A team has computed the NNLO (two-loop) final-state quark-pair correction to the decay of a neutral axial-vector current (Z) into massless quarks using Implicit Regularization (IReg) in the large-N_f limit. The work tests, at two loops, the recursive subtraction of ultraviolet subdivergences and the cancellation of infrared singularities between virtual and real contributions, all without relying on analytic continuation of the spacetime dimension.

The motivation is methodological. In precision multi-loop calculations, fixed-dimension regularization schemes can be advantageous because they avoid analytically continuing intrinsically four-dimensional structures, such as γ₅ matrices and Levi-Civita tensors, to d dimensions. That dimensional continuation introduces ambiguities and forces the introduction of symmetry-restoring counterterms, complicating in particular calculations involving chiral quarks and the chiral structure of the Standard Model.

After renormalization and phase-space integration, the regulator-dependent logarithms cancel and the known N_f contribution to the inclusive rate is recovered. The result provides a non-trivial check of gauge invariance, renormalization consistency, and perturbative unitarity within IReg, and validates the recursive treatment of divergences at two loops in this framework.

The relevance extends beyond this particular channel: if IReg passes such NNLO tests, it could become a reliable alternative to conventional dimensional regularization for precision calculations at future colliders, where higher-order radiative corrections are essential to test the Standard Model against possible signs of new physics.