Next-to-next-to-leading order QCD■EW corrections to Z-boson pair production at electron-positron colliders

We present a comprehensive analytic calculation of the next-to-next-to-leading order QCD■EW corrections to Z-boson pair production at electron-positron colliders.The two-loop master integrals essential to this calculation are evaluated using the differential equation method.In this paper,we detail the formulation and solution of the canonical differential equations for the two-loop three-point master integrals with two on-shell Z-boson external legs and a massive internal quark in the loops.These canonical master integrals are systematically expanded as a Taylor series in the dimensional regulator,ε=(4-d)/2,up to the order of ε^(4),with coefficients expressed in terms of Goncharov polylogarithms up to weight four.Upon applying our analytic expressions of these master integrals to the phenomenological analysis of Z-pair production,we observe that the O(aa_(s))corrections manifest at a level of approximately one percent when compared to the leading-order predictions,underscoring their significance for comparisons with future high-precision experimental data.

Status and accuracy of the Monte Carlo generators for luminosity measurements

The status and accuracy of the precision Monte Carlo generators used for luminosity measurements at flavour factories is reviewed. It is shown that, thanks to a considerable, long-term effort in tuned comparisons between the predictions of independent programs, as well as in the validation of the generators against the presently available calculations of the next-to-next-to-leading order QED corrections to Bhabha scattering, the theoretical accuracy reached by the most precise tools is of about one per mille. This error estimate is valid for realistic experimental cuts, appears to be quite robust and is already sufficient for very accurate luminosity measurements. However, recent progress and possible advances to further improve it are also discussed.