Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Light mesons

We continue the investigation of mesons in terms of the spectral integral equation initiated before for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$b\bar b$$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$c\bar c$$ \end{document} systems; we consider the light-quark (u, d, s) mesons with masses M ≤ 3 GeV. The calculations have been performed for the mesons lying on linear trajectories in the (n, M2) planes, where n is the radial quantum number. Our consideration relates to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$q\bar q$$ \end{document} states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as π(0−+), ρ(1−−), ω(1−−), ϕ(1−−), a0(0++), a1(1++), a2(2++), b1(1+−), f2(2++), π2(2−+), ρ3(3−−), ω3(3−−), ϕ3(3−−), π4(4−+) at n ≤ 6. We obtained the wave functions and mass values of mesons lying on these trajectories. The corresponding trajectories are linear, in agreement with data. We have calculated the two-photon decays π, a0(980), a2(1320), f2(1285), f2(1525) and radiative transitions ρ, ω → γπ, which agree qualitatively with the experiment. On this basis, we extract the singular part of the interaction amplitude, which corresponds to the so-called “confinement interaction.” The description of the data requires the presence of the strong t-channel singularities for both scalar and vector exchanges.