Proton magnetic structure revisited: Insights from Patterson function analysis

We employ the Patterson function to investigate the magnetization density distribution of the proton. Our findings indicate that this distribution is strictly non-negative, a result derived via inverse Fourier transform of squared form factor magnitudes, which avoids phase ambiguities and rests on a rigorous mathematical basis. Based on experimental data, we identify a radius at half-maximum Patterson magnetization density ( h _{P M} ^p ) of approximately 0.08 fm. This value may represent an upper bound for the proton magnetic radius—substantially smaller than reported values in the literature, which range between 0.75 fm and 0.89 fm. This disparity highlights potential limitations in conventional techniques such as dispersion analyses, lattice QCD, and scattering methods, and invites renewed scrutiny of underlying assumptions. Rather than challenging current frameworks directly, our approach offers a complementary, model-independent pathway toward clarifying the proton’s internal structure. Notably, a comparative analysis reveals that the Patterson charge distribution is slightly more extended than its magnetization counterpart, suggesting the proton’s charge radius may marginally exceed its magnetic radius.