Infrared Renormalons and Power Suppressed Effects in $e^+e^-$ Jet Events

TL;DR

The work investigates infrared renormalon–driven power-suppressed corrections to jet-shape observables in $e^+e^-$ annihilation using the large $n_f$ limit of QCD. It decomposes contributions into a factorized Sudakov piece and non-factorizable four-parton terms, analyzing cancellations of infrared divergences in dimensional regularization. The results show that different observables acquire leading $1/Q$ corrections in this limit (notably $\igl\langle 1-t\bigr\rangle$, oblateness, and EEC across angles), while others like thrust and the $c$-parameter may not at leading order; four-parton effects produce observable-dependent power coefficients and can break simple factorization. The authors propose a general conjecture that leading power corrections take the form $α_S^n(Q)/Q$, suggesting a classification of jet shapes by the index $n$ and highlighting the potential for subleading $n_f$ effects to generate $1/Q$ terms even in observables that are clean at leading order.

Abstract

We study the effect of infrared renormalons upon shape variables that are commonly used to determine the strong coupling constant in $e^+e^-$ annihilation into hadronic jets. We consider the model of QCD in the limit of large $n_f$. We find a wide variety of different behaviours of shape variables with respect to power suppressed effects induced by infrared renormalons. In particular, we find that oblateness is affected by $1/Q$ non--perturbative effects even away from the two jet region, and the energy--energy correlation is affected by $1/Q$ non--perturbative effects for all values of the angle. On the contrary, variables like thrust, the $c$ parameter, the heavy jet mass, and others, do not develop any $1/Q$ correction away from the two jet region at the leading $n_f$ level. We argue that $1/Q$ corrections will eventually arise at subleading $n_f$ level, but that they could maintain an extra $\as(Q)$ suppression. We conjecture therefore that the leading power correction to shape variables will have in general the form $α^n_{\rm S}(Q)/Q$, and it may therefore be possible to classify shape variables according to the value of $n$.

Figures (3)

• Figure 1: Dominant diagrams for $e^+e^-$ into jets in the large $n_f$ limit.
• Figure 2: Labeling of external lines for three-- and four--parton processes.
• Figure 3: Oblateness in the collinear limit.