Proton generalized parton distributions from electromagnetic form factors: A theoretically constrained phenomenological reconstruction

Abstract

We present a theoretically constrained phenomenological reconstruction of the unpolarized, chiral-even, leading-twist proton generalized parton distributions $H^q$ and $E^q$. At zero skewness, valence-quark distributions are combined with flavor-dependent exponential profiles calibrated simultaneously against phenomenological representations of the proton and neutron electromagnetic form factors. The construction imposes exact valence and anomalous-magnetic-moment normalizations, the low-scale condition $B^{u+d}(0)=0$, the required endpoint behavior, and the complete Gaussian impact-parameter positivity bound. The resulting parametrization provides a reasonable description of the electromagnetic form factors and their slopes while revealing the tension between strict GPD consistency and a precision reproduction of all low-$Q^2$ observables within the adopted ansatz. We extend the distributions to nonzero skewness using normalized double distributions and introduce an independent $D$-term to complete the relevant Mellin polynomials. We examine electromagnetic and energy--momentum-tensor form factors, impact-parameter distributions, positivity, polynomiality, and illustrative mechanical properties. The analysis distinguishes information constrained by electromagnetic data from additional assumptions governing skewness and the mechanical sector, thereby providing a transparent elastic baseline for future studies of nucleon-to-resonance transition GPDs.