The dipion mass spectrum in e+e- annihilation and τ decay: a dynamical (ρ, ω, φ) mixing approach

Abstract

We readdress the problem of finding a simultaneous description of the pion form factor data in e+e- annihilations and in τ decays. For this purpose, we work in the framework of the hidden local symmetry Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical ρ, ω and φ fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the four-momentum flowing into the vector meson lines. This allows us to define a dynamical, i.e. s-dependent, vector meson mixing scheme. The model is overconstrained by extending the framework in order to include the description of all meson radiative (VPγ and Pγγ couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking (ω/φ→π+π-) decay modes. The model provides a simultaneous, consistent and good description of the e+e- and τ dipion spectra. The expression for the pion form factor in the latter case is derived from those in the former case by switching off the isospin breaking effects specific to e+e- and switching on those for τ decays. Besides, the model also provides a good account of all decay modes of the form VPγ and Pγγ as well as the isospin breaking decay modes. It leads us to propose new reference values for the ρ0→e+e- and ω→π+π- partial widths, which are part of our description of the pion form factor. Other topics (φ→KK̄, the ρ meson mass and width parameters) are briefly discussed. As the e+e- data are found to be perfectly consistent with τ data up to identified isospin breaking effects, one finds no reason to cast any doubt on them and, therefore, on the theoretical estimate of the muon anomalous moment aμ derived from them. Therefore, our work turns out to confirm the relevance of the reported 3.3σ discrepancy between this theoretical estimate of aμ and its direct BNL measurement.