Dispersive representation of the pion vector form factor in $\tau \to \pi \pi {\nu }_{\tau }$ decays

Abstract

We propose a dispersive representation of the charged pion vector form factor that is consistent with chiral symmetry and fulfills the constraints imposed by analyticity and unitarity. Unknown parameters are fitted to the very precise data on ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays obtained by Belle, leading to a good description of the corresponding spectral function up to a $\pi \pi$ squared invariant mass $s\simeq 1.5$ GeV${}^2$. We discuss the effect of isospin corrections, and obtain the values of low energy observables. For larger values of $s$, this representation is complemented with a phenomenological description to allow its implementation in the new TAUOLA hadronic currents.

22 pages, 4 figures. Determination of rho(770) pole parameters substantially improved using a new method, based on rational approximants. Other results unchanged. Version to be published in EPJC

References in corpus (27)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR
• Towards a consistent estimate of the chiral low-energy constants
• Measurement of sigma(e+ e- -> pi+ pi-) from threshold to 0.85 GeV^2 using Initial State Radiation with the KLOE detector
• Precision measurement of $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma )/\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma )$ and determination of the ${\pi }^{+}{\pi }^{-}$ contribution to the muon anomaly with the KLOE detector
• The muon g-2 and the bounds on the Higgs boson mass
• An Update of the HLS Estimate of the Muon g-2
• Lepton flavour violating semileptonic tau decays in constrained MSSM-seesaw scenarios
• Spectral distribution for the decay tau -> nu_tau K pi
• K pi vector form factor, dispersive constraints and tau -> nu_tau K pi decays
• One meson radiative tau decays
• Gravitational and higher-order form factors of the pion in chiral quark models
• Long-distance radiative corrections to the di-pion tau lepton decay
• What can be learned from the Belle spectrum for the decay tau- -> nu_tau K_S pi-
• K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays
• Resonance Chiral Lagrangian analysis of ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays
• Vector Meson Dominance as a first step in a systematic approximation: the pion vector form factor
• Padé Approximants and Resonance Poles
• Study of high-multiplicity 3-prong and 5-prong tau decays at BABAR
• Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region
• Pion electromagnetic form factor, perturbative QCD, and large-Nc Regge models
• Electromagnetic form factor of pion in the field theory inspired approach
• Parametrization-free determination of the shape parameters for the pion electromagnetic form factor
• Constraining the Hadronic Contributions to the Muon Anomalous Magnetic Moment
• Theoretical inputs and errors in the new hadronic currents in TAUOLA
• MC generator TAUOLA: implementation of Resonance Chiral Theory for two and three meson modes. Comparison with experiment
• Hunting resonance poles with Rational Approximants

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• Lepton-flavour violation in hadronic tau decays and $\mu -\tau$ conversion in nuclei
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• CP asymmetry in $\tau \to K_S\pi {\nu }_{\tau }$ decays within the Standard Model and beyond
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• Isospin breaking corrections in $2\pi$ production in tau decays and $e^{+}{e}^{-}$ annihilation: consequences for the muon $g-2$ and CVC tests
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• Study of predominant hadronic modes of $\tau$-lepton using a Monte Carlo generator TAUOLA
• Hadronic and radiative decays of the tau lepton
• Electromagnetic corrections in hadronic tau decays
• Isospin-breaking corrections to ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays and the muon $g-2$
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• Prospects for discovery of the τ^- \to π^- \ell^+ \ell^- ν_τdecays