The discrepancy between τ and e + e − spectral functions revisited and the consequences for the muon magnetic anomaly

M. Davier; A. Hoecker; G. López Castro; B. Malaescu; X. H. Mo; G. Toledo Sánchez; P. Wang; C. Z. Yuan; Z. Zhang

doi:10.1140/epjc/s10052-009-1219-4

2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C (2010) 66: 127-136
https://doi.org/10.1140/epjc/s10052-009-1219-4

Regular Article - Theoretical Physics

The discrepancy between τ and e ⁺ e ⁻ spectral functions revisited and the consequences for the muon magnetic anomaly

M. Davier³, A. Hoecker², G. López Castro⁴, B. Malaescu³, X. H. Mo¹, G. Toledo Sánchez⁵, P. Wang¹, C. Z. Yuan¹ and Z. Zhang³^*

¹ Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China
² CERN, 1211, Geneva 23, Switzerland
³ Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS, Université Paris-Sud 11, Orsay, France
⁴ Departamento de Física, Cinvestav, Apartado Postal 14-740, 07000, Mexico, D.F., Mexico
⁵ Instituto de Física, UNAM, A.P. 20-364, 01000, Mexico, D.F., Mexico

^* e-mail: zhangzq@lal.in2p3.fr

Received: 1 July 2009
Revised: 24 October 2009
Published online: 26 January 2010

Abstract

We revisit the procedure for comparing the π π spectral function measured in τ decays to that obtained in e ⁺ e ⁻ annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input and find improved agreement between the τ ⁻→π ⁻ π ⁰ ν _τ branching fraction measurement and its prediction using the isospin-breaking-corrected e ⁺ e ⁻→π ⁺ π ⁻ spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g−2 using e ⁺ e ⁻ and τ data with the new corrections and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement.