Covariant extension of the GPD overlap representation at low Fock states

Abstract

We present a novel approach to compute generalized parton distributions within the lightfront wave function overlap framework. We show how to systematically extend generalized parton distributions computed within the DGLAP region to the ERBL one, fulfilling at the same time both the polynomiality and positivity conditions. We exemplify our method using pion lightfront wave functions inspired by recent results of non-perturbative continuum techniques and algebraic nucleon lightfront wave functions. We also test the robustness of our algorithm on reggeized phenomenological parameterizations. This approach paves the way to a better understanding of the nucleon structure from non-perturbative techniques and to a unification of generalized parton distributions and transverse momentum dependent parton distribution functions phenomenology through lightfront wave functions.

A Nakanishi-based model illustrating the covariant extension of the pion GPD overlap representation and its ambiguities

“…It can be thereupon formally and rigorously concluded [24,36] that H(x, ξ, t) − sgn(ξ)D(x/ξ, t) results from the Radon transform [37,38] of a given distribution F D 2 ,…”

Universality of Generalized Parton Distributions in Light-Front Holographic QCD

“…One can also obtain effective lightfront wave functions (LFWFs) [28,55] which are relevant for the computation of FFs and PDFs, including polarization dependent distributions [43,44,47]. LFWFs are also used to study the skewness ξ-dependence of the GPDs [41,45,48,50,51], and other parton distributions such as the Wigner distribution functions [38,43]. The downside of the above phenomenological extensions of the holographic model is the large number of parameters required to describe simultaneously PDFs and FFs for each flavor.…”

Nucleon Parton Distribution Amplitude: A Scalar Diquark Picture

“…It allows us to write Bethe-Salpeter and Faddeev amplitudes in terms of a known momentum-dependent kernel and a momentumindependent Nakanishi weight function. Interestingly, PTIR is proved to be valid at all order of perturbation theory, and has already been used successfully in the meson sector to compute PDAs and beyond, Parton Distribution Functions (PDFs) and Generalised Parton Distributions (GPDs) (see [5,[28][29][30][31][32][33][34][35][36][37][38]).…”