Nonperturbative hyperfine contribution to the $b_1$ and $h_1$ meson masses

Abstract

Due to 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 $\approx 1620$ MeV. For the isoscalar meson a correlation between the mass of $h_1$(1170) $(h_1(1380))$ and $M_{cog}(1^3{P}_J)$ composed from light (strange) quarks also takes place.

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References in corpus (1)

• QCD string in light-light and heavy-light mesons

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