Single weak boson production at TeV e +e − colliders

Abstract

We present exact tree level matrix elements for all the single weak boson production processes to order e 3 in very high energy e +e − collisions; e +e − → e ± v (−) c W ∓, e +e − Z, v c v c Z and γγZ. The electron mass is kept finite so that the differential and total cross sections are accurate up to terms of order m e 2/ s. The weak boson distributions are compared with those obtained by the equivalent photon/electron approximation (EPA), which works reasonably well at high vector boson transverse momenta but fails at small transverse momenta for the processes e +e −→ e +e −Z and γγZ. A simple modification of the EPA formulae is found to give a reasonable overall description of the distributions for all the single weak boson production processes. Electron helicity-flip amplitudes are found to contribute at the percent level at most, which can be reproduced accurately by a novel collinear approximation with equivalent real photon or electron distributions in an electron. Interference effects between the annihilation and non-annihilation diagrams are found to be significant only below the weak boson pair production threshold. Also explained is a straightforward method to incorporate the leptonic and parton level hadronic decays of the weak bosons into the production amplitudes.