BabaYaga@NLO at Present and Future \(e^+e^-\) Colliders. Celebrating 25 years of BabaYaga

Precise QED radiative corrections for low- and high-energy electron–positron colliders are essential for accurate simulations of luminosity processes and precision tests of the Standard Model. We review the historical formulation and the recent developments of the <span class="sf">BabaYaga@NLO</span> event generator, which implements a QED Parton Shower (PS) matched with fixed-order calculations. We discuss the theoretical formulation of the code, as well as the assessment of its theoretical accuracy. Applications at low- and high-energy \(e^+e^-\) colliders are presented, including the latest result, together with the perspectives for future improvements, in view of the demanding precision requirements of future machines at the intensity frontier. Abstract Published by the Jagiellonian University 2026 authors