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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

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: $\sqrt{s}=200\,\hbox{GeV}$.