FRIF Workshop on First Principles Non-Perturbative QCD of Hadron Jets Review of Power Corrections in DIS

Event shape variables are known to exhibit rather large hadronisation effects, not treated by purely perturbative calculations. It has been shown [1] that the size of these corrections varies as (Λ/Q), with Q being the hard scale of the process, for most of the event shape observables. This article focuses on power corrections in the approach initiated by Dokshitzer and Webber [2], since these are the most complete theory and often used in comparisons to data. There is a wealth of studies performed in ee annihilation which gives support to this concept, cf. to contribution R002 in these proceedings. It is interesting to extend these studies to deep-inelastic scattering (DIS), in order to investigate the universality of the ansatz and to check for possible modifications of the hadronisation process due to the presence of a proton remnant. After power corrections to mean values of event shapes variables became available [3], the H1 and later also the ZEUS Collaboration published analyses which corroborated this concept [4, 5]. A comprehensive review on the subject of event shapes can be found in [6]. When comparing the ep scattering to ee annihilation, one moves from an s-channel to a t-channel exchange, with the negative four momentum transferred Q corresponding to the center of mass energy √ s. At HERA a large range of the scale is available in a single experiment, typically stretching 5 < Q < 115GeV. The theoretical treatment is complicated by initial state singularities related to the incoming proton, which are absorbed in the parton density functions (pdf). In order to reject the proton dissociation part of an event (the remnant), the event shapes are calculated in the Breit frame of reference, where the separation between particles from the hard scattering and the remnant is clearest. The boost to the Breit frame is determined by the event kinematics and the boosted particles are separated into hemispheres with pseudorapidity η < 0 (current hemisphere) and η > 0 (remnant hemisphere). Usually only particles of the current hemisphere enter the event shape definition, where this hemisphere resembles to some extend one half of an ee event. In order to ensure infrared safety at all orders a minimal energy in the current hemisphere is applied as part of the observable’s definition, e.g. ECH > Q/10.