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Final-state radiation and line-shape distortion in resonance pair production

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

TL;DR

Final-state QED corrections can significantly distort resonance-line shapes in pair production, depending on how the invariant-mass observable is defined. The ZZ case is solved exactly, and a double-pole plus leading-log resummation framework reproduces the distortions and yields practical rules-of-thumb, which are then extended to W-pair production at LEP2. The results provide quantitative estimates of peak shifts and height reductions, guiding Monte Carlo implementations and improving precision in W-mass measurements. These findings connect FSR-induced line-shape distortions to the ISR distortions known from LEP1 and offer a gauge-invariant, per-resonance treatment suitable for realistic multi-resonance processes. The work provides actionable guidance for experiments and event generators to account for final-state radiation in precision resonance studies.

Abstract

In this letter it is shown how final-state QED corrections to the production of a pair of resonances can distort the line shape of such a resonance in a sizeable way. This effect depends on the definition of the line shape and can reach up to 30%, depending on the final state. The mechanism is first displayed for a particular case of ZZ production, for which an exact and approximate treatment can be given. The approximate method is then applied to W-pair production. In addition some simple rules of thumb are given for accurately estimating the characteristic distortion effects, like the mass shift and peak reduction.

Final-state radiation and line-shape distortion in resonance pair production

TL;DR

Final-state QED corrections can significantly distort resonance-line shapes in pair production, depending on how the invariant-mass observable is defined. The ZZ case is solved exactly, and a double-pole plus leading-log resummation framework reproduces the distortions and yields practical rules-of-thumb, which are then extended to W-pair production at LEP2. The results provide quantitative estimates of peak shifts and height reductions, guiding Monte Carlo implementations and improving precision in W-mass measurements. These findings connect FSR-induced line-shape distortions to the ISR distortions known from LEP1 and offer a gauge-invariant, per-resonance treatment suitable for realistic multi-resonance processes. The work provides actionable guidance for experiments and event generators to account for final-state radiation in precision resonance studies.

Abstract

In this letter it is shown how final-state QED corrections to the production of a pair of resonances can distort the line shape of such a resonance in a sizeable way. This effect depends on the definition of the line shape and can reach up to 30%, depending on the final state. The mechanism is first displayed for a particular case of ZZ production, for which an exact and approximate treatment can be given. The approximate method is then applied to W-pair production. In addition some simple rules of thumb are given for accurately estimating the characteristic distortion effects, like the mass shift and peak reduction.
Paper Structure (4 sections, 19 equations, 1 figure)

This paper contains 4 sections, 19 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The $Z$-pair example: exact calculation
  3. The $Z$-pair example: approximations
  4. Some comments on the $W$ line shape at LEP2

Figures (1)

  • Figure 1: The FSR-induced distortion of the line shape $d\sigma/(d \tilde{M}_{1}^{2}\,d M_{2}^{2})$ corresponding to process (\ref{['eq:process']}) for $M_2=M_Z$. Centre-of-mass energy: $\sqrt{s}=200\,\hbox{GeV}$.