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

A. M. Badalian·B. L. G. Bakker
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Abstract

Due to the nonperturbative contribution to the hyperfine splitting the mass of the $n^1P_1$ state is strongly correlated with the center of gravity $M_{\rm cog}(n^3P_J)$ of the $n^3P_J$ multiplet: $M(n^1P_1)$ is less than $M_{\rm cog}(n^3P_J)$ 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 $1^3P_J$ multiplet. The predicted mass of $b_1(2^1P_1)$ is $\approx 1620$ MeV. For the isoscalar meson a correlation between the mass of $h_1$(1170) $(h_1(1380))$ and $M_{cog}(1^3P_J)$ composed from light (strange) quarks also takes place.

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A. M. Badalian, B. L. G. Bakker. 2001-07-26. Nonperturbative hyperfine contribution to the $b_1$ and $h_1$ meson masses. https://doi.org/10.1103/physrevd.64.114010

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