Threshold Resummation in Momentum Space from Effective Field Theory

Methods from soft-collinear effective theory are used to perform the threshold resummation of Sudakov logarithms for the deep-inelastic structure function $F_2(x,Q^2)$ in the end-point region $x\to 1$ directly in momentum space. An explicit all-order formula is derived, which expresses the short-distance coefficient function $C$ in the convolution $F_2=C\otimes {\varphi }_q$ in terms of Wilson coefficients and anomalous dimensions defined in the effective theory. Contributions associated with the physical scales $Q^2$ and $Q^2(1-x)$ are separated from nonperturbative hadronic physics in a transparent way. A crucial ingredient to the momentum-space resummation is the exact solution to the integro-differential evolution equation for the jet function, which is derived. The methods developed in this Letter can be applied to many other hard QCD processes.