Pion $β$ decay and $τ\toππν_τ$ beyond leading logarithms
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866911442194661376 |
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| author | Cirigliano, Vincenzo Hoferichter, Martin Valori, Nicola |
| author_facet | Cirigliano, Vincenzo Hoferichter, Martin Valori, Nicola |
| contents | The consistent matching of short-distance contributions and hadronic matrix elements is crucial for precise predictions of weak processes involving hadrons. In this Letter, we address this point for charged-current processes involving two pions -- pion $β$ decay $π^\pm\toπ^0 e^\pmν_e$ and hadronic $τ$ decays $τ^\pm\toπ^\pmπ^0ν_τ$ -- whose decay rates depend on the so-called $γW$ box correction. Using recent results from lattice QCD, we show how to formulate the matching beyond leading-logarithmic accuracy, in particular, how to cancel the dependence on the scheme choice for evanescent operators. As main results, we obtain a prediction for the decay rate of pion $β$ decay with theory uncertainties improved by a factor of three, which renders theory uncertainties negligible for future determinations of $V_{ud}$ even beyond the reach of the PIONEER experiment, and an evaluation of isospin-breaking corrections to $τ\toππν_τ$ with negligible uncertainty from the short-distance matching, as necessary for a future $τ$-based determination of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11253 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pion $β$ decay and $τ\toππν_τ$ beyond leading logarithms Cirigliano, Vincenzo Hoferichter, Martin Valori, Nicola High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory The consistent matching of short-distance contributions and hadronic matrix elements is crucial for precise predictions of weak processes involving hadrons. In this Letter, we address this point for charged-current processes involving two pions -- pion $β$ decay $π^\pm\toπ^0 e^\pmν_e$ and hadronic $τ$ decays $τ^\pm\toπ^\pmπ^0ν_τ$ -- whose decay rates depend on the so-called $γW$ box correction. Using recent results from lattice QCD, we show how to formulate the matching beyond leading-logarithmic accuracy, in particular, how to cancel the dependence on the scheme choice for evanescent operators. As main results, we obtain a prediction for the decay rate of pion $β$ decay with theory uncertainties improved by a factor of three, which renders theory uncertainties negligible for future determinations of $V_{ud}$ even beyond the reach of the PIONEER experiment, and an evaluation of isospin-breaking corrections to $τ\toππν_τ$ with negligible uncertainty from the short-distance matching, as necessary for a future $τ$-based determination of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon. |
| title | Pion $β$ decay and $τ\toππν_τ$ beyond leading logarithms |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2602.11253 |