# The Dipion Mass Spectrum In $e^+e^-$ Annihilation and $\tau$ Decay: A Dynamical ($\rho, \omega, \phi$) Mixing Approach

Abstract : We readdress the problem of finding a simultaneous description of the pion form factor data in e+e- annihilations and in tau decays. For this purpose, we work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify the vector meson mass term by including the pion and kaon loop contributions. This leads us to define the physical rho0, omega and phi fields as linear combinations of their ideal partners, with coefficients being meromorphic functions of s, the square of the 4-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 (V P gamma and P gamma gamma couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking (omega/phi --> pi+ pi-) decay modes. The model provides a simultaneous, consistent and good description of the e+e- and tau dipion spectra. The expression for 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 tau decays. Besides, the model also provides a good account of all decay modes of the form V P gamma, P gamma gamma as well as the isospin breaking decay modes. It leads us to propose new reference values for the rho0 --> e+ e- and omega --> pi+ pi- partial widths which are part of our description of the pion form factor. Other topics (phi --> K Kbar, the rho meson mass and width parameters) are briefly discussed. The most important consequence of this work is indirect and confirms the known 3.3 sigma discrepancy between the direct BNL measurement of the muon anomalous moment and its theoretical estimate relying on e+e- data.
Document type :
Journal articles
Domain :

http://hal.in2p3.fr/in2p3-00192680
Contributor : Dominique Girod <>
Submitted on : Thursday, November 29, 2007 - 11:02:09 AM
Last modification on : Friday, April 10, 2020 - 5:04:14 PM

### Citation

M. Benayoun, P. David, L. del Buono, O. Leitner, H. B. O'Connell. The Dipion Mass Spectrum In $e^+e^-$ Annihilation and $\tau$ Decay: A Dynamical ($\rho, \omega, \phi$) Mixing Approach. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2007, volume 55, pp.199-236. ⟨10.1140/epjc/s10052-008-0586-6⟩. ⟨in2p3-00192680⟩

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