Abstract
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.
Highlights
The investigation of the quark-gluon dynamics based on both perturbative and nonperturbative methods is one of the most important subjects of hadron phenomenology
We revisit the standard representation of the Radon transform, which is well known in the mathematical literature
In the first part of this section, we show that the restricted support of the double distributions (DD) function in the physical domain can conditionally lead to the physical restrictions for the generalized parton distributions (GPDs) variables z and ξ
Summary
The investigation of the quark-gluon dynamics based on both perturbative and nonperturbative methods is one of the most important subjects of hadron phenomenology. In [8], the relations between the GPDs and DDs in the context of both the direct and inverse Radon transforms have been studied for the first time. In the present paper, we focus on the physical aspects of the inverse Radon transformation problem in the context of GPDs (we refer the readers to [9] for the modern recent studies). We revisit the (inverse) Radon transforms that connect the DDs with GPDs. We have found a new term that, as we show, is essentially related to the T-odd k⊥-dependent parton distributions. We demonstrate that the restrictions applied on the support of the DDs may lead to the corresponding restrictions for the support of GPDs. The paper is logically divided into two parts: the first part is devoted to the rather mathematical abstract issues related to the (inverse) Radon transforms. The second part is concentrated on the direct physical application of the new contribution to the process descriptions through the transverse-momentum dependent parton distributions
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