Experimental Verification of the Kramers-Kronig Relation at High Energy

The real part of the forward amplitude for Compton scattering on protons was measured through the interference between the Compton and Bethe-Heithler amplitudes by detecting the zero-degree electron pairs asymmetrically. The measurement was made at an average photon energy of $〈k〉=2.2\mathrm{}$ GeV, and an average momentum transfer to the recoil proton $〈t〉=-0.027\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. The result confirms the prediction of the Kramers-Kronig relation.