NNLO Final-State Quark-Pair Corrections in Implicit Regularization
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 Nf. 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 Nf 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 γ5 matrices and Levi-Civita tensors, thereby reducing ambiguities and symmetry-restoring counterterms.
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BibTeX
@misc{rosado2026nnlo,
title = {{NNLO Final-State Quark-Pair Corrections in Implicit Regularization}},
author = {Ricardo J. C. Rosado and Adriano Cherchiglia and Marcos Sampaio and Brigitte Hiller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40395},
eprint = {2610.40395},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40395},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - NNLO Final-State Quark-Pair Corrections in Implicit Regularization
AU - Ricardo J. C. Rosado
AU - Adriano Cherchiglia
AU - Marcos Sampaio
AU - Brigitte Hiller
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40395
UR - https://arxiv.org/abs/2610.40395
AB - 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.
ER -