Upgraded breaking of the HLS model: a full solution to the τ−e + e − and ϕ decay issues and its consequences on g−2 VMD estimates

M. Benayoun; P. David; L. DelBuono; F. Jegerlehner

doi:10.1140/epjc/s10052-011-1848-2

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2012) 72: 1848
https://doi.org/10.1140/epjc/s10052-011-1848-2

Regular Article - Experimental Physics

Upgraded breaking of the HLS model: a full solution to the τ−e ⁺ e ⁻ and ϕ decay issues and its consequences on g−2 VMD estimates

M. Benayoun¹^*, P. David¹, L. DelBuono¹ and F. Jegerlehner²^,3

¹ LPNHE des Universités Paris VI et Paris VII, IN2P3/CNRS, 75252, Paris, France
² Institut für Physik, Humboldt–Universität zu Berlin, Newtonstrasse 15, 12489, Berlin, Germany
³ Deutsches Elektronen–Synchrotron (DESY), Platanenallee 6, 15738, Zeuthen, Germany

^* e-mail: benayoun@in2p3.fr

Received: 7 June 2011
Revised: 21 November 2011
Published online: 3 January 2012

Abstract

The muon anomalous magnetic moment a _μ and the hadronic vacuum polarization are examined using data analyzed within the framework of a suitably broken HLS model. The analysis relies on all available scan data samples and leaves provisionally aside the existing ISR data. Our HLS model based global fit approach allows for a better check of consistency between data sets and we investigate how results depend on different strategies which may be followed. Relying on global fit qualities, we find several acceptable solutions leading to ambiguities in the reconstructed value for (a _μ)_th. Among these, the most conservative solution is $a_{\mu}^{\mathrm{had,LO}}[\mathrm{HLS\ improved}]=687.72(4.63) \times10^{-10}$ and (a _μ)_th=11 659 175.37(5.31)×10⁻¹⁰ corresponding to a 4.1σ significance for the difference Δa _μ=(a _μ)_exp−(a _μ)_th. It is also shown that the various contributions accessible through the model yield uniformly a factor 2 improvement of their uncertainty. The breaking procedure implemented in the HLS model is an extension of the former procedure based on a mechanism defined by Bando, Kugo and Yamawaki (BKY). This yields a quite satisfactory simultaneous description of most e ⁺ e ⁻ annihilation channels up to and including the ϕ meson (π ⁺ π ⁻, π ⁰ γ, ηγ, π ⁺ π ⁻ π ⁰, K ⁺ K ⁻, $K^{0} \overline{K}^{0}$ ) and of a set of 10 (mostly radiative) decay widths of light mesons. It also allows to achieve the proof of consistency between the e ⁺ e ⁻→π ⁺ π ⁻ annihilation and the τ ^±→π ^± π ⁰ ν decay and gives a solution to the reported problem concerning the measured partial width ratio $\varGamma(\phi\to K^{+}K^{-})/\varGamma(\phi\to K^{0} \overline{K}^{0})$ . Prospects for improving the VMD based estimates of a _μ are emphasized.