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

Abstract

In ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ collisions, the integrated luminosity is generally measured from the rate of low-angle Bhabha interactions ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to {\mathrm{e}}^{+}{\mathrm{e}}^{-}$. 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.

Comments: 28 pages, 13 tables, 4 figures. Revision submitted to Physics Letters B. With respect to v1: 1) Hadronic vacuum polarization (VPhad) updated from FJ'17 to FJ'19, and compared to DHMZ'20 and KNT'20. 2) Leptonic vacuum polarization (VPlept) updated from LO to NNNLO. 3) Number of light neutrino species changed from 2.9975 to 2.9970 with new VPhad, and from 2.9970 to 2.9963 with new VPlept