Further investigation of dilepton-based center-of-mass energy measurements at e$^{+}$e$^{-}$ colliders

TL;DR

This paper advances dilepton-based methods for measuring the e$^{+}$e$^{-}$ collider center-of-mass energy, analyzing limitations from beam, detector, and radiative corrections across energies from 90 GeV to 1 TeV.

Contribution

It introduces new estimators for beam energies and investigates their limitations, enhancing precision in energy measurements at e$^{+}$e$^{-}$ colliders.

Findings

Limitations from beam energy spread and detector resolution are quantified.

New estimators for electron and positron energies are proposed.

Implications for mass measurements of Z, W, H, and top quark are discussed.

Abstract

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.