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The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop splitting functions in perturbative QCD that control the evolution of quark non-singlet distributions. We confirm previous partial…

High Energy Physics - Phenomenology · Physics 2026-04-27 Thomas Gehrmann , Andreas von Manteuffel , Vasily Sotnikov , Tong-Zhi Yang

We have obtained a general solution of evolution equations for QCD twist-2 string operators in form of expansion over complete set of orthogonal eigenfunctions of evolution kernels in coordinate-space representation. In the leading…

High Energy Physics - Phenomenology · Physics 2009-10-31 N. Kivel , L. Mankiewicz

We study, to all orders in perturbative QCD, the universal behavior of the saturation momentum $Q_s(L)$ controlling the transverse momentum distribution of a fast parton propagating through a dense QCD medium with large size $L$. Due to the…

High Energy Physics - Phenomenology · Physics 2023-07-26 Paul Caucal , Yacine Mehtar-Tani

Phenomenological studies of transverse momentum dependent (TMD) parton distributions rely on the expansion in small values of the transverse separation of fields, where TMD parton distributions match onto collinear parton distribution…

High Energy Physics - Phenomenology · Physics 2023-09-07 Simone Rodini , Alessio Carmelo Alvaro , Barbara Pasquini

We investigate the twist three distribution function $e(x)$ in light-front Hamiltonian perturbation theory. In light-front gauge, by eliminating the constrained field, we find a mass term, an intrinsic transverse momentum dependent term and…

High Energy Physics - Phenomenology · Physics 2014-11-20 Asmita Mukherjee

A collection of results is presented relevant for the analysis of azimuthal asymmetries in inclusive two-hadron production at BELLE. The aim of this overview is to provide theoretical ingredients necessary to extract the Collins effect…

High Energy Physics - Phenomenology · Physics 2008-11-26 Daniel Boer

Using soft collinear effective field theory, we derive the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) operator. We check the factorization theorem at one-loop level and compute the corresponding…

High Energy Physics - Phenomenology · Physics 2020-05-06 Alexey A. Vladimirov , Andreas Schäfer

The partons' transverse momentum can be explored with QCD lattice simulations by studying the quasi-transverse-momentum-dependent parton distribution functions (qTMDPDFs), which are factorized in terms of physical TMDPDFs and soft factors…

High Energy Physics - Phenomenology · Physics 2023-12-19 Óscar del Río , Alexey Vladimirov

We report on the first global analysis of transverse momentum dependent helicity distributions of the proton. The analysis is performed at next-to-leading order with the evolution factor at next-to-next-to-leading-logarithmic accuracy.…

High Energy Physics - Phenomenology · Physics 2025-04-01 Ke Yang , Tianbo Liu , Peng Sun , Yuxiang Zhao , Bo-Qiang Ma

We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD…

High Energy Physics - Phenomenology · Physics 2022-08-22 Zhi Hu , Siqi Xu , Chandan Mondal , Xingbo Zhao , James P. Vary

Transverse momentum dependent (TMD) distribution and fragmentation functions are described as Fourier transforms of matrix elementscontaining nonlocal combinations of quark and gluon fields. These matrix elements also contain a gauge link…

High Energy Physics - Phenomenology · Physics 2022-03-02 P. J. Mulders , M. G. A. Buffing , A. Mukherjee

Within a perturbative approach to Quantum Chromodynamics (QCD), we show how to extend ordinary DGLAP longitudinal evolution equations to include the radiative transverse momentum generated in the collinear branching regime. Considering…

High Energy Physics - Phenomenology · Physics 2008-11-26 Federico A. Ceccopieri

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

We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator…

High Energy Physics - Phenomenology · Physics 2020-01-08 Ming-Xing Luo , Xing Wang , Xiaofeng Xu , Li Lin Yang , Tong-Zhi Yang , Hua Xing Zhu

We study gradient corrections to the transport equation for energetic light partons in dense QCD environments. In the diffusion limit, the transport dynamics is solely controlled by small-angle elastic scatterings, leading to transverse…

High Energy Physics - Phenomenology · Physics 2023-03-29 João Barata , Andrey V. Sadofyev , Xin-Nian Wang

We review the nucleon's twist-3 polarized structure functions from the viewpoint of gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton…

High Energy Physics - Phenomenology · Physics 2009-10-31 Jiro Kodaira , Kazuhiro Tanaka

We describe a procedure to determine moments of parton distribution functions of any order in lattice quantum chromodynamics (QCD). The procedure is based on the gradient flow for fermion and gauge fields. The flowed matrix elements of…

High Energy Physics - Lattice · Physics 2024-10-03 Andrea Shindler

To study the heavy quark production processes, we use the transverse momentum dependent (TMD, or unintegrated) gluon distribution function in a proton obtained recently using the Kimber-Martin-Ryskin prescription from the Bessel-inspired…

High Energy Physics - Phenomenology · Physics 2021-10-04 A. V. Kotikov , A. V. Lipatov , P. Zhang

We initiate the study of transverse momentum-dependent (TMD) fragmentation functions for heavy quarks, demonstrate their factorization in terms of novel nonperturbative matrix elements in heavy-quark effective theory (HQET), and prove new…

High Energy Physics - Phenomenology · Physics 2023-10-06 Rebecca von Kuk , Johannes K. L. Michel , Zhiquan Sun

The transverse spin of interacting light quarks is described by two independent non-perturbative inputs, twist-2 transversity and twist-3 quark-gluon correlators, while for free massive quarks they are related by the equations of motion.…

High Energy Physics - Phenomenology · Physics 2007-05-23 O. V. Teryaev