The Drell-Yan process is studied in the framework of TMD factorization in the Sudakov region $sgg Q^2gg q_perp^2$ corresponding to recent LHC experiments with $Q^2$ of order of mass of Z-boson and transverse momentum of DY pair $sim$ few tens GeV. Th
e DY hadronic tensors are expressed in terms of quark and quark-gluon TMDs with ${1over Q^2}$ and ${1over N_c^2}$ accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting hadronic tensors depend on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^perp$. The corresponding qualitative and semi-quantitative predictions seem to agree with LHC data on five angular coefficients $A_0-A_4$ of DY pair production. The remaining three coefficients $A_5-A_7$ are determined by quark-quark-gluon TMDs multiplied by extra ${1over N_c}$ so they appear to be relatively small in accordance with LHC results.
The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $sgg Q^2gg q_perp^2$ with ${1over Q^2}$ accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading
order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^perp$. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.
We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those tha
t contain the invariant amplitude determining the gluon PDF in the light-cone $z^2 to 0$ limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the $ln (-z^2)$-dependence at short distances $z^2$. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.
We discuss conformal properties of TMD operators and present the result of the conformal rapidity evolution of TMD operators in the Sudakov region.
The structure constants of twist-two operators with spin $j$ in the BFKL limit $g^2rightarrow 0, jrightarrow 1$ but ${g^2over j-1}sim 1$ are determined from the calculation of the three-point correlator of twist-two light-ray operators in the triple
Regge limit. It is well known that the anomalous dimensions of twist-two operators in this limit are determined by the BFKL intercept. Similarly, the obtained structure constants are determined by an analytic function of three BFKL intercepts.
We present calculation of the correlation function of three twist-2 operators in the BFKL limit. The calculation is performed in N = 4 SYM but the result is valid in other gauge theories such as QCD. The obtained leading order structure constant is exact for any number of colors.
I discuss how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at small $xll 1$ to linear evolution at moderate $xsim 1$.
We compute the correlation function of three twist-2 operators in N = 4 SYM in the leading BFKL approximation at any N_c. In this limit, the result is applicable to other gauge theories, including QCD.
A polarized $ep/eA$ collider (Electron--Ion Collider, or EIC), with polarized proton and light-ion beams and unpolarized heavy-ion beams with a variable center--of--mass energy $sqrt{s} sim 20$ to $sim100$~GeV (upgradable to $sim 150$ GeV) and a lumi
nosity up to $sim 10^{34} , textrm{cm}^{-2} textrm{s}^{-1}$, would be uniquely suited to address several outstanding questions of Quantum Chromodynamics, and thereby lead to new qualitative and quantitative information on the microscopic structure of hadrons and nuclei. During this meeting at Jefferson Lab we addressed recent theoretical and experimental developments in the spin and the three--dimensional structure of the nucleon (sea quark and gluon spatial distributions, orbital motion, polarization, and their correlations). This mini--review contains a short update on progress in these areas since the EIC White paper~cite{Accardi:2012qut}.
We generalize local operators of the leading twist-2 of N=4 SYM theory to the case of complex Lorentz spin j using principal series representation of sl(2,R). We give the direct computation of correlation function of two such non-local operators in t
he BFKL regime when j -> 1. The correlator appears to have the expected conformal coordinate dependence governed by the anomalous dimension of twist-2 operator in NLO BFKL approximation predicted by Kotikov and Lipatov.
