Initial state QED radiation aspects for future $e^+e^-$ colliders
S. Frixione, E. Laenen, C.M. Carloni Calame, A. Denner, S. Dittmaier,, T. Engel, L. Flower, L. Gellersen, S. Hoeche, S. Jadach, M.R. Masouminia, G., Montagna, O. Nicrosini, F. Piccinini, S. Pl\"atzer, A. Price, J. Reuter, M., Rocco, M. Sch\"onherr, A. Signer, T. Sj\"ostrand

TL;DR
This paper reviews theoretical and phenomenological aspects of initial-state QED radiation for future $e^+e^-$ colliders, providing technical insights and pedagogical explanations to address upcoming challenges in collider physics.
Contribution
It offers a comprehensive overview of initial state radiation treatments and theoretical developments relevant for future $e^+e^-$ collider experiments.
Findings
Descriptions of Monte Carlo approaches to initial state radiation
Explanation of theoretical developments with potential phenomenological impact
Accessible pedagogical presentation for both experts and non-experts
Abstract
This white paper concerns theoretical and phenomenological aspects relevant to the physics of future colliders, in particular regarding initial-state QED radiation. The contributions each contain key technical aspects, and are formulated in a pedagogical manner so as to render them accessible also to those who are not directly working on these and immediately-related topics. This should help both experts and non-experts understand the theoretical challenges that we shall face at future colliders. Specifically, this paper contains descriptions of the treatment of initial state radiation from several Monte Carlo collaborations, as well as contributions that explain a number of more theoretical developments with promise of future phenomenological impact.
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