# Exponentiation in QED and Quasi-Stable Charged Particles

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## Abstract

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## 1. Introduction

`BHLUMI`[7] and

`KORALZ`[8]. The latter one has been then replaced by a next-generation-code

`KKMC`[9] which includes recoil in production-decay interferences of the Z-resonance. The partial solutions related to the charged W bosons have been implemented in the

`YFSWW3`program [10] where exponentiation of the emission in the $WW$ pair production ($ee\to WW$) with the recoil has been done and in

`WINHAC`[11] in which exponentiation of radiation in the W decay ($W\to {f}_{1}{f}_{2}$) is implemented for the single-W process.

## 2. Toy Model with Single W

#### 2.1. Classical YFS Resummation from External Legs

#### 2.2. Inclusion of Emission from W Boson

## 3. W-Pair Production and Decay

## 4. Summary

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Yennie, D.R.; Frautschi, S.C.; Suura, H. The infrared divergence phenomena and high-energy processes. Ann. Phys.
**1961**, 13, 379–452. [Google Scholar] [CrossRef] - Greco, M.; Pancheri-Srivastava, G.; Srivastava, Y. Radiative Corrections for Colliding Beam Resonances. Nucl. Phys.
**1975**, B101, 234–262. [Google Scholar] [CrossRef] - Greco, M.; Pancheri-Srivastava, G.; Srivastava, Y. Radiative Corrections to e
^{+}e^{−}→ μ^{+}μ^{−}Around the Z0. Nucl. Phys.**1980**, B171, 118. [Google Scholar] [CrossRef] - Jadach, S.; Ward, B.F.L.; Was, Z. Coherent exclusive exponentiation for precision Monte Carlo calculations. Phys. Rev.
**2001**, D63, 113009. [Google Scholar] [CrossRef] - Jadach, S.; Płaczek, W.; Skrzypek, M. QED Exponentiation for quasi-stable charged particles: The e
^{−}e^{+}→ W^{−}W^{+}process. arXiv**2019**, arXiv:1906.09071. [Google Scholar] - Jadach, S. Yennie-Frautschi-Suura Soft Photons in Monte Carlo Event Generators. Unpublished. 1987. Available online: http://inspirehep.net/record/244950 (accessed on 15 October 2019).
- Jadach, S.; Richter-Was, E.; Ward, B.F.L.; Was, Z. Monte Carlo program BHLUMI-2.01 for Bhabha scattering at low angles with Yennie-Frautschi-Suura exponentiation. Comput. Phys. Commun.
**1992**, 70, 305–344. [Google Scholar] [CrossRef] - Jadach, S.; Ward, B.F.L.; Was, Z. The Monte Carlo program KORALZ, version 3.8, for the lepton or quark pair production at LEP/SLC energies. Comput. Phys. Commun.
**1991**, 66, 276–292. [Google Scholar] [CrossRef] [Green Version] - Jadach, S.; Ward, B.F.L.; Was, Z. The Precision Monte Carlo event generator KK for two fermion final states in e
^{+}e^{−}collisions. Comput. Phys. Commun.**2000**, 130, 260–325. [Google Scholar] [CrossRef] - Jadach, S.; Płaczek, W.; Skrzypek, M.; Ward, B.F.L.; Wa̧s, Z. The Monte Carlo event generator YFSWW3 version 1.16 for W pair production and decay at LEP2/LC energies. Comput. Phys. Commun.
**2001**, 140, 432–474. [Google Scholar] [CrossRef] - Placzek, W.; Jadach, S. Multiphoton radiation in leptonic W-boson decays. Eur. Phys. J.
**2003**, C29, 325–339. [Google Scholar] [CrossRef]

**Figure 3.**The soft-photon emissions from external legs and from the W propagator in the single W toy model.

**Figure 4.**The soft-photon emission from external legs and W boson factorized into the production and decay multiple soft-photon emissions and one W propagator.

**Figure 5.**LHS: the classical YFS61 soft photon emission in W-pair production and decay. RHS: a new extended scheme with real and virtual emissions from Ws and all interferences, P–D and D–D.

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**MDPI and ACS Style**

Jadach, S.; Płaczek, W.; Skrzypek, M.
Exponentiation in QED and Quasi-Stable Charged Particles. *Symmetry* **2019**, *11*, 1389.
https://doi.org/10.3390/sym11111389

**AMA Style**

Jadach S, Płaczek W, Skrzypek M.
Exponentiation in QED and Quasi-Stable Charged Particles. *Symmetry*. 2019; 11(11):1389.
https://doi.org/10.3390/sym11111389

**Chicago/Turabian Style**

Jadach, Stanisław, Wiesław Płaczek, and Maciej Skrzypek.
2019. "Exponentiation in QED and Quasi-Stable Charged Particles" *Symmetry* 11, no. 11: 1389.
https://doi.org/10.3390/sym11111389