Phenomenology of Power Corrections in Fragmentation Processes in e^+ e^- Annihilation

TL;DR

The paper investigates power-suppressed corrections to fragmentation in $e^+e^-$ annihilation using a framework dominated by ultraviolet contributions and infrared renormalons. It derives the $x$-dependence of leading higher-twist effects, shows that $1/(xQ)^2$ corrections arise in gluon fragmentation, and demonstrates that resummation yields $1/Q$ corrections to individual cross sections that cancel in the total. A practical four-parameter parametrization is proposed to model these corrections in data analyses, enabling improved extractions of the strong coupling $\alpha_s$ from fragmentation observables. The work also discusses the robustness of the gluon contribution, the role of small-$x$ dynamics, and the interplay between perturbative and nonperturbative effects in integrated observables.

Abstract

We analyse power corrections to longitudinal and transverse fragmentation processes in e^+ e^- annihilation, based on the assumption of ultraviolet dominance of power corrections. Under this assumption, we determine the dependence of power corrections on the scaling variable x from the infrared renormalon asymptotics of leading power coefficient functions. Our results suggest that the longitudinal and transverse gluon fragmentation coefficient functions receive corrections of order 1/(x Q)^2. The power expansion breaks down at x<Λ/Q and has to be resummed. This resummation leads to 1/Q corrections to the longitudinal and transverse cross section, which cancel for the total cross section. We provide a simple parametrization of the x dependence of 1/Q^2 corrections to fragmentation processes and investigate perturbative corrections to the longitudinal cross section in higher orders, in view of a determination of the strong coupling.

Figures (9)

• Figure 1: Example of a 'primary' quark contribution to the squared amplitude for $d\sigma_P^q/dx$. The set of all diagrams includes all attachments of the chain of fermion loops to the external quark line, the diagrams with a cut gluon line and an arbitrary number of fermion-loop insertions.
• Figure 2: Example of a 'secondary' quark contribution to the squared amplitude for $d\sigma_P^q/dx$. The set of all diagrams includes all attachments of the chains of fermion loops to the external quark line and an arbitrary number of fermion-loop insertions.
• Figure 3: Shape of $1/Q^2$ power correction $H_{2,L}(x)$ to the longitudinal fragmentation cross section. Dashed line: primary quark contribution. Dotted Line: secondary quark contribution. Solid line: sum of both.
• Figure 4: Shape of $1/Q^2$ power correction $H_{2,T}(x)$ to the transverse fragmentation cross section. Dashed line: primary quark contribution. Dotted Line: secondary quark contribution. Solid line: sum of both.
• Figure 5: Shape of $1/Q^2$ power correction $H_{2,L+T}(x)$ to the sum of longitudinal and transverse fragmentation cross sections. Dashed line: primary quark contribution. Dotted Line: secondary quark contribution. Solid line: sum of both.