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Electroweak Radiative Corrections to Resonant Charged Gauge Boson Production

Doreen Wackeroth, Wolfgang Hollik

TL;DR

This work develops a gauge-invariant O(α) electroweak correction framework for resonant W production in general 4-fermion processes, casting the cross section near the W peak as a convolution of a process-specific hard cross section with a universal QED radiator function. By a YFS-based decomposition, photonic (QED) corrections are separated into initial, final, and interference pieces, yielding a QED-like factor that multiplies the Born cross section, while non-photonic (weak) corrections are absorbed into a modified weak term that factorizes into partial W production and decay widths. The approach accommodates both constant- and s-dependent W widths and uses soft-photon exponentiation to sum leading logarithms, with explicit results for the W decay width including 1-loop EW and QCD effects. Numerically, the corrections shift the W line shape and reduce the peak cross section, with a mild sensitivity to m_t and M_H, illustrating the importance of including these corrections for precision W-boson measurements at colliders.

Abstract

The electroweak O(alpha) contribution to the resonant single W production in a general 4-fermion process is discussed with particular emphasis on a gauge invariant decomposition into a QED-like and weak part. The cross section in the vicinity of the resonance can be represented in terms of a convolution of a `hard' Breit-Wigner-cross section, comprising the (m_t,M_H)-dependent weak 1-loop corrections, with an universal radiator function. The numerical impact of the various contributions on the W line shape are discussed, together with the concepts of s-dependent and constant width approach. Analytic formulae for the W decay width are also provided including the 1-loop electroweak and QCD corrections.

Electroweak Radiative Corrections to Resonant Charged Gauge Boson Production

TL;DR

This work develops a gauge-invariant O(α) electroweak correction framework for resonant W production in general 4-fermion processes, casting the cross section near the W peak as a convolution of a process-specific hard cross section with a universal QED radiator function. By a YFS-based decomposition, photonic (QED) corrections are separated into initial, final, and interference pieces, yielding a QED-like factor that multiplies the Born cross section, while non-photonic (weak) corrections are absorbed into a modified weak term that factorizes into partial W production and decay widths. The approach accommodates both constant- and s-dependent W widths and uses soft-photon exponentiation to sum leading logarithms, with explicit results for the W decay width including 1-loop EW and QCD effects. Numerically, the corrections shift the W line shape and reduce the peak cross section, with a mild sensitivity to m_t and M_H, illustrating the importance of including these corrections for precision W-boson measurements at colliders.

Abstract

The electroweak O(alpha) contribution to the resonant single W production in a general 4-fermion process is discussed with particular emphasis on a gauge invariant decomposition into a QED-like and weak part. The cross section in the vicinity of the resonance can be represented in terms of a convolution of a `hard' Breit-Wigner-cross section, comprising the (m_t,M_H)-dependent weak 1-loop corrections, with an universal radiator function. The numerical impact of the various contributions on the W line shape are discussed, together with the concepts of s-dependent and constant width approach. Analytic formulae for the W decay width are also provided including the 1-loop electroweak and QCD corrections.

Paper Structure

This paper contains 16 sections, 203 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. $W$ production and $W$ width in leading order
  3. Electroweak radiative corrections in ${\cal O}(\alpha)$ to the $W$ production
  4. The definition of a QED-form factor to the $W$ production
  5. The modified weak 1-loop correction to the $W$ production
  6. Summary
  7. Numerical discussion
  8. Unstable particles and gauge invariance
  9. The partial $W$ width in ${\cal O}(\alpha^2)$
  10. Feynman-rules
  11. The form factors
  12. The form factor describing the photonic 1-loop corrections
  13. The form factors describing the pure weak 1-loop corrections
  14. The form factor describing the soft photon radiation
  15. The hard photon contribution
  16. ...and 1 more sections

Figures (9)

  • Figure 1: $W$ production in the 4-fermion process at leading order
  • Figure 2: 1-loop corrections to the $W$ production in the 4-fermion process ($\Phi^+$: Higgs-ghost, $u^+,u^{\gamma}$: Faddeev-Popov-ghosts; the non-photonic contribution to the $W$ self energy is symbolised by the shaded loop; an explicit representation can be found in [22], e.g.)
  • Figure 3: Real photon contribution in ${\cal O}(\alpha)$ to the $W$ production in the 4-fermion process
  • Figure 4: The 'hard' cross section $\overline\sigma_w(s)$ of Eq. 3.45 compared to the Born-cross section for $\nu_e e^+\rightarrow \nu_{\mu} \mu^+$
  • Figure 5: The effect of initial state bremsstrahlung in ${\cal O}(\alpha)$ described by $\sigma_{i,s+h}^{(0+1)}(s)$ of Eq. 3.29 and after soft photon exponentiation (Eq. 3.31)
  • ...and 4 more figures