Nonperturbative hyperfine contribution to the b_{1} and h_{1} meson masses

Because of the nonperturbative contribution to the hyperfine splitting the mass of the ${n}^{1}{P}_{1}$ state is strongly correlated with the center of gravity ${M}_{\mathrm{cog}}{(n}^{3}{P}_{J})$ of the ${n}^{3}{P}_{J}$ multiplet: ${M(n}^{1}{P}_{1})$ is less than ${M}_{\mathrm{cog}}{(n}^{3}{P}_{J})$ by about 40 MeV (20 MeV) for the $1P(2P)$ state. For ${b}_{1}(1235)$ the agreement with experiment is reached only if ${a}_{0}(980)$ belongs to the ${1}^{3}{P}_{J}$ multiplet. The predicted mass of ${b}_{1}{(2}^{1}{P}_{1})$ is $\ensuremath{\approx}1620\mathrm{MeV}.$ For the isoscalar meson a correlation between the mass of ${h}_{1}(1170)$ $[{h}_{1}(1380)]$ and ${M}_{\mathrm{cog}}{(1}^{3}{P}_{J})$ composed from light (strange) quarks also takes place.