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

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 $\alpha^n_{\rm S}(Q)/Q$, and it may therefore be possible to classify shape variables according to the value of $n$.