On the leptonic decays of the τ
Abstract
In view of potential future improvements in the branching fractions of leptonic τ decays τ→ℓντν̅ℓ, ℓ=e,μ, it is timely to derive the corresponding Standard-Model predictions beyond next-to-leading order. We provide such benchmark values for the fully inclusive decay widths, profiting from higher-order corrections that have been studied in the MS̅ scheme up to three-loop order in the case of muon decay. To obtain complete next-to-next-to-leading-order results, we perform a numerical calculation of the two-loop coefficients in the on-shell scheme, including an evaluation of the hadronic effects, and compare the leptonic results to the known MS̅ coefficients where available. Our final results are presented in the MS̅ scheme, to be able to also include an estimate of the three-loop contribution. In addition, we comment on radiative and rare decays, whose consideration is critical for the conversion between MS̅ and on-shell results.
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BibTeX
@misc{hoferichter2026leptonic,
title = {{On the leptonic decays of the $τ$}},
author = {Martin Hoferichter and Alberto Lusiani and Yannick Ulrich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10670},
eprint = {2610.10670},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10670},
}
RIS
TY - UNPB
TI - On the leptonic decays of the τ
AU - Martin Hoferichter
AU - Alberto Lusiani
AU - Yannick Ulrich
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10670
UR - https://arxiv.org/abs/2610.10670
AB - In view of potential future improvements in the branching fractions of leptonic τ decays τ→ℓν_τν̅_ℓ, ℓ=e,μ, it is timely to derive the corresponding Standard-Model predictions beyond next-to-leading order. We provide such benchmark values for the fully inclusive decay widths, profiting from higher-order corrections that have been studied in the MS̅ scheme up to three-loop order in the case of muon decay. To obtain complete next-to-next-to-leading-order results, we perform a numerical calculation of the two-loop coefficients in the on-shell scheme, including an evaluation of the hadronic effects, and compare the leptonic results to the known MS̅ coefficients where available. Our final results are presented in the MS̅ scheme, to be able to also include an estimate of the three-loop contribution. In addition, we comment on radiative and rare decays, whose consideration is critical for the conversion between MS̅ and on-shell results.
ER -