Precise Extraction of α_{em}(m_{Z}^{2}) at the Tera-Z Stage of a Future Circular Collider.

The current projected sensitivity on the electromagnetic coupling α_{em}(m_{Z}^{2}) represents a bottleneck for the precision electroweak program at FCC-ee. We propose a novel methodology to extract this coupling directly from Z-pole data. By comparing the differential distribution of electrons, muons, and positrons in the forward region, the approach achieves a projected statistical sensitivity below the 10^{-5} level, representing a significant improvement over other methods. We assess the impact of leading parametric uncertainties including that of the top quark mass.