Non-factorizable photonic corrections to ee->WW->4fermions

TL;DR

The paper develops and implements a gauge-consistent, double-pole approximation framework for non-factorizable photonic corrections to W-pair mediated four-fermion production in e+e- collisions, including the full off-shell Coulomb singularity and the interplay with production/decay corrections. It provides analytic expressions for both virtual and real non-factorizable corrections, reduces the relevant 5-point integrals to 4- and 3-point functions, and validates the results against Be97aBe97b while noting differences with Me96 due to phase-space embedding. Numerically, the authors quantify effects on invariant-mass, angular, and lepton-energy distributions, discuss ambiguities from phase-space parametrization, and offer a practical framework for Monte Carlo implementations. The work extends to related processes and yields predictions that are important for precise W-mass measurements at LEP2 and future colliders.

Abstract

We study the non-factorizable corrections to W-pair-mediated four-fermion production in ee annihilation in double-pole approximation. We show how these corrections can be combined with the known corrections to the production and the decay of on-shell W-boson pairs, and how the full off-shell Coulomb singularity is included. Moreover, we find that the actual form of the real non-factorizable corrections depends on the parametrization of phase space, more precisely, on the definition of the invariant masses of the resonant W bosons. For the usual parametrization the full analytical results for the non-factorizable corrections are presented. Our analytical and numerical results for the non-factorizable corrections agree with a recent calculation, which was found to differ from a previous one. The detailed numerical discussion covers the invariant-mass distribution, various angular distributions, and the lepton-energy distribution for leptonic final states.

Figures (15)

• Figure 1: Examples of non-factorizable photonic corrections in ${\cal O}(\alpha)$. The shaded blobs stand for all tree-level graphs contributing to ${\rm e^+}$ e^+${\rm e^-}$ e^-$\to{\rm W^+}$ W^+${\rm W^-}$ W^-$$. Whenever Feynman diagrams with intermediate would-be Goldstone bosons $\phi^\pm$ instead of $W^\pm$ bosons are relevant, the inclusion of such graphs is implicitly understood.
• Figure 2: Further examples of non-factorizable photonic corrections in ${\cal O}(\alpha)$.
• Figure 3: Example of a non-factorizable real correction.
• Figure 4: Real bremsstrahlung diagram containing non-factorizable and factorizable contributions.
• Figure 5: Illustration of the contour ${\cal C}$ of (\ref{['auxint']}) in the complex $q_0$ plane. The open circles indicate the "particle poles" located at $q_0(p_i)=(2{\bf q}{\bf p}_i-p_i^2+m_i^2)/(2p_{i0})$.