A team of theoretical physicists has computed for the first time the O(αs²α) corrections to the inclusive cross-section for Z-boson production in the threshold limit. The work completes the set of quark form factors at that order, including the previously missing singlet contributions, and marks a key step toward the mixed quantum chromodynamics and electroweak corrections required by future collider precision programmes.

Lepton-pair production in hadron collisions —the Drell-Yan process— is a benchmark measurement for determining fundamental Standard Model parameters such as the electroweak mixing angle and the masses of the W and Z bosons. The experimental precision targeted by the next generation of colliders demands theoretical predictions that incorporate mixed higher-order corrections in the strong coupling αs and the electroweak coupling α, a calculation that has so far been incomplete.

To construct the soft-virtual cross-section, the authors combined renormalization group invariance, the K+G evolution equation, and universal soft-collinear factorization. This approach captures the dominant logarithmic enhancements near threshold and allows the most relevant contributions to be resummed without having to compute the full O(αs²α) correction across the entire phase space.

The results improve the theoretical scale uncertainties and significantly reduce the dependence on the electroweak input scheme. The calculation lays the groundwork for completing the O(αs²α) corrections away from threshold, an indispensable requirement for the precision programmes of future colliders.