Abstract
Amongst the bound states produced by the strong interaction, radially excited meson and nucleon states offer an important phenomenological window into the long-range behavior of the coupling constant in Quantum Chromodynamics. We here report on some technical details related to the computation of the bound state's eigenvalue spectrum in the framework of Bethe-Salpeter and Faddeev equations.
Highlights
Amongst the bound states produced by the strong interaction, radially excited meson and nucleon states offer an important phenomenological window into the longrange behavior of the coupling constant in Quantum Chromodynamics
A great deal of research activity in hadron physics is concerned with hadron structure and revolves around two fundamental questions: what constituents are the hadrons made of and how does Quantum Chromodynamics (QCD), the strong interaction component of the Standard Model, produce them? These are simple questions which, may not entail simple answers
To understand the measurable content of QCD, spectroscopy is a valuable and time-honored tool — suffice it to mention the inestimable progress made in the computation of atomic or molecular spectra and subsequent comparison with experiments that lead to a deeper understanding of Quantum Electrodynamics
Summary
A great deal of research activity in hadron physics is concerned with hadron structure and revolves around two fundamental questions: what constituents are the hadrons made of and how does Quantum Chromodynamics (QCD), the strong interaction component of the Standard Model, produce them? These are simple questions which, may not entail simple answers. The Bethe-Salpeter equation’s Poincaré-invariant solutions can be cast in the form, Γ0− (p, P) = γ5 i IDE0− (p, P) + P/ F0− (p, P) + /p(p · P) G0− (p, P) + σμν pμPν H0− (p, P) , (3) Note that this Euclidean-metric basis, Aα(p, P) = γ5 i ID, P/ , /p(p · P), σμν pμPν , is nonorthogonal with respect to the Dirac trace. This is the most basic method of computing the largest eigenvalue λ0(P2) and its associated eigenvector to any required accuracy and is referred to as power or von Mises iteration The trajectory of this eigenvalue function for a range of P2 values yields the ground-state meson mass, that is one finds λ0(P2) = 1 when P2 = −m20
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