Making a working hypothesis of Abelian dominance at a long-distance scale, we analyze the U(1) problem as well as the confinement problem in the $\mathrm{SU}(N)$ Yang-Mills theory with the vacuum angle $\ensuremath{\theta}$. We show that quarks are confined only when $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}$ is a rational number such that $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}\ensuremath{\ne}\frac{(1+nN)}{\mathrm{mN}}$, $n$ and $m$ being integers. We also calculate a correlation function of the topological charge density $Q(x)={(16{\ensuremath{\pi}}^{2})}^{\ensuremath{-}1}\mathrm{Tr}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}^{*}(x)$ at $\ensuremath{\theta}=0$. We derive that $\ensuremath{\int}{d}^{4}x〈T{Q(x)Q(0)}〉=\frac{{N}^{2}}{128{\ensuremath{\pi}}^{4}(N\ensuremath{-}1){({\ensuremath{\alpha}}^{\ensuremath{'}})}^{2}}$, where ${\ensuremath{\alpha}}^{\ensuremath{'}}$ denotes the Regge slope of mesons. This formula yields \ensuremath{\sim}${(150\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V})}^{4}$ in case of SU(3), which gives rise to a mass \ensuremath{\sim} 550 MeV to the ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson through a chiral anomaly in QCD with massless quarks. This numerical result would explain the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass reasonably well in the approximation where pions are massless Goldstone bosons.