All real and virtual infrared singularities in the standard analysis of the perturbative Quantum Electrodynamics (like that of Yennie–Frautschi–Suura) are associated with photon emissions from the external legs in the scattering process. External particles are stable, with the zero decay width. Such singularities are well understood at any perturbative order and are resummed. The case of production and decay of the semi-stable neutral particles, like the Z-boson or the \(\tau \)-lepton, with the narrow decay width, \(\Gamma /M \ll 1\), is also well understood at any perturbative order and soft-photon resummation can be done. For an absent or loose upper cut-off on the total photon energy \(\omega \), production and decay processes of the semi-stable (neutral) particles decouple approximately and can be considered quasi-independently. In particular, the soft-photon resummation can be done separately for the production and the decay, treating a semi-stable (neutral) particle as stable. QED interference contributions between the production and decay stages are suppressed by the \(\Gamma /M\) factor. If experimental precision \(\omega \) is comparable with or better than \(\Gamma /M\), these interferences have to be included. In the case of \(\omega \ll \Gamma \) decoupling of production and decay does not work any more and the role of semi-stable particles is reduced to the same role as that of other internal off-shell particles. So far, consistent treatment of the soft photon resummation for semi-stable charged particles like the \(W^\pm \) bosons is not available in the literature, and the aim of this work is to present a solution to this problem. Generally, this should be feasible because the underlying physics is the same as in the case of neutral semi-stable resonances—in the limit of \(\Gamma /M \ll 1\) the production and decay processes for charged particles also necessarily decouple due to long lifetime of intermediate particles. Technical problems to be solved in this work are related to the fact that semi-stable charged particle are able to emit photons. Practical importance of the presented technique to the \(e^+e^-\rightarrow W^+W^-\) process at the Future electron–positron Circular Collider (FCC-ee) is underlined.

扰动量子电动力学的标准分析中所有真实和虚拟红外奇点（例如Yennie–Frautschi–Suura的奇异点）都与散射过程中来自外部分支的光子发射相关。外部粒子稳定，衰减宽度为零。这样的奇异点在任何扰动阶数下都是很好理解的，并且可以恢复。半稳定中性粒子（例如Z-玻色子或\（\ tau \）-轻子）的产生和衰减情况也具有较窄的衰减宽度\（\ Gamma / M \ ll 1 \）。在任何微扰级都可以很好地理解，并且可以完成软光子的恢复。对于总光子能量\（\ omega \）的上界缺少或不完整，半稳定（中性）粒子的产生和衰减过程近似解耦，可以被认为是准独立的。特别是，可以分别对软光子恢复进行生产和衰减，将半稳定（中性）粒子视为稳定粒子。产生阶段和衰减阶段之间的QED干扰贡献被\（\ Gamma / M \）因子抑制。如果实验精度\（\ omega \）与\（\ Gamma / M \）相当或更好，则必须包括这些干扰。在\（\ omega \ ll \ Gamma \）的情况下生产和衰变的解耦不再起作用，并且半稳定粒子的作用降低到与其他内部壳外粒子相同的作用。到目前为止，在文献中尚无统一的方法来处理像\（W ^ \ pm \）玻色子这样的半稳定带电粒子的软光子恢复。该工作的目的是提出解决这个问题的方法。通常，这应该是可行的，因为基础物理与中性半稳定共振的情况相同-在\（\ Gamma / M \ ll 1 \）的极限内由于中间粒子的长寿命，带电粒子的产生和衰减过程也必定会解耦。在这项工作中要解决的技术问题与半稳定带电粒子能够发射光子这一事实有关。强调了所提出的技术对未来电子-正电子圆形对撞机（FCC-ee）的\（e ^ + e ^-\ rightarrow W ^ + W ^-\）过程的实际重要性。