Abstract
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 correlator with only one free parameter. The singly virtual pion transition form factor and the decay width of omega to pion and photon are independent of this parameter and can serve as cross-checks of the results. The free parameter is determined from a fit of the omega-pion transition form factor. The resulting pion-vector-vector correlator is used to calculate the decay widths of omega to pion and dielectron and to pion and dimuon and finally the widths of the rare decay pion to dielectron and of the Dalitz decay pion to photon and dielectron. Incorporating radiative QED corrections the calculations of neutral-pion decays are compared to the KTeV results. We find a deviation of 2 sigma or less for the rare pion decay.
Highlights
The parameters are constrained by the operator product expansion at leading order where two or all three momenta are considered as large
Since we study with pseudoscalar– vector–vector (PVV) an order parameter of chiral symmetry breaking [5] one expects that the second multiplets are close to the physical states that are the first excitations on top of the ground states
In the present work we explore the uncertainty of the two-hadron saturation” (THS) approximation by changing the masses of the second multiplets from the first to the second physical excitations
Summary
For a quantitative determination of the branching ratio of the considered rare pion decay it is necessary to know where and how fast the pion transition form factor reaches its asymptotic form which in turn depends on the various combinations of virtualities These considerations show that one needs information from various QCD regimes: The threshold regime governed by the chiral anomaly, the regime of hadronic resonances, and, the regime of asymptotically high energies dictated by quarks and asymptotic freedom. If both vector currents have the same large virtuality, the corresponding asymptotic limit is reached very late for the π VV correlator as obtained from THS This finding points to the relevance of details of hadronic physics above 1 GeV. While we cannot expect to reach the accuracy of a dispersive approach concerning lowenergy quantities, our framework has the advantage to provide a smooth and physical connection between the low- and high-energy region and between the quark- and hadron-based correlators. We provide a brief discussion of this point in the corresponding sections
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