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 $\pi (0^{-+})$, $\rho (1^{--})$, $\omega (1^{--})$, $\varphi (1^{--})$, $a_0(0^{++})$, $a_1(1^{++})$, $a_2(2^{++})$, $b_1(1^{+-})$, $f_2(2^{++})$, ${\pi }_2(2^{-+})$, ${\rho }_3(3^{--})$, ${\omega }_3(3^{--})$, ${\varphi }_3(3^{--})$, ${\pi }_4(4^{-+})$ 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.

Comments: 48 pages, 24 figures