Finding jets and summing soft gluons: a new algorithm

We examine a new algorithm for finding jets ine⁺e^– annihilation, using a jet measure based on relative transverse momentum. We perform an analytic calculation of the three-jet fraction at lowest order, and compare our result with the standard jet-finding algorithm. For soft gluons in an abelian theory it is shown that the leading double logarithms exponentiate, unlike the situation for the commonly used algorithm based on invariant mass. In QCD we find that there are leading non-abelian logarithms, and we calculate these explicitly atO(_s²). We discuss the modifications to the algorithm which are needed when the mass of a parton cluster is taken into account. The hope is that the new algorithm will allow an improved theoretical analysis at smaller values of the resolution parametery_T, and hence an improved fit to the experimental data.Nick Brown was tragically killed on 13th June, 1991. This paper is dedicated to his memory