A. Gehrmannderidder et Ewn. Glover, A COMPLETE O(ALPHA-ALPHA(S)) CALCULATION OF THE PHOTON-) ANNIHILATION(1 JET RATE IN E(+)E(), Nuclear physics. B, 517(1-3), 1998, pp. 269-323
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.