Light-Cone Dominance in the Presence of Singularities Elsewhere in Coordinate Space

To exemplify the special role played by the light cone ($y^2=0\mathrm{}$) in highly inelastic electroproduction, we study the contribution to electroproduction of singularities on other hyperboloids, $y^2=a^2>0\mathrm{}$. A light-cone singularity is shown to dominate by at least the power ${\nu }^{\frac{3}{4}}$ over an equivalent singularity on the hyperboloid $y^2=a^2$ in the Bjorken limit. Moreover, the leading contribution from a singularity at $y^2=a^2$ is shown not to scale as a power of $\nu$ multiplying a function of $x=\frac{Q^2}{2M\nu }$, but instead to oscillate with the (asymptotically infinite) frequency ${\left[a^{2}M\nu \mathrm{}\right(1-x\left)\right]}^{\frac{1}{2}}$ in the Bjorken limit.