PION FORM FACTOR AND REACTIONS e+e− → ωπ0 AND e+e− → π+π−π+π− AT ENERGIES UP TO 2 – 3 GEV IN THE MANY-CHANNEL APPROACH

N N Achasov,A A Kozhenikov

doi:10.1142/s2010194514604098

Abstract

Using the field-theory-inspired expression for the pion electromagnetic form factor Fπ, a good description of the data in the range -10 < s < 1 GeV2 is obtained upon taking into account the pseudoscalar-pseudoscalar (PP) loops. When the vector-pseudoscalar (VP) and the axial vector-pseudoscalar (AP) loops are taken into account in addition to the PP ones, a good description of the BABAR data on the reaction e+e− → π+π− is obtained at energies up to 3 GeV. The inclusion of the VP and AP loops demands the treatment of the reactions e+e− → ωπ0 and e+e− → π+π−π+π−. This task is performed with the SND data on ωπ0 production and the BABAR data on π+π−π+π− production, both in e+e− annihilation, by taking into account ρ(770) and the heavier ρ(1450), ρ(1700), and ρ(2100) resonances. The problems arising from including of the VP and AP loops are pointed out and discussed.

Highlights

Using the field-theory-inspired expression for the pion electromagnetic form factor Fπ, a good description of the data in the range −10 < s < 1 GeV2 is obtained upon taking into account the pseudoscalar-pseudoscalar (PP) loops
When the vector-pseudoscalar (VP) and the axial vector-pseudoscalar (AP) loops are taken into account in addition to the PP ones, a good description of the BABAR data on the reaction e+e− → π+π− is obtained at energies up to 3 GeV
The inclusion of the VP and AP loops demands the treatment of the reactions e+e− → ωπ[0] and e+e− → π+π−π+π−

Summary

Then the expression for the reaction amplitude takes the form

The dispersion relations for the polarization operators are used under assumption of quasi-two body intermediate hadronic states: Π(RPRP )(s) s gR2 P P 6π2. Pion form factor and reactions e+e− → ωπ[0] and e+e− → π+π−π+π− at energies. The quantities to fit are the bare cross section σe+e−→π+π− undressed from vacuum polarization of the photon but the final state radiation of charged pion included, and the cross sections of the reactions e+e− → ωπ[0] and e+e− → π+π−π+π−. Their expressions are Two fitting given in schemes

In at

Scheme I