On the Universality of the Leading, $1/Q$ Power Corrections in QCD

We discuss $1/Q$ corrections to hard processes in QCD where $Q$ is a large mass parameter like the total energy in $e^+e^-$ annihilation. The main problem we address ourselves to is whether these corrections to different processes (concentrating for definiteness on the Thrust and the Drell-Yan cross section) can be related to each other in a reliable way so that the phenomenology of the $1/Q$ corrections can be developed. We derive first the relation valid to lowest order using both the renormalon and finite-gauge-boson mass techniques to check its independence on the infrared cut- off procedure. We then argue that the $1/Q$ corrections are due to soft gluons which factorize into a universal factor such that the lowest order relations are preserved in higher orders.