Spectral quark model and low-energy hadron phenomenology

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Abstract
We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with the help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well with recent lattice calculations. A large number of predictions and relations, valid at the low-energy scale of the model, can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc. These quantities, obtained at a low-energy scale of the model, have the correct properties, as requested by symmetries and anomalies. They also have pure twist expansion, free of logarithmic corrections, as requested by the QCD factorization property.