The HLS approach to $(g-2)_μ$~: A Solution to the "$τ$ versus $e^+e^- $" Puzzle

Abstract

The Hidden Local Symmetry (HLS) Model provides a framework able to encompass several physical processes and gives a unfied description of these in an energy range extending up to the $ϕ$ mass. Supplied with appropriate symmetry breaking schemes, the HLS Model gives a broken Effective Lagrangian (BHLS). The BHLS Lagrangian gives rise to a fit procedure in which a simultaneous description of the $e^+ e^-$ annihilations to $π^+π^-$, $π^0 γ$, $ηγ$, $π^+π^- π^0$, $K^+ K^-$, $K_L K_S$ and of the dipion spectrum in the decay $τ^\pm \rightarrow π^\pm π^0 ν$ can be performed. Supplemented with a few pieces of information on the $ρ^0-ω-ϕ$ system, the $τ$ dipion spectrum is shown to predict accurately the pion form factor in $e^+ e^-$ annihilations. Physics results derived from global fits involving or excluding the $τ$ dipion spectra are found consistent with each others. Therefore, no obvious mismatch between the $τ$ and $e^+e^- $ physics properties arises and the $τ-e^+e^- $ puzzle vanishes within the broken HLS Model.