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Non-factorizable corrections to W-pair production

W. Beenakker, A. P. Chapovsky, F. A. Berends

TL;DR

The paper analyzes non-factorizable QED corrections to W-pair mediated four-fermion production in e^+e^- collisions using a double-pole, soft-photon framework. It presents two analytical calculation approaches and a gauge-invariant definition that includes Coulomb-type contributions, revealing discrepancies with earlier work and the absence of final-state mass logarithms. Numerically, these corrections shift the W line-shape at the percent level (≈1–2 MeV in the mass peak at LEP2 energies) and vanish for ZZ- or ZH-mediated processes, supporting neglect of such corrections in current LEP2 analyses. Overall, the work clarifies the gauge structure and practical impact of non-factorizable QED effects on invariant-mass distributions while showing limited influence on angular observables and triple gauge-boson coupling studies.

Abstract

In this paper we study the non-factorizable QED corrections to W-pair-mediated (charged-current) four-fermion production in electron-positron collisions. A brief account of the obtained analytical results is given. They turn out to be different from the ones published in the literature. For the first time numerical results are presented, in particular the effects on the W line-shape. These effects are of the order of a per cent. Applying the same methods to ZZ- or ZH-mediated four-fermion production, the non-factorizable $O(α)$ corrections to the Z or H line-shape vanish.

Non-factorizable corrections to W-pair production

TL;DR

The paper analyzes non-factorizable QED corrections to W-pair mediated four-fermion production in e^+e^- collisions using a double-pole, soft-photon framework. It presents two analytical calculation approaches and a gauge-invariant definition that includes Coulomb-type contributions, revealing discrepancies with earlier work and the absence of final-state mass logarithms. Numerically, these corrections shift the W line-shape at the percent level (≈1–2 MeV in the mass peak at LEP2 energies) and vanish for ZZ- or ZH-mediated processes, supporting neglect of such corrections in current LEP2 analyses. Overall, the work clarifies the gauge structure and practical impact of non-factorizable QED effects on invariant-mass distributions while showing limited influence on angular observables and triple gauge-boson coupling studies.

Abstract

In this paper we study the non-factorizable QED corrections to W-pair-mediated (charged-current) four-fermion production in electron-positron collisions. A brief account of the obtained analytical results is given. They turn out to be different from the ones published in the literature. For the first time numerical results are presented, in particular the effects on the W line-shape. These effects are of the order of a per cent. Applying the same methods to ZZ- or ZH-mediated four-fermion production, the non-factorizable corrections to the Z or H line-shape vanish.

Paper Structure

This paper contains 8 sections, 23 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Non-factorizable corrections: analytical results
  3. Virtual corrections for purely leptonic final states
  4. Real-photon radiation for purely leptonic final states
  5. Gauge-invariant definition of non-factorizable corrections
  6. Semi-leptonic and purely hadronic final states
  7. Numerical results
  8. Conclusions

Figures (3)

  • Figure 1: Virtual diagrams contributing to the manifestly non-factorizable $W$-pair corrections. The scalar functions corresponding to these diagrams are denoted by $D_{0123}$, $D_{0124}$, and $E_{01234}$.
  • Figure 2: The relative non-factorizable correction $\delta_{nf}(M_1,M_2,\cos\theta_1)$ to the decay angular distribution $d\sigma/[dM_1 dM_2 d\cos\theta_1]$ for fixed values of the invariant masses $M_{1,2}$ [in GeV]. Centre-of-mass energy: $\sqrt{s}=184~\hbox{GeV}$.
  • Figure 3: The relative non-factorizable correction $\delta_{nf}(M)$ to the single invariant-mass distributions $d\sigma/dM$. Shown are the corrections to the distributions with respect to $M_1$ and $M_{av}$. Centre-of-mass energy: $\sqrt{s}=184~\hbox{GeV}$.