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 b b and c c 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, M 2) planes, where n is the radial quantum number. Our consideration relates to the q q 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−−), a 0(0++), a 1(1++), a 2(2++), b 1(1+−), f 2(2++), π 2(2−+), ρ 3(3−−), ω 3(3−−), ϕ 3(3−−), π 4(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, a 0(980), a 2(1320), f 2(1285), f 2(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.