Proton charge structure revisited: Insights from Patterson function analysis

We apply the Patterson function to derive the charge density distribution of the proton. The resulting Patterson charge density is found to be essentially non-negative, indicating that the intrinsic charge distribution of the proton shares this property. By directly determining the radius at half-maximum Patterson charge density (hPEp = 0.08 fm), we establish a model-independent upper bound on the proton’s charge radius.This value differs substantially from traditional estimates between 0.84 and 0.90 fm, offering fresh insight into the persistent “proton radius puzzle.” Our analysis suggests the need for complementary methods to evaluate proton structure, with Patterson analysis serving as a rigorous mathematical approach. Additionally, structural features observed in the Patterson density imply the presence of internal proton substructure. These findings are rooted in computational methodology and await experimental confirmation.