Threshold Resummation for Semi-Inclusive Single-Hadron Production with Effective Field Theory

Abstract

Large double-logarithmic corrections are induced by soft gluon emissions near threshold in the semi-inclusive $e^{+}{e}^{-}$ annihilation (SIA) distributions, and must be resummed to all-orders in perturbation theory for reliable theoretical predictions. Building on strategy developed for threshold resummation for DIS structure function in momentum space using soft-collinear effective theory (SCET), we present the explicit formalism for SIA cross section. We then perform the resummation directly in momentum space for ${\gamma }^{\ast }\to q\bar{q}$, $H\to gg$ and $H\to b\bar{b}$ to N${}^4$LL accuracy and demonstrate good convergence. We anticipate that these results will benefit the extraction of the light-quark, the heavy-quark as well as the gluon fragmentation functions.