Improved Bhabha cross section at LEP and the number of light neutrino species

TL;DR

This paper provides an improved calculation of the Bhabha scattering cross section at LEP, reducing uncertainties and refining the measurement of light neutrino species, resolving a long-standing tension with the Standard Model.

Contribution

The authors present a more accurate prediction of the Bhabha cross section, decreasing its value and uncertainty, which leads to a revised and more precise estimate of the number of light neutrino species.

Findings

Reduced Bhabha cross section by 0.048%

Uncertainty on Bhabha cross section decreased to ±0.037%

Number of light neutrino species determined as 2.9963 ± 0.0074

Abstract

In $\rm e^+ \rm e^-$ collisions, the integrated luminosity is generally measured from the rate of low-angle Bhabha interactions $\rm e^+ e^- \to e^+ e^- $. In the published LEP results, the inferred theoretical uncertainty of $\pm 0.061\%$ on the predicted rate is significantly larger than the reported experimental uncertainties. We present an updated and more accurate prediction of the Bhabha cross section in this letter, which is found to reduce the Bhabha cross section by about $0.048\%$, and its uncertainty to $\pm 0.037\%$. When accounted for, these changes modify the number of light neutrino species (and its accuracy), as determined from the LEP measurement of the hadronic cross section at the Z peak, to $N_\nu = 2.9963 \pm 0.0074$. The 20-years-old $2 \sigma$ tension with the Standard Model is gone.