QED Interference in Charge Asymmetry Near the Z Resonance at Future Electron-Positron Colliders

Abstract

The measurement of the charge asymmetry $A_{FB}(e^-e^+\to μ^-μ^+)$ will play an important role at the high-luminosity circular electron-positron collider FCCee considered for construction at CERN. In particular, near the Z resonance, $\sqrt{s} \simeq M_Z \pm 3.5$ GeV, $A_{FB}$ will provide a very precise value of the pure electromagnetic coupling constant $α_{QED}(M_Z)$, which is vitally important for overall tests of the Standard Model. For this purpose, $A_{FB}$ will be measured at the FCCee with an experimental error better than $δA_{FB} \simeq 3\cdot 10^{-5},$ at least a factor 100 more precisely than at past LEP experiments! The important question is whether the effect of interference between photon emission in the initial and final state can be removed from the $A_{FB}$ data at the same precision level using perturbative QED calculations. A first quantitative study of this problem is presented here, with the help of the KKMC program and a newly developed calculation based on soft photon resummation, matched with NLO and NNLO fixed-order calculations. It is concluded that a factor of 10 improvement with respect to the LEP era is obtained. We also present a clear indication that reducing the uncertainty of charge asymmetry near the Z peak due to IFI down to $δA_{FB} \simeq 3\cdot 10^{-5}$, i.e. the expected experimental precision at FCCee, is feasible.