Resummation of non-global QCD observables

We discuss issues related to the resummation of non-global observables in QCD, those that are sensitive to radiation in only a part of phase space. Examples of such observables are certain single-hemisphere event shapes in e(+)e(-) and DIS. Compared to global observables (those sensitive to all emissions, e.g., the e(+)e(-) thrust) a new class of single-logarithmic terms arises. These have been neglected in recent calculations in the literature. For a whole set of single hemisphere e(+)e(-) and DIS event, shapes, we analytically evaluate the first such term, at order alpha (2)(s), and give numerical results for the resummation of these terms in the large-N-C limit. (C) 2001 Elsevier Science B.V. All rights reserved.