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Prof. Dr. Reinhard Alkofer: The time-like pion form factor and the gamma pi to pi pi form factor from functional QCD
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Europe/Berlin
HS1
HS1
TUM Physics Department
James-Franck-Str. 1, Garching
Description
A study of the time-like pion electromagnetic form factor in a Poincaré-covariant bound state formalism in the isospin symmetric limit is presented [1]. Starting from a quark interaction kernel representing gluon-intermediated interactions for valence-type quarks, non-valence effects are included by introducing pions as explicit degrees of freedom. The two most important qualitative aspects are, in view of the presented study, the opening of the dominant ρ-meson decay channel and the presence of a multi-particle branch cut setting in when the two-pion threshold is crossed. Based on a recent respective computation of the quark-photon vertex, the pion electromagnetic form factor for space-like and time-like kinematics is calculated. The obtained results for its absolute value and its phase compare favourably to the available experimental data, and they are analysed in detail by confronting them to the expectations from the isospin-symmetric version of a vector-meson dominance model.
Based on the same approach the form factor F3pi(s,t,u) for the anomalous process γ∗π→ππ is calculated in the isospin limit for several values of the light current-quark mass (i.e., the pion mass) [2]. In particular, for the physical pion mass the form factor F3pi(s,t,u) is determined for time-like Mandelstam s between the threshold and the ρ-meson mass. Predictions will be presented for the kinematics relevant for the Primakoff reaction studied with COMPASS/AMBER at CERN.
[1] A.S. Miramontes, H. Sanchis Alepuz and R. Alkofer,
Based on the same approach the form factor F3pi(s,t,u) for the anomalous process γ∗π→ππ is calculated in the isospin limit for several values of the light current-quark mass (i.e., the pion mass) [2]. In particular, for the physical pion mass the form factor F3pi(s,t,u) is determined for time-like Mandelstam s between the threshold and the ρ-meson mass. Predictions will be presented for the kinematics relevant for the Primakoff reaction studied with COMPASS/AMBER at CERN.
[1] A.S. Miramontes, H. Sanchis Alepuz and R. Alkofer,
``Elucidating the effect of intermediate resonances in the quark interaction kernel on the timelike electromagnetic pion form factor,''
Phys. Rev. D 103 (2021) 116006
[arXiv:2102.12541 [hep-ph]].
[2] A.S. Miramontes, G. Eichmann and R. Alkofer,
[2] A.S. Miramontes, G. Eichmann and R. Alkofer,
``Timelike form factor for the anomalous process $\gamma^\ast \pi \rightarrow \pi \pi$,''
[arXiv:2504.20899 [hep-ph]].
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