Pion generalized parton distributions: A path toward phenomenology

An Introductory Lecture on Generalised Parton Distributions

“…where Θ is the Heaviside function. This forward limit has been at the core of GPD modelling strategies in the past decades [26][27][28][29][30][31], as unpolarised PDFs are nowadays well known from phenomenological extractions on a wide kinematic range in x.…”

“…Different modelling assumptions have been suggested for the tdependent PDF, from the simple product of the PDF with the EFF [26], to Regge-motivated phenomenological models [59]. It was used in the case of the pion [30,60,61] to provide phenomenologically-motivated pion GPDs models and also in the case of the nucleon, where it was used to extract, in a model-dependent way, GPDs from exclusive processes [62,63]. The success of this Ansatz comes from the facts that it is simple to implement, that it is driven by the PDF and EFFs which are much better known quantities, and that it generates phenomenologically meaningful results.…”

“…However, since the inverse Radon problem is infamously ill-posed in the sense of Hadammard, one expects that numerical noise will need to be tamed. The choice which has been made to tackle this problem is to approximate the DD space through finite element methods [30,56]. Within this framework, the DD space is discretised into elements (see fig.…”

“…The interested reader can find numerical details in ref. [30]. We will only highlight that through this method, the system converges toward a solution, providing that the rank of the matrix R is maximal.…”

“…We already highlighted the small-|t| cut, but one also needs to cut on the invariant mass of the nπ system. Such additional cuts make the phase space allowed for Sullivan-DVCS measurement very challenging at current facilities (especially JLab 12) [60], but may allow us to extract pion GPDs at future facilities, such as the electron-ion colliders [30,61]. Let us also mention that if feasible, the Sullivan-DVCS process will allow us to probe the structure of a virtual pion, and thus, virtuality effects may need to be considered to recover the structure of a real pion [139,140].…”