Shedding light on shadow generalized parton distributions
Eric Moffat, Adam Freese, Ian C. Cloët, Thomas Donohoe, Leonard Gamberg, Wally Melnitchouk, Andreas Metz, Alexei Prokudin, N. Sato
Abstract
The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called ``shadow GPDs'' (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale ${Q}^{2}$) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale ${Q}_{0}^{2}$) by data that has a finite ${Q}^{2}$ range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that ${Q}^{2}$ evolution, given empirical data over a wide range of skewness ($\ensuremath{\xi}$) and ${Q}^{2}$ scales, constrains the SGPDs studied at low $x$ and low $\ensuremath{\xi}$. If this finding generalizes to all SGPDs---and we have not been able to find any SGPDs with qualitatively different behavior---then this potentially makes extraction of GPDs from DVCS possible over a limited range of $x$ and $\ensuremath{\xi}$.