We present a fit of the transverse momentum spectrum for Drell-Yan and semi-inclusive deep inelastic scattering data, based on transverse momentum dependent (TMD) factorization at N LL accuracy. Our analysis shows good agreement with the data and confirms the findings of previous studies. Based on this, we extract the unpolarized TMD parton distribution functions, the TMD fragmentation functions, and the Collins-Soper kernel. Compared to earlier works, our study incorporates several improvements, including large-$\textit{x}$ resummation, flavor and fragmentation function dependence, among others. Additionally, we supplement our extraction with an analysis of the transverse momentum moments of the extracted distributions.

Taiwan

Valentin Moos

Spain

Ignazio Scimemi

Alexey Vladimirov

Pia Zurita

Determination of unpolarized TMD distributions from the fit of Drell-Yan and SIDIS data at N

We critically examine the back-to-back limit of the energy-energy correlation (EEC) in $\textit{e}$ $\textit{e}$ annihilation as a potential source of information on the Collins-Soper kernel and the strong coupling constant. The analysis is performed within the framework of transverse momentum dependent (TMD) factorization at next-to-next-to-next-to-next-to-leading logarithmic (N LL) accuracy, using a global fit to all available experimental data. Contrary to previous claims, we demonstrate that the current data do not provide meaningful constraints on either the Collins-Soper kernel or $\textit{α}$ .

Alejandro Cuerpo

Assessing the sensitivity of energy-energy correlations in $\textit{e}$

We investigate the collinear matching of transverse momentum dependent (TMD) distributions at large values of $\textit{x}$, computing and resumming the leading large-$\textit{x}$ asymptotics for matching coefficients. The large-$\textit{x}$ resummation is done directly within TMD distributions, ensuring the process-independence of the result. The derived resummation formulas are valid for all TMD distributions (except the pretzelosity). Their application improves perturbative convergence, provides practical estimation for unknown higher-order contributions, and sets restrictions for the nonperturbative part of models. Using the known anomalous dimensions, resummation can reach N LL, often exceeding the accuracy of known coefficient functions.

Oscar Rio

United States

Alexei Prokudin

Transverse momentum distributions at large-$\textit{x}$

The transverse momentum dependent (TMD) factorization theorem accommodates various types of power corrections. Among them, the least studied are $\textit{q}$ $\textit{/Q}$ corrections, which become significant at large values of transverse momentum. These corrections partially originate from higher-twist TMD distributions, which exhibit singularity at small transverse distances. We propose a decomposition that reveals this singularity explicitly, and makes the $\textit{q}$ $\textit{/Q}$ correction manifest. As a concrete application, we consider the next-to-leading power correction for the angular distributions in Drell-Yan, and determine the leading $\textit{q}$ $\textit{/Q}$ corrections. These corrections are significant for the angular distributions $\textit{A}$ and $\textit{A}$ , in complete agreement with the data.

Arturo Arroyo-Castro

Leading $\textit{q}$

We present a comprehensive study of the angular structure functions for Drell-Yan leptons in Z/γ-boson production within the framework of the transverse momentum dependent (TMD) factorization theorem, including kinematic power corrections (KPCs). We find good agreement with the data in the applicability region of the TMD factorization theorem. The inclusion of KPCs allows us to describe all angular coefficients in a frame-independent manner using only the leading-twist TMD distributions: the unpolarized and the Boer-Mulders functions. The value of the Boer-Mulders function is determined using the ATLAS measurement of the A 2 angular coefficient. The analysis is performed at N4LL perturbative order. Additionally, we discuss the technical implementation and impact of KPCs on the phenomenology of TMD distributions.

Sara Piloñeta

Angular distributions of Drell-Yan leptons in the TMD factorization approach

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 factorization formalism at the next-to-leading power. All perturbative elements of the factorization theorem—coefficient functions and evolution kernels—are presented at one-loop accuracy. We found several differences with earlier derivations, which are due to accounting for nontrivial kinematics of the quark-gluon interference terms. As a side result, we present the definition and evolution of twist-three TMD fragmentation functions, including the leading-order evolution kernel.

France

Simone Rodini

Transverse momentum dependent factorization for SIDIS at next-to-leading power

Twist-3 collinear parton distribution functions (PDFs) are matrix elements of quark-gluon-quark or three-gluons light-cone operators. They depend on three momentum fraction variables, which are restricted to a hexagon region, and the evolution kernels are defined via two-dimensional convolution in these variables. We present the numerical realisation of the twist-3 evolution equations at leading order in the strong coupling for all kinds of twist-3 PDF (quark, gluon, chiral-even/odd, etc). We provide two independent codes (in C and Fortran) that have been extensively cross-checked, and are ready-to-use. We supplement the paper with a review of known properties of twist-3 PDFs.

Germany

Italy

Lorenzo Rossi

Numerical implementation of evolution equations for twist-3 collinear PDFs

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear distributions. We define weighted integrals of TMDs that we call Transverse Momentum Moments (TMMs) and prove that TMMs are equal to collinear distributions evaluated in some minimal subtraction scheme. The conversion to the modified minimal subtraction (<math><mover><mi>MS</mi><mo>¯</mo></mover></math>) scheme can be done by a calculable factor, which we derive up to three loops for some cases. We discuss in detail the zeroth, the first, and the second TMMs and provide phenomenological results for them based on the current extractions of TMDs. The results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures.

Oscar del Rio

Transverse momentum moments

We present an extraction of unpolarized transverse momentum dependent parton distributions functions (TMDPDFs) and Collins-Soper kernel from the fit of Drell-Yan and weak-vector boson production data. The TMDPDF are parameterized, as commonly done, using their (large transverse momentum) asymptotic matching to PDF. The analysis is done at the next-to-next-to-next-to-next-to leading logarithmic accuracy (N4LL) (performed only approximately because PDF evolution is known so far at next-to-next-to leading order (NNLO)). The non-perturbative model used for TMDPDF is flavor dependent to reduce the colllinear PDF bias. The estimation of uncertainties is done with the replica method and, for the first time, it includes the propagation of uncertainties due to the collinear distributions.

Extraction of unpolarized transverse momentum distributions from the fit of Drell-Yan data at N4LL

The partons’ transverse momentum can be explored with QCD lattice simulations by studying the quasitransverse-momentum-dependent parton distribution functions (qTMDPDFs), which are factorized in terms of physical TMDPDFs and soft factors in the limit of the large hadron’s momentum. We present the next-to-next-to-leading order (NNLO) calculation of the coefficient function for this factorization. Together with already known expressions for anomalous dimensions, this result allows analysis of lattice data at NNLO perturbative accuracy.