Two-hadron saturation for the pseudoscalar–vector–vector correlator and phenomenological applications

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2015-12, Vol.75 (12), p.1-19, Article 586
• Main Authors: Husek, Tomáš, Leupold, Stefan
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Channels; Correlation; Decomposition; Deviation; Elementary Particles; Form factors; Hadrons; Heavy Ions; Mathematical analysis; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Pions; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory; Texts
• ISSN: 1434-6044; 1434-6052; 1434-6052
• DOI: 10.1140/epjc/s10052-015-3778-x

The pseudoscalar–vector–vector correlator is constructed using two meson multiplets in the vector and two in the pseudoscalar channel. The parameters are constrained by the operator product expansion at leading order where two or all three momenta are considered as large. Demanding in addition the Brodsky–Lepage limit one obtains (in the chiral limit) a pion-vector-vector ( π VV) correlator with only one free parameter. The singly virtual pion transition form factor F π 0 γ γ ∗ and the decay width of ω → π 0 γ are independent of this parameter and can serve as cross-checks of the results. The free parameter is determined from a fit of the ω – π transition form factor F π 0 ω γ ∗ . The resulting π VV correlator is used to calculate the decay widths ω → π 0 e + e - and ω → π 0 μ + μ - and finally the widths of the rare decay π 0 → e + e - and of the Dalitz decay π 0 → e + e - γ . Incorporating radiative QED corrections the calculations of π 0 decays are compared to the KTeV results. We find a deviation of 2 σ or less for the rare pion decay.