QED exponentiation for quasi-stable charged particles: the

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