Predictions for all processes e^+e^- -> 4 fermions + gamma

TL;DR

This work delivers a complete tree-level treatment of $e^+e^-\to 4f$ and $e^+e^-\to 4f\gamma$ processes within the Electroweak Standard Model for massless, polarized fermions, reducing all final states to a compact set of gauge-invariant amplitudes. Using Weyl–van der Waerden spinor methods in a non-linear gauge, the authors derive two generic amplitude structures that generate all six-fermion final states and extend them to radiative processes with a photon. They implement two independent Monte Carlo generators employing multi-channel phase-space integration with adaptive weight optimization, including up to 128 (4f) and 928 (4f gamma) channels, and investigate finite-width schemes, finding the complex-mass approach to be Ward-identities preserving and numerically reliable. Numerical results cover integrated cross sections and photon-energy distributions, revealing important contributions from non-resonant diagrams and QCD gluon-exchange in certain channels, and showing the running-width scheme to be inadequate at higher energies. The study provides cross-checks against existing results (e.g., CERN 96 tables and Ae91) and offers a robust framework for precise predictions at LEP2 and future linear colliders, including a building block for ${\cal O}(\alpha)$ radiative corrections to four-fermion production.

Abstract

The complete matrix elements for e^+ e^- -> 4f and e^+ e^- -> 4f + gamma are calculated in the Electroweak Standard Model for polarized massless fermions. The matrix elements for all final states are reduced to a few compact generic functions. Monte Carlo generators for e^+ e^- -> 4f and e^+ e^- -> 4f + gamma are constructed. We compare different treatments of the finite widths of the electroweak gauge bosons; in particular, we include a scheme with a complex gauge-boson mass that obeys all Ward identities. The detailed discussion of numerical results comprises integrated cross sections as well as photon-energy distributions for all different final states.

Figures (1)

• Figure 1: Generic diagrams for ${\rm e^+}$ e^+${\rm e^-}$ e^-$\to 4f$