Abstract
Domain model of QCD allows for description of wide range of meson observables, dynamical chiral symmetry breaking, and resolution of $U_A(1)$ and strong $CP$ problems. The purpose of the present study is transition form-factor of neutral pseudoscalar mesons, and how they are influenced by the typical vacuum configurations of the model -- almost everywhere homogeneous Abelian (anti-)self-dual fields. Asymptotic behavior of the calculated pion form-factor supports Belle trend, but the asymptotic value of $Q^2F_{\pi\gamma^*\gamma}$ differs from the prediction of factorization theorems.
Highlights
Experimental data for pion transition form factor Fπγ∗γ obtained by the BaBar collaboration [1] indicate growth of Q2Fπγ∗γ at large Q2 that is inconsistent with rigid prediction of QCD factorization theorems [2]
Particular source of contributions that could explain BaBar trend is the QCD vacuum described by ensemble of almost everywhere homogeneous Abelianself-dual fields with nonzero scalar condensate F2 — the key feature of the domain model [4,5,6,7,8] — that can possibly mix short and long-range dynamics
Chiral symmetry is spontaneously broken by vacuum field, there exists nonzero scalar quark condensate qq
Summary
Experimental data for pion transition form factor Fπγ∗γ obtained by the BaBar collaboration [1] indicate growth of Q2Fπγ∗γ at large Q2 that is inconsistent with rigid prediction of QCD factorization theorems [2]. Results of experiments on pion transition form factor Fπγ∗γ carried out by the Belle [3] collaboration published later demonstrate qualitatively different behavior at large momenta, though they still allow violation of bound (1). Particular source of contributions that could explain BaBar trend is the QCD vacuum described by ensemble of almost everywhere homogeneous Abelian (anti-)self-dual fields with nonzero scalar condensate F2 — the key feature of the domain model [4,5,6,7,8] — that can possibly mix short and long-range dynamics. The UA(1) problem is resolved without introducing the strong charge-parity (CP) violation This approach demonstrated its power in description of wide range of meson phenomenology (masses of light, heavy-light and double-heavy mesons, leptonic decay constants, transition constants, all of the above including excited mesons). All calculations are performed with the same set of parameters that was used for calculation of meson spectra [4], see table 1
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