We develop an approach based on the light-cone sum rules at the leading order of ${\alpha }_S$ to calculate the gravitational form factors $\mathbb{A}(t)$ and $\mathbb{B}(t)$ for the valence quark combinations in a nucleon. Within the proposed model, the predictions for the gravitational form factor $\mathbb{D}(t)$ ($D$-term contributions) have been presented. Comparison with the experimental data and with the results of different models is discussed.

We consider the direct photon production in a two hadron collision with one of the hadrons transversely polarized. By using the contour gauge for gluon fields, we find that there are new twist-\(3\) terms present in the hadron tensor of the considered process in addition to the standard twist-\(3\) terms. In this work, we demonstrate that the significance of these new terms are twofold: first, they are crucial to both the QED and the QCD gauge invariance and, second, their contributions to the hadron tensor are at least the same as those from the standard ones. We also study the resulting effects which are responsible for the universality breaking of the corresponding twist-\(3\) parton distributions.

We revisit the standard representation of the (inverse) Radon transform, which is well known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional contribution, which is essentially related to the generalized transverse-momentum dependent parton distribution and double-distribution functions. We discuss the possible relationship of this term with the Sivers function.

We consider the gauge invariant Drell-Yan hadron tensor which includes the standard and nonstandard diagram contributions. The nonstandard diagram contribution appeared owing to the complexity of the twist three $B^V(x_1,x_2)$-function where the gluon pole manifests. We use the contour gauge conception which allows us to fix easily the spurious uncertainties in the gluon propagator. The contour gauge condition is generated by the corresponding Wilson lines in both the standard and nonstandard diagrams. We demonstrate the substantial role of the nonstandard diagram for forming of the relevant contour in the Wilson path-ordered exponential that leads to the spurious singularity fixing.