Masses of light mesons and analytical confinement

Abstract

Spectrum of masses of light pseudoscalar ($\pi ,K,\eta ,{\eta }^{\prime }$) and vector ($\rho ,K^{\ast },\omega ,\varphi$) mesons can be explained on the base of the following assumptions: (1) analytical confinement (propagators of quarks and gluons are entire analytical functions of the Gaussian type), (2) mesons are bound states of quark and gluons (the Bethe-Salpeter equation in the one-gluon exchange approximation) and (3) QCD coupling constant ${\alpha }_s(M)$ is a monotone decreasing function of mass of a bound state $M$. The decay constants $f_{\pi }$ and $f_K$ are calculated.

18 pages, 3 figures