A COMPLETE O(ALPHA-ALPHA(S)) CALCULATION OF THE PHOTON-) ANNIHILATION(1 JET RATE IN E(+)E()

We present a complete calculation of the photon + 1 jet rate in e(+)e( -) annihilation up to O(acr,). Although formally of next-to-leading or der in perturbation theory, this calculation contains several ingredie nts appropriate to a next-to-next-to-leading order calculation of jet observables. In particular, we describe a generalization of the common ly used phase space slicing method to isolate the singularities presen t when more than one particle is unresolved. Within this approach, we analytically evaluate the singularities associated with the following double unresolved regions: triple collinear, soft/collinear and double single collinear configurations as well as those from the collinear l imit of virtual graphs. By comparing the results of our calculation wi th the existing data on the photon + 1 jet rate from the ALEPH Collabo ration at CERN, we make a next-to-leading order determination of the p rocess-independent non-perturbative quark-to-photon fragmentation func tion Dq-->gamma(z, mu(F)) at O(alpha alpha(s)). As a first application of this measurement allied with our improved perturbative calculation , we determine the dependence of the isolated photon + 1 jet cross sec tion in a democratic clustering approach on the jet resolution paramet er y(cut) at next-to-leading order. The next-to-leading order correcti ons to this observable are moderate but improve the agreement between theoretical prediction and experimental data. (C) 1998 Elsevier Scienc e B.V.