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

Abstract

To exemplify the special role played by the light cone (${y}^{2}=0$) in highly inelastic electroproduction, we study the contribution to electroproduction of singularities on other hyperboloids, ${y}^{2}={a}^{2}>0$. A light-cone singularity is shown to dominate by at least the power ${\ensuremath{\nu}}^{\frac{3}{4}}$ 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 $\ensuremath{\nu}$ multiplying a function of $x=\frac{{Q}^{2}}{2M\ensuremath{\nu}}$, but instead to oscillate with the (asymptotically infinite) frequency ${[{a}^{2}M\ensuremath{\nu}(1\ensuremath{-}x)]}^{\frac{1}{2}}$ in the Bjorken limit.