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DOE OSTI2025

Tomography of the rho meson in the QCD instanton vacuum: Transverse momentum dependent parton distribution functions

We analyze the rho meson unpolarized and polarized transverse momentum dependent parton distribution functions (TMDPDFs) in the instanton liquid model (ILM). The corresponding TMDs in ILM are approximated by a constituent quark beam function in the leading Fock state multiplied by a rapidity-dependent factor resulting from the staple-shaped Wilson lines, for fixed longitudinal momentum, transverse separation, and rapidity. At the resolution of the ILM, all of the rho meson TMDs are symmetric in parton 𝑥 for fixed transverse momentum, and Gaussian-like in the transverse momentum for fixed parton 𝑥. The latter is a direct consequence of the profiling of the quark zero modes in the ILM. The evolved TMDs at higher rapidity using the Collins-Soper kernel, and higher resolution using the renormalization group, show substantial skewness towards low parton 𝑥.

Gluons↗

DOE OSTI2025

Tomography of pions and kaons in the QCD vacuum: Transverse momentum dependent parton distribution functions

We evaluate the pion and kaon transverse momentum dependent parton distribution functions in the instanton liquid model, a model of the QCD vacuum at low resolution. The relevant transverse momentum distributions (TMDs) are factored into a constituent quark distribution times a rapidity dependent soft factor from staple-shaped Wilson lines, for fixed parton longitudinal momentum and transverse separation. The results are evolved to higher rapidities using the Collins-Soper kernel and higher resolution using renormalization group evolution. The comparison to existing extractions of pion TMDs from Drell-Yan data is briefly discussed.

classical solutions in field theory↗

DOE OSTI2024

Phenomenology of TMD parton distributions in Drell-Yan and 𝑍 0 boson production in a hadron structure oriented approach

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to transverse momentum dependent (TMD) phenomenology applied to Drell-Yan-like processes, including lepton pair production at moderate 𝑄 2 and 𝑍 0 boson production. We compare and contrast general features of our methodology with other common practices and emphasize aspects that we view as improvements. Separately, we discuss the importance of treatments that preserve various theoretical properties of the nonperturbative parts of TMD parametrizations for future applications that have the extraction of hadron structure as a primary goal. These include the HSO’s preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear parton density functions, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions. In our examples, we show that there is significant sensitivity at moderate 𝑄 2 to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear parton densities. However, we also find that evolving to 𝑄 2 =𝑀$^2_𝑍$, without fitting, results in a satisfactory postdiction of existing data for 𝑍0 production, nearly independently of the modeling of nonperturbative transverse momentum behavior. We argue that this demonstrates that moderate 𝑄 measurements should be given greater weight than high 𝑄 measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonperturbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Lattice QCD Calculations of Transverse-Momentum-Dependent Soft Function through Large-Momentum Effective Theory

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a 2 + 1 flavor CLS dynamic ensemble with a = 0.098 fm. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentumtransfer pseudoscalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function—the Collins-Soper evolution kernel—based on the large-momentum evolution of the quasi-TMD wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗