The neutral weak force between an electron and a target particle, mediated by the Z boson, can be isolated by measuring the fractional change under a mirror reflection of the scattering probability of relativistic longitudinally polarized electrons off unpolarized targets. This technique yields neutral weak force measurements at a length scale of 1 femtometer, in contrast to high energy collider measurements that probe much smaller length scales. Study of the variation of the weak force over a range of length scales provides a stringent test of theory, complementing collider measurements. We describe a recent measurement of the neutral weak force between two electrons by the E158 experiment at the Stanford Linear Accelerator Center. While the weak force between an electron and positron has been extensively studied, that between two electrons had never directly been measured. We conclude by discussing prospects for even more precise measurements at future facilities.

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