Session Q11: Transverse-Momentum-Dependent Phenomena

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In this talk I will review the current status of transverse momentum dependent (TMD) physics and related phenomena, including both unpolarized and polarized observables. Such studies give us insight into the 3-dimensional structure of hadrons. The focus of the talk will be on recent developments in theory and phenomenology regarding the extraction of TMD parton distribution functions and fragmentation functions (TMDs). The talk will also cover connections of TMDs to aspects of high-energy physics and lattice QCD. Some upcoming measurements at existing and future facilities, and their impact on TMD physics, will also be highlighted.   

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The Collins-Soper kernel relates transverse momentum-dependent parton distribution functions (TMDPDFs) at different energy scales. For small parton transverse momentum qT, this kernel is non-perturbative and can only be determined with controlled uncertainties through experiment or first-principles calculations. Results from the first exploratory determination of the Collins-Soper kernel using the lattice formulation of Quantum Chromodynamics are presented, in which the Nf=0 kernel is calculated for transverse momentum scales in the range 250 MeV < qT <2 GeV. The remaining systematic uncertainties and preliminary unquenched lattice QCD results are discussed.   

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In this talk, I'll discuss our recent global analysis of the Sivers asymmetry which was performed within the transverse momentum dependent (TMD) factorization formalism. In this work, we simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from W/Z boson at RHIC at next-to-leading order (NLO) and next-to-next-to-leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tension arises when trying to describe the spin asymmetries of W/Z bosons at RHIC. We find that the quality of the description of W/Z vector boson asymmetry data could be strongly sensitive to the DGLAP evolution of the Qiu-Sterman function. I'll present a discussion on this effect, possible implications for measurements of the transverse-spin asymmetries at the future Electron-Ion Collider, as well as comparisons of the extracted Sivers function obtained in other recent extractions.   

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We apply the formalism developed earlier $[1,2]$ for studying the small-$x$ asymptotics of transverse momentum dependent parton distribution functions (TMDs) to construct the small-$x$ asymptotics of the quark Sivers function. We explicitly construct the transversely polarized, fundamental ``Wilson line'' operator to sub-sub-eikonal order. We then express the Sivers function in terms of dipole scattering amplitudes containing the transversely polarized ``Wilson line'', and show that the main term which contributes to the Sivers function is the spin-dependent odderon, similar to the case of the gluon Sivers function derived by Boer, Eschevarria, Mulders and Zhou [3] (see also [4]). \vskip 0.2in \noindent [1] Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D99, 054032 (2019). \newline [2] Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D99, 054033 (2019). \newline [3] D. Boer, M. G. Echevarria, P. Mulders, and J. Zhou, Phys. Rev. Lett. 116, 122001 (2016). \newline [4] L. Szymanowski and J. Zhou, Phys. Lett. B760, 249 (2016).   

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I’ll discuss evolution of the small-x gluon helicity operator in the rapidity factorization approach. The operator, which is constructed from a polarized Wilson line with one non-eikonal local operator insertion, gives rise to helicity TMDs at small x. To obtain the evolution equation I employ the background field method and derive the form of the leading sub-eikonal correction to the gluon propagator in the background-Feynman gauge. In the end I’ll discuss relation to the large-x polarized DGLAP evolution.   

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Our calculations for all leading twist structure functions describing the pion induced Drell-Yan process will be presented. In this work the light-front constituent quark model, the spectator model, and available extractions from the experimental data are used as input for the non-perturbative transverse momentum dependent parton distribution functions (TMDs). These TMDs are evolved to the scale of COMPASS Drell-Yan measurements by implementing the TMD evolution at Next-to Leading Logarithmic precision for the first time for all asymmetries. Our results show compatibility with the first experimental information, help to interpret the data from ongoing experiments, and will allow to quantitatively assess the models in future when more precise data will become available.   

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We present a phenomenological study of the transverse momentum distribution (TMD) parton distribution fuction (PDF) of the pion, from pion-induced Drell-Yan (DY) lepton-pair production with existing pion DY data. We describe the matching of the high-transverse momentum (pT) collinear fixed order perturbative QCD pT spectrum, with the low-pT TMD spectrum using using the state-of-the-art Collins-Soper-Sterman (CSS) TMD factorization formalism. Within the global QCD analysis framework of the JAM (Jefferson Lab Angular Momentum) Collaboration, we extract the pion TMD PDF using Bayesian inference. This setup will allow us to perform a simultaneous and self-consistent determination of pion and nucleon TMD PDFs from hard processes and map out the 3-D structure of pions.   

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We show that the transverse momentum dependent parton distribution functions (TMDPDFs), important for understanding 3D hadron structure and describing high-energy experiments, can be formulated in the framework of the large-momentum effective theory(LaMET). We show that the quasi-TMDPDFs, calculable on lattice, factorize at large momentum limit into physical-TMDPDFs and reduced soft functions. We show that the reduced soft function can be realized as a form-factor and can be extracted by combining lattice calculable quasi-light-front wave functions and light-meson form-factors at large momentum transfer. This paves the wave for first-principle determination of TMDPDFs and Drell-Yan cross sections.