics 2023-07-07 Kai-Bao Chen , Tianbo Liu , Yu-Kun Song , Shu-Yi Wei

The semi-inclusive deep-inelastic scattering (SIDIS) is the golden process for investigating the nucleon's transverse momentum-dependent (TMD) structure. We present the complete expression for SIDIS structure functions in the TMD…

High Energy Physics - Phenomenology · Physics 2025-01-15 Simone Rodini , Alexey Vladimirov

We present a review of current Transverse Momentum Dependent (TMD) phenomenology focusing our attention on the unpolarized TMD parton distribution function and the Sivers function. The paper introduces and comments about the new…

High Energy Physics - Phenomenology · Physics 2015-06-23 Stefano Melis

We assess the current phenomenological status of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) and study the effect of consistently including perturbative QCD (pQCD) evolution.…

High Energy Physics - Phenomenology · Physics 2015-03-18 S. Mert Aybat , Ted C. Rogers

By considering semi-inclusive deep-inelastic scattering and the (complementary) $q_T$-spectrum for Drell-Yan lepton pair production we derive the QCD evolution for all the leading-twist transverse momentum dependent distribution and…

High Energy Physics - Phenomenology · Physics 2014-07-10 Miguel G. Echevarria , Ahmad Idilbi , Ignazio Scimemi