First constraint on Born-rule violations at high-energy colliders

We obtain an experimental constraint on possible Born-rule violations at high-energy colliders. We model Born-rule violations with differential scattering cross sections $d\sigma/d\Omega$ subject to an angular smearing by a narrow Gaussian of width $\varepsilon$ (with respect to $x=\cos\theta$ for scattering angle $\theta$). For large-angle Bhabha ($e^{+}e^{-} \rightarrow e^{+}e^{-}$) scattering, at a centre-of-mass energy $\sqrt{s}=29\, \mathrm{GeV}$, data from the PEP collider at SLAC allow us to set an upper bound of $\varepsilon<0.042$ at $95\%$ confidence. This corresponds to a Gaussian smearing over an angular range of twice the experimental bin width, and hence provides a physically meaningful limit on deviations from the Born rule. Future prospects for improving this limit are discussed.