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arXiv · 2610.40395

NNLO Final-State Quark-Pair Corrections in Implicit Regularization

Ricardo J. C. Rosado·Adriano Cherchiglia·Marcos Sampaio·Brigitte Hiller
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Abstract

We investigate the NNLO final-state quark-pair correction to the decay of a neutral axial-vector current ($Z$) into massless quarks within Implicit Regularization (IReg), in the limit of large $N_f$. Our calculation tests, at two loops, the recursive subtraction of ultraviolet subdivergences and the cancellation of infrared singularities between virtual and real contributions in a framework that does not rely on analytical continuation in spacetime dimension. 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 NNLO check of gauge invariance, renormalization consistency, and perturbative unitarity in IReg. In precision multi-loop calculations, fixed-dimension regularization methods can be advantageous by avoiding the dimensional continuation of intrinsically four-dimensional structures, such as $γ_5$ matrices and Levi-Civita tensors, thereby reducing ambiguities and symmetry-restoring counterterms.

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Ricardo J. C. Rosado, Adriano Cherchiglia, Marcos Sampaio, Brigitte Hiller. 2026-10-29. NNLO Final-State Quark-Pair Corrections in Implicit Regularization. https://arxiv.org/abs/2610.40395

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