Mass Splitting of L=1 States of Quarkonium and Lorentz Structure of Long-range Confinement Potential

Abstract：

The Lorentz nature of the linear confinement potential between the quark-antiquark pair is analyzed by using the fine mass splitting data of L=1 spin triplets of the quarkonium. It is found that the linear confinement potential has a mixed nature of the Lorentz scalar and vector (0 ≤ η ≤ 29%, and η=0 represents the pure Lorentz scalar nature). By analyzing tentatively measured χ(1¹P₁) and γ(1¹P₁) masses,it is shown that in the linear confinement potential,a pure Lorentz scaler nature is required for the former meson, while the mixture of 79% Lorentz scalar and 21% Lorentz vector is required for the latter.