On the universality of the leading, power corrections in QCD

Abstract

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. Euclidean space, such as the total cross section for e + e − → hadrons. The power like corrections can also be studied [2] by means of infrared renormalons since the latter are particular graphs sensitive to large distances. Thus, all the general properties are observed and the nonperturbative contribution results in an overall factor which can be large numerically.The advantage of the renormalon technique is that it can be applied to any infrared safe quantity and it is by using this technique and its variations that 1/Q corrections were discovered recently [3,4,5,6,7,8]. One of the modifications of the renormalon technique is introduction of finite gluon mass (λ) in the evaluation of the lowest order radiative corrections

Resummation of the jet broadening in DIS

“…Accordingly the only NP correction to the broadening comes directly from the transverse momentum of low-momentum particles emitted into the current hemisphere. (This is similar to the effect which reduces the naively calculated power correction to the heavy-jet mass by a factor of two [31,32]). …”

QCD at moderately large distances

“…As has long been expected [ 7,8,9,10], these variables possess relatively large 1/Q confinement correction effects.…”

Power corrections to event shapes and factorization

“…Some time ago, it was shown that perturbation theory itself suggests the exponents p (but not the scales λ p ) for the leading power corrections to the mean values of various event shapes [3,4,5,6]. The simplicity of these results, and the successes of fits to the data based upon them, were somewhat surprising, because previously nonperturbative effects were estimated primarily by comparison to event generators.…”