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 $\pi(0^{ -+})$, $\rho(1^{ --})$, $\omega(1^{ --})$, $\phi(1^{ --})$, $a_0(0^{ ++})$, $a_1(1^{ ++})$, $a_2(2^{ ++})$, $b_1(1^{ +-})$, $f_2(2^{ ++})$, $\pi_2(2^{ -+})$, $\rho_3(3^{ --})$, $\omega_3(3^{ --})$, $\phi_3(3^{ --})$, $\pi_4(4^{ -+})$ 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 $\pi\to \gamma\gamma$, $a_0(980)\to \gamma\gamma$, $a_2(1320)\to \gamma\gamma$, $f_2(1285)\to \gamma\gamma$, $f_2(1525)\to \gamma\gamma$ and radiative transitions $\rho\to\gamma\pi$, $\omega\to\gamma\pi$, 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.
Categories: hep-ph