Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge III.} Light mesons

Abstract

We continue the investigation of mesons in terms of the spectral integral equation initiated before [hep-ph/0510410, hep-ph/0511005] for the $b\bar b$ and $c\bar c$ systems: in this paper we consider the light-quark ($u, d,s$) mesons with masses $M\le 3$ 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 $q\bar q$ 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 $n\le 6$. 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 $π\to γγ$, $a_0(980)\to γγ$, $a_2(1320)\to γγ$, $f_2(1285)\to γγ$, $f_2(1525)\to γγ$ and radiative transitions $ρ\toγπ$, $ω\toγπ$, that 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.