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Improved Calculation of Radiative Corrections to τ→ππν_{τ} Decays.

Gilberto Colangelo¹, Martina Cottini¹, Martin Hoferichter¹

¹University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Sidlerstrasse 5, 3012 Bern, Switzerland.

Physical Review Letters

|March 27, 2026

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Area of Science:

Particle Physics
Quantum Field Theory
Hadronic Physics

Background:

Hadronic tau decays are essential for a data-driven evaluation of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon.
Precise calculation of radiative corrections to tau → ππντ decays is a prerequisite for this evaluation.

Purpose of the Study:

To present an improved, model-independent analysis of radiative corrections to tau → ππντ decays.
To incorporate effects beyond pointlike pions in loop diagram evaluations for enhanced accuracy.

Main Methods:

Implemented structure-dependent corrections via a dispersive representation of the pion form factor.
Devised strategies for matching to chiral perturbation theory and stable implementation of real corrections down to the two-pion threshold.
Performed dispersive fits to available tau → ππντ spectra.

Main Results:

Structure-dependent corrections lead to significant changes compared to previous calculations, especially near the ρ(770) resonance.
Higher-order isospin-breaking corrections are necessary due to strong threshold enhancement.
Consequences for isospin-breaking corrections in the evaluation of aμHVP,LO[ππ,τ] are discussed.

Conclusions:

The improved analysis provides more reliable radiative corrections for tau decays.
This enhances the precision of the data-driven determination of the muon's anomalous magnetic moment.