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We show that transverse-momentum-dependent parton distribution functions (TMDPDFs), important non-perturbative quantities for describing the properties of hadrons in high-energy scattering processes such as Drell-Yan and semi-inclusive deep-inelastic scattering with observed small transverse momentum, can be obtained from Euclidean QCD calculations in the framework of large-momentum effective theory (LaMET). We present a LaMET factorization of the Euclidean quasi-TMDPDFs in terms of the physical TMDPDFs and off-light-cone soft function at leading order in $1/P^z$ expansion, with the perturbative matching coefficient satisfying a renormalization group equation. We also discuss the implementation in lattice QCD with finite-length gauge links as well as the rapidity-regularization-independent factorization for Drell-Yan cross section.
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We show possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions in addition to the leading twist-2 ones by investigating all the possible decomposition of a quark correlation function in the Lorentz-invariant way. The Hermiticity and parity invariance are imposed in the decomposition; however, the time-reversal invariance is not used due to an active role of gauge links in the TMDs. Therefore, there exist time-reversal-odd functions in addition to the time-reversal even ones in the TMDs. We list all the functions up to twist-4 level because there were missing terms associated with the lightcone vector $n$ in previous works on the twist-2 part and there was no correlation-function study in the twist-3 and 4 parts for spin-1 hadrons. We show that 40 TMDs exist in the tensor-polarized spin-1 hadron in twists 2, 3, and 4. Some expressions of twist-2 structure functions are modified from previous derivations due to the new terms with $n$, and we find 30 new structure functions in twists 3 and 4 in this work. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtain new sum rules for the time-reversal-odd structure functions, $ int d^2 k_T h_{LT}= int d^2 k_T h_{LL} = int d^2 k_T h_{3LL} =0$. In addition, we indicate that new transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs are rare observables to find explicit color degrees of freedom in terms of color flow, which cannot be usually measured because the color is confined in hadrons.
We compare recent, seemingly different, approaches to TMD-factorization (due to Echevarria, Idilbi, and Scimemi and to Collins), and show that they are the same, apart from an apparent difference in their definition of the MSbar{} renormalization scheme.
We apply recent developments in large momentum effective theory (LaMET) to formulate a non-perturbative calculation of the single-transverse spin asymmetry in terms of the quasi transverse-momentum-dependent quark distribution functions from the so-called Sivers mechanism. When the spin asymmetry is defined as the ratio of the quark Sivers function over the spin averaged distribution, it can be directly calculated in terms of the relevant quasi distributions with the soft functions and perturbative matching kernels cancelling out. Apart from the general formula presented, we have verified the result in the small transverse distance limit at one-loop order, which reduces to a collinear expansion at twist-three level.
We provide a concise overview on transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q_T spectra of Higgs and vector bosons for low q_T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present an application of a new tool, TMDlib, to parton density fits and parameterizations.
We present a summary of a recent workshop held at Duke University on Partonic Transverse Momentum in Hadrons: Quark Spin-Orbit Correlations and Quark-Gluon Interactions. The transverse momentum dependent parton distribution functions (TMDs), parton-to-hadron fragmentation functions, and multi-parton correlation functions, were discussed extensively at the Duke workshop. In this paper, we summarize first the theoretical issues concerning the study of partonic structure of hadrons at a future electron-ion collider (EIC) with emphasis on the TMDs. We then present simulation results on experimental studies of TMDs through measurements of single spin asymmetries (SSA) from semi-inclusive deep-inelastic scattering (SIDIS) processes with an EIC, and discuss the requirement of the detector for SIDIS measurements. The dynamics of parton correlations in the nucleon is further explored via a study of SSA in D (`D) production at large transverse momenta with the aim of accessing the unexplored tri-gluon correlation functions. The workshop participants identified the SSA measurements in SIDIS as a golden program to study TMDs in both the sea and valence quark regions and to study the role of gluons, with the Sivers asymmetry measurements as examples. Such measurements will lead to major advancement in our understanding of TMDs in the valence quark region, and more importantly also allow for the investigation of TMDs in the sea quark region along with a study of their evolution.
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