Further investigation of dilepton-based center-of-mass energy measurements at e⁺e⁻ colliders

Methods for measuring the absolute center-of-mass energy using dileptons from e$^{+}$e$^{-}$ collision events are further developed with an emphasis on accelerator, detector, and physics limitations. We discuss two main estimators, the lepton momentum-based center-of-mass energy estimator, $\sqrt{s}_{p}$, discussed previously, and new estimators for the electron and positron colliding beam energies, denoted $E^{\text{C}}_{-}$ and $E^{\text{C}}_{+}$. In this work we focus on the underlying limitations from beam energy spread, detector resolution, and the modeling of higher-order QED radiative corrections associated with photon emissions originating from initial-state-radiation (ISR), final-state-radiation (FSR), and their interference. We study the consequent implications for the potential of these methods at center-of-mass energies ranging from 90 GeV to 1 TeV relevant to a number of potential accelerator realizations in the context of measurements of masses of the Z, W, H, top quark, and new particles. The statistical importance of the Bhabha channel for Higgs factories is noted. Additional extensive work on improving the modeling of the luminosity spectrum including the use of copulas is also reported.