Power Corrections and Renormalons in $e^+e^-$ Fragmentation Functions
M. Dasgupta, B. R. Webber
TL;DR
The paper develops a dispersive, massive-gluon framework to estimate infrared power corrections to $e^+e^-$ fragmentation functions, focusing on the transverse, longitudinal, and asymmetric channels. It shows that leading nonperturbative corrections scale as $1/Q^2$ for individual coefficient functions, but gluon-induced small-$x$ singularities can promote some contributions to $1/Q$ in the separated cross sections, while these cancel in the total cross section. The authors derive explicit $x$-space and moment-space expressions for quark and gluon coefficient functions at $1/Q^2$ and discuss subleading $1/Q^4$ and beyond, highlighting how cancellations reconcile the dispersive approach with sum rules. The results clarify observed paradoxes in the data, connect with hadronization concepts, and provide a practical method to extract nonperturbative parameters such as $A_1$ from fragmentation observables.
Abstract
We estimate the power corrections (infrared renormalon contributions) to the coefficient functions for the transverse, longitudinal and asymmetric fragmentation functions in $e^+e^-$ annihilation, using a method based on the analysis of one-loop Feynman graphs containing a massive gluon. The leading corrections have the expected $1/Q^2$ behaviour, but the gluonic coefficients of the longitudinal and transverse contributions separately have strong singularities at small $x$, which cancel in their sum. This leads to $1/Q$ corrections to the longitudinal and transverse parts of the annihilation cross section, which cancel in the total cross section.